power-law mass function: Topics by Science.gov

Sample records for power-law mass function

Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

PubMed Central

Lagrue, Clément; Poulin, Robert; Cohen, Joel E.

2015-01-01

How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor’s law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution. PMID:25550506
Parasitism alters three power laws of scaling in a metazoan community: Taylor's law, density-mass allometry, and variance-mass allometry.

PubMed

Lagrue, Clément; Poulin, Robert; Cohen, Joel E

2015-02-10

How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor's law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution.
Initial mass function of planetesimals formed by the streaming instability

NASA Astrophysics Data System (ADS)

Schäfer, Urs; Yang, Chao-Chin; Johansen, Anders

2017-01-01

The streaming instability is a mechanism to concentrate solid particles into overdense filaments that undergo gravitational collapse and form planetesimals. However, it remains unclear how the initial mass function of these planetesimals depends on the box dimensions of numerical simulations. To resolve this, we perform simulations of planetesimal formation with the largest box dimensions to date, allowing planetesimals to form simultaneously in multiple filaments that can only emerge within such large simulation boxes. In our simulations, planetesimals with sizes between 80 km and several hundred kilometers form. We find that a power law with a rather shallow exponential cutoff at the high-mass end represents the cumulative birth mass function better than an integrated power law. The steepness of the exponential cutoff is largely independent of box dimensions and resolution, while the exponent of the power law is not constrained at the resolutions we employ. Moreover, we find that the characteristic mass scale of the exponential cutoff correlates with the mass budget in each filament. Together with previous studies of high-resolution simulations with small box domains, our results therefore imply that the cumulative birth mass function of planetesimals is consistent with an exponentially tapered power law with a power-law exponent of approximately -1.6 and a steepness of the exponential cutoff in the range of 0.3-0.4.
First constraints on the stellar mass function of star-forming clumps at the peak of cosmic star formation

NASA Astrophysics Data System (ADS)

Dessauges-Zavadsky, Miroslava; Adamo, Angela

2018-06-01

Star-forming clumps dominate the rest-frame ultraviolet morphology of galaxies at the peak of cosmic star formation. If turbulence driven fragmentation is the mechanism responsible for their formation, we expect their stellar mass function to follow a power-law of slope close to -2. We test this hypothesis performing the first analysis of the stellar mass function of clumps hosted in galaxies at z ˜ 1 - 3.5. The sample is gathered from the literature with similar detection thresholds and stellar masses determined in a homogeneous way. To overcome the small number statistics per galaxy (each galaxy hosts up to a few tens of clumps only), we combine all high-redshift clumps. The resulting clump mass function follows a power-law of slope ˜-1.7 and flattens at masses below 2 × 107 M⊙. By means of randomly sampled clump populations, drawn out of a power-law mass function of slope -2, we test the effect of combining small clump populations, detection limits of the surveys, and blending on the mass function. Our numerical exercise reproduces all the features observed in the real clump mass function confirming that it is consistent with a power-law of slope ≃ -2. This result supports the high-redshift clump formation through fragmentation in a similar fashion as in local galaxies, but under different gas conditions.
A Dual Power Law Distribution for the Stellar Initial Mass Function

NASA Astrophysics Data System (ADS)

Hoffmann, Karl Heinz; Essex, Christopher; Basu, Shantanu; Prehl, Janett

2018-05-01

We introduce a new dual power law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a unified framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modified lognormal power law (MLP) distribution, the DPL distribution has a power law at the high mass end, as a result of exponential growth of mass coupled with equally likely stopping of accretion at any time interval. Unlike the MLP, a power law decay also appears at the low mass end of the IMF. This feature is closely connected to the accretion stopping probability rising from an initially low value up to a high value. This might be associated with physical effects of ejections sometimes (i.e., rarely) stopping accretion at early times followed by outflow driven accretion stopping at later times, with the transition happening at a critical time (therefore mass). Comparing the DPL to empirical data, the critical mass is close to the substellar mass limit, suggesting that the onset of nuclear fusion plays an important role in the subsequent accretion history of a young stellar object.
On the mass function of stars growing in a flocculent medium

NASA Astrophysics Data System (ADS)

Maschberger, Th.

2013-12-01

Stars form in regions of very inhomogeneous densities and may have chaotic orbital motions. This leads to a time variation of the accretion rate, which will spread the masses over some mass range. We investigate the mass distribution functions that arise from fluctuating accretion rates in non-linear accretion, ṁ ∝ mα. The distribution functions evolve in time and develop a power-law tail attached to a lognormal body, like in numerical simulations of star formation. Small fluctuations may be modelled by a Gaussian and develop a power-law tail ∝ m-α at the high-mass side for α > 1 and at the low-mass side for α < 1. Large fluctuations require that their distribution is strictly positive, for example, lognormal. For positive fluctuations the mass distribution function develops the power-law tail always at the high-mass hand side, independent of α larger or smaller than unity. Furthermore, we discuss Bondi-Hoyle accretion in a supersonically turbulent medium, the range of parameters for which non-linear stochastic growth could shape the stellar initial mass function, as well as the effects of a distribution of initial masses and growth times.
The Exoplanet Mass-Ratio Function From the MOA-II Survey: Discovery of a Break and Likely Peak at a Neptune Mass

NASA Technical Reports Server (NTRS)

Suzuki, D.; Bennett, D. P.; Sumi, T.; Bond, I. A.; Rogers, L. A.; Abe, F.; Asakura, Y.; Bhattacharya, A.; Donachie, M.; Freeman, M.;

2016-01-01

We report the results of the statistical analysis of planetary signals discovered in MOA-II microlensing survey alert system events from 2007 to 2012. We determine the survey sensitivity as a function of planet star mass ratio, q, and projected planet star separation, s, in Einstein radius units. We find that the mass-ratio function is not a single power law, but has a change in slope at q approx.10(exp -4), corresponding to approx. 20 Stellar Mass for the median host-star mass of approx. 0.6 M. We find significant planetary signals in 23 of the 1474 alert events that are well-characterized by the MOA-II survey data alone. Data from other groups are used only to characterize planetary signals that have been identified in the MOA data alone. The distribution of mass ratios and separations of the planets found in our sample are well fit by a broken power-law model. We also combine this analysis with the previous analyses of Gould et al. and Cassan et al., bringing the total sample to 30 planets. The unbroken power-law model is disfavored with a p-value of 0.0022, which corresponds to a Bayes factor of 27 favoring the broken power-law model. These results imply that cold Neptunes are likely to be the most common type of planets beyond the snow line.

A COSMIC COINCIDENCE: THE POWER-LAW GALAXY CORRELATION FUNCTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watson, Douglas F.; Berlind, Andreas A.; Zentner, Andrew R.

We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of {xi}(r), the galaxy two-point correlation function. While {xi}(r) at large scales is set by primordial fluctuations, departures from a power law are governed by galaxy pair counts at small scales, subject to nonlinear dynamics. We assume that galaxies reside within dark matter halos and subhalos. Therefore, the shape of the correlation function at small scales depends on the amount of halo substructure. We use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal massmore » loss and, to a lesser extent, dynamical friction dramatically deplete the number of subhalos within larger host halos over time, resulting in a {approx}90% reduction by z = 0 compared to the number of distinct mergers that occur during the assembly of a host halo. We show that these nonlinear processes resulting in this depletion are essential for achieving a power law {xi}(r). We investigate how the shape of {xi}(r) depends on subhalo mass (or luminosity) and redshift. We find that {xi}(r) breaks from a power law at high masses, implying that only galaxies of luminosities {approx}< L{sub *} should exhibit power-law clustering. Moreover, we demonstrate that {xi}(r) evolves from being far from a power law at high redshift, toward a near power-law shape at z = 0. We argue that {xi}(r) will once again evolve away from a power law in the future. This is in large part caused by the evolving competition between the accretion and destruction rates of subhalos over time, which happen to strike just the right balance at z {approx} 0. We then investigate the conditions required for {xi}(r) to be a power law in a general context. We use the halo model, along with simple parameterizations of the halo occupation distribution, to probe galaxy occupation at various masses and redshifts. We show that the key ingredients determining the shape of {xi}(r) are the fraction of galaxies that are satellites, the relative difference in mass between the halos of isolated galaxies and halos that contain a single satellite on average, and the rareness of halos that host galaxies. These pieces are intertwined and we find no simple, universal rule for which a power law {xi}(r) will occur. However, we do show that the physics responsible for setting the galaxy content of halos do not care about the conditions needed to achieve a power law {xi}(r) and that these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of {xi}(r) for L{sub *} and fainter galaxy samples at low redshift is a cosmic coincidence.« less
The Halo Occupation Distribution of Active Galactic Nuclei

NASA Astrophysics Data System (ADS)

Chatterjee, Suchetana; Nagai, D.; Richardson, J.; Zheng, Z.; Degraf, C.; DiMatteo, T.

2011-05-01

We investigate the halo occupation distribution of active galactic nuclei (AGN) using a state-of-the-art cosmological hydrodynamic simulation that self-consistently incorporates the growth and feedback of supermassive black holes and the physics of galaxy formation (DiMatteo et al. 2008). We show that the mean occupation function can be modeled as a softened step function for central AGN and a power law for the satellite population. The satellite occupation is consistent with weak redshift evolution and a power law index of unity. The number of satellite black holes at a given halo mass follows a Poisson distribution. We show that at low redshifts (z=1.0) feedback from AGN is responsible for higher suppression of black hole growth in higher mass halos. This effect introduces a bias in the correlation between instantaneous AGN luminosity and the host halo mass, making AGN clustering depend weakly on luminosity at low redshifts. We show that the radial distribution of AGN follows a power law which is fundamentally different from those of galaxies and dark matter. The best-fit power law index is -2.26 ± 0.23. The power law exponent do not show any evolution with redshift, host halo mass and AGN luminosity within statistical limits. Incorporating the environmental dependence of supermassive black hole accretion and feedback, our formalism provides the most complete theoretical tool for interpreting current and future measurements of AGN clustering.
On the apparent power law in CDM halo pseudo-phase space density profiles

NASA Astrophysics Data System (ADS)

Nadler, Ethan O.; Oh, S. Peng; Ji, Suoqing

2017-09-01

We investigate the apparent power-law scaling of the pseudo-phase space density (PPSD) in cold dark matter (CDM) haloes. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log-log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar; scalelengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inwards, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.
Cosmological Evolution of Massive Black Holes: Effects of Eddington Ratio Distribution and Quasar Lifetime

NASA Astrophysics Data System (ADS)

Cao, Xinwu

2010-12-01

A power-law time-dependent light curve for active galactic nuclei (AGNs) is expected by the self-regulated black hole growth scenario, in which the feedback of AGNs expels gas and shut down accretion. This is also supported by the observed power-law Eddington ratio distribution of AGNs. At high redshifts, the AGN life timescale is comparable with (or even shorter than) the age of the universe, which sets a constraint on the minimal Eddington ratio for AGNs on the assumption of a power-law AGN light curve. The black hole mass function (BHMF) of AGN relics is calculated by integrating the continuity equation of massive black hole number density on the assumption of the growth of massive black holes being dominated by mass accretion with a power-law Eddington ratio distribution for AGNs. The derived BHMF of AGN relics at z = 0 can fit the measured local mass function of the massive black holes in galaxies quite well, provided the radiative efficiency ~0.1 and a suitable power-law index for the Eddington ratio distribution are adopted. In our calculations of the black hole evolution, the duty cycle of AGN should be less than unity, which requires the quasar life timescale τQ >~ 5 × 108 years.
Exact analytic solution of position-dependent mass Schrödinger equation

NASA Astrophysics Data System (ADS)

Rajbongshi, Hangshadhar

2018-03-01

Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.
An ALMA Archival Study of the Clump Mass Function in the Large Magellanic Cloud

NASA Astrophysics Data System (ADS)

Brunetti, Nathan

2017-11-01

This thesis presents 1.3 mm and 3.1 mm continuum maps of seven star forming regions within the Large Magellanic Cloud (LMC) as observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). The data were taken as part of six projects retrieved from the ALMA public archive plus one project observed specifically for this work. We developed a technique to combine Band 3 and Band 6 maps to estimate dust-only emission corrected for free-free emission contamination. We also present an automated clean masking script, with a listing of the code, which we adapted and used for all of the imaging in this thesis. From these observations we identify 32 molecular clumps in the LMC and estimate their total mass from their dust emission. We derive a cumulative clump mass function (N(≥M) ≈ M(α+1)) and fit it with a double power law to find α_low = -1.76+0.07-0.1, α_high = -3.3+0.3-0.6, and a break mass of 2500+700-300 M⊙. Comparing to the clump mass function derived by Indebetouw et al. (2013) from carbon monoxide spectral line emission for 30 Doradus-10 shows a consistent mass range of clumps between 205 M⊙ and 5740 M⊙ as well as consistency between their single power law fit and our low mass power law index. Also comparing to core and clump mass functions from several star forming regions in the Milky Way we find consistency between most of their high mass indices and our low mass index, which is where the clump mass ranges overlap.
THE PANCHROMATIC HUBBLE ANDROMEDA TREASURY. IV. A PROBABILISTIC APPROACH TO INFERRING THE HIGH-MASS STELLAR INITIAL MASS FUNCTION AND OTHER POWER-LAW FUNCTIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.

2013-01-10

We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlomore » sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF slope recovery in this paper are lower limits, as we do not explicitly consider all possible sources of uncertainty, including dynamical effects (e.g., mass segregation), unresolved binaries, and non-coeval populations. We briefly discuss how each of these effects can be incorporated into extensions of the present framework. Finally, we emphasize that the technique and lessons learned are applicable to more general problems involving power-law fitting.« less
The Copernicus Complexio: a high-resolution view of the small-scale Universe

NASA Astrophysics Data System (ADS)

Hellwing, Wojciech A.; Frenk, Carlos S.; Cautun, Marius; Bose, Sownak; Helly, John; Jenkins, Adrian; Sawala, Till; Cytowski, Maciej

2016-04-01

We introduce Copernicus Complexio (COCO), a high-resolution cosmological N-body simulation of structure formation in the ΛCDM model. COCO follows an approximately spherical region of radius ˜17.4 h-1 Mpc embedded in a much larger periodic cube that is followed at lower resolution. The high-resolution volume has a particle mass of 1.135 × 105 h-1 M⊙ (60 times higher than the Millennium-II simulation). COCO gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms ˜60 haloes of galactic size, each resolved with about 10 million particles. We confirm the power-law character of the subhalo mass function, overline{N}(>μ )∝ μ ^{-s}, down to a reduced subhalo mass Msub/M200 ≡ μ = 10-6, with a best-fitting power-law index, s = 0.94, for hosts of mass = 1012 h-1 M⊙. The concentration-mass relation of COCO haloes deviates from a single power law for masses M200 < afew × 108 h-1 M⊙, where it flattens, in agreement with results by Sanchez-Conde et al. The host mass invariance of the reduced maximum circular velocity function of subhaloes, ν ≡ Vmax/V200, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalized radial distribution of subhaloes is approximately universal (I.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual haloes. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts.
The ACS Survey of Galactic Globular Clusters. VIII. Effects of Environment on Globular Cluster Global Mass Functions

NASA Astrophysics Data System (ADS)

Paust, Nathaniel E. Q.; Reid, I. Neill; Piotto, Giampaolo; Aparicio, Antonio; Anderson, Jay; Sarajedini, Ata; Bedin, Luigi R.; Chaboyer, Brian; Dotter, Aaron; Hempel, Maren; Majewski, Steven; Marín-Franch, A.; Milone, Antonino; Rosenberg, Alfred; Siegel, Michael

2010-02-01

We have used observations obtained as part of the Hubble Space Telescope/ACS Survey of Galactic Globular Clusters to construct global present-day mass functions for 17 globular clusters utilizing multi-mass King models to extrapolate from our observations to the global cluster behavior. The global present-day mass functions for these clusters are well matched by power laws from the turnoff, ≈0.8 M sun, to 0.2-0.3 M sun on the lower main sequence. The slopes of those power-law fits, α, have been correlated with an extensive set of intrinsic and extrinsic cluster properties to investigate which parameters may influence the form of the present-day mass function. We do not confirm previous suggestions of correlations between α and either metallicity or Galactic location. However, we do find a strong statistical correlation with the related parameters central surface brightness, μ V , and inferred central density, ρ0. The correlation is such that clusters with denser cores (stronger binding energy) tend to have steeper mass functions (a higher proportion of low-mass stars), suggesting that dynamical evolution due to external interactions may have played a key role in determining α. Thus, the present-day mass function may owe more to nurture than to nature. Detailed modeling of external dynamical effects is therefore a requisite for determining the initial mass function for Galactic globular clusters.
Taylor's law and body size in exploited marine ecosystems.

PubMed

Cohen, Joel E; Plank, Michael J; Law, Richard

2012-12-01

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density-mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance-mass allometry). Marine size spectra are known to exhibit density-mass allometry, but variance-mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size-at-entry fishing, in which only fish above a certain size may legally be caught.
Taylor's law and body size in exploited marine ecosystems

PubMed Central

Cohen, Joel E; Plank, Michael J; Law, Richard

2012-01-01

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density-mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance-mass allometry). Marine size spectra are known to exhibit density-mass allometry, but variance-mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size-at-entry fishing, in which only fish above a certain size may legally be caught. PMID:23301181
The Panchromatic Hubble Andromeda Treasury. IV. A Probabilistic Approach to Inferring the High-mass Stellar Initial Mass Function and Other Power-law Functions

NASA Astrophysics Data System (ADS)

Weisz, Daniel R.; Fouesneau, Morgan; Hogg, David W.; Rix, Hans-Walter; Dolphin, Andrew E.; Dalcanton, Julianne J.; Foreman-Mackey, Daniel T.; Lang, Dustin; Johnson, L. Clifton; Beerman, Lori C.; Bell, Eric F.; Gordon, Karl D.; Gouliermis, Dimitrios; Kalirai, Jason S.; Skillman, Evan D.; Williams, Benjamin F.

2013-01-01

We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M >~ 1 M ⊙). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, α, are unbiased and that the uncertainty, Δα, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on α, and provide an analytic approximation for Δα as a function of the observed number of stars and mass range. Comparison with literature studies shows that ~3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield langαrang = 2.46, with a 1σ dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF slope recovery in this paper are lower limits, as we do not explicitly consider all possible sources of uncertainty, including dynamical effects (e.g., mass segregation), unresolved binaries, and non-coeval populations. We briefly discuss how each of these effects can be incorporated into extensions of the present framework. Finally, we emphasize that the technique and lessons learned are applicable to more general problems involving power-law fitting. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
THE VMC SURVEY. XVIII. RADIAL DEPENDENCE OF THE LOW-MASS, 0.55–0.82 M{sub ⊙} STELLAR MASS FUNCTION IN THE GALACTIC GLOBULAR CLUSTER 47 TUCANAE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chaoli; Li, Chengyuan; De Grijs, Richard

2015-12-20

We use near-infrared observations obtained as part of the Visible and Infrared Survey Telescope for Astronomy (VISTA) Survey of the Magellanic Clouds (VMC), as well as two complementary Hubble Space Telescope (HST) data sets, to study the luminosity and mass functions (MFs) as a function of clustercentric radius of the main-sequence stars in the Galactic globular cluster 47 Tucanae. The HST observations indicate a relative deficit in the numbers of faint stars in the central region of the cluster compared with its periphery, for 18.75 ≤ m{sub F606W} ≤ 20.9 mag (corresponding to a stellar mass range of 0.55 < m{sub *}/M{sub ⊙} < 0.73). The stellar numbermore » counts at 6.′7 from the cluster core show a deficit for 17.62 ≤ m{sub F606W} ≤ 19.7 mag (i.e., 0.65 < m{sub *}/M{sub ⊙} < 0.82), which is consistent with expectations from mass segregation. The VMC-based stellar MFs exhibit power-law shapes for masses in the range 0.55 < m{sub *}/M{sub ⊙} < 0.82. These power laws are characterized by an almost constant slope, α. The radial distribution of the power-law slopes α thus shows evidence of the importance of both mass segregation and tidal stripping, for both the first- and second-generation stars in 47 Tuc.« less

ALMA Reveals Molecular Cloud N55 in the Large Magellanic Cloud as a Site of Massive Star Formation

NASA Astrophysics Data System (ADS)

Naslim, N.; Tokuda, K.; Onishi, T.; Kemper, F.; Wong, T.; Morata, O.; Takada, S.; Harada, R.; Kawamura, A.; Saigo, K.; Indebetouw, R.; Madden, S. C.; Hony, S.; Meixner, M.

2018-02-01

We present the molecular cloud properties of N55 in the Large Magellanic Cloud using 12CO(1–0) and 13CO(1–0) observations obtained with Atacama Large Millimeter Array. We have done a detailed study of molecular gas properties, to understand how the cloud properties of N55 differ from Galactic clouds. Most CO emission appears clumpy in N55, and molecular cores that have young stellar objects (YSOs) show larger linewidths and masses. The massive clumps are associated with high and intermediate mass YSOs. The clump masses are determined by local thermodynamic equilibrium and virial analysis of the 12CO and 13CO emissions. These mass estimates lead to the conclusion that (a) the clumps are in self-gravitational virial equilibrium, and (b) the 12CO(1–0)-to-H2 conversion factor, {X}{CO}, is 6.5 × 1020 cm‑2 (K km s‑1)‑1. This CO-to-H2 conversion factor for N55 clumps is measured at a spatial scale of ∼0.67 pc, which is about two times higher than the {X}{CO} value of the Orion cloud at a similar spatial scale. The core mass function of N55 clearly show a turnover below 200 {M}ȯ , separating the low-mass end from the high-mass end. The low-mass end of the 12CO mass spectrum is fitted with a power law of index 0.5 ± 0.1, while for 13CO it is fitted with a power law index 0.6 ± 0.2. In the high-mass end, the core mass spectrum is fitted with a power index of 2.0 ± 0.3 for 12CO, and with 2.5 ± 0.4 for 13CO. This power law behavior of the core mass function in N55 is consistent with many Galactic clouds.
Developing and bounding ice particle mass- and area-dimension expressions for use in atmospheric models and remote sensing

DOE PAGES

Erfani, Ehsan; Mitchell, David L.

2016-04-07

Here, ice particle mass- and projected area-dimension ( m- D and A- D) power laws are commonly used in the treatment of ice cloud microphysical and optical properties and the remote sensing of ice cloud properties. Although there has long been evidence that a single m- D or A- D power law is often not valid over all ice particle sizes, few studies have addressed this fact. This study develops self-consistent m- D and A- D expressions that are not power laws but can easily be reduced to power laws for the ice particle size (maximum dimension or D) rangemore » of interest, and they are valid over a much larger D range than power laws. This was done by combining ground measurements of individual ice particle m and D formed at temperature T < –20 °C during a cloud seeding field campaign with 2-D stereo (2D-S) and cloud particle imager (CPI) probe measurements of D and A, and estimates of m, in synoptic and anvil ice clouds at similar temperatures. The resulting m- D and A- D expressions are functions of temperature and cloud type (synoptic vs. anvil), and are in good agreement with m- D power laws developed from recent field studies considering the same temperature range (–60 °C < T < –20 °C).« less
On the probability distribution function of the mass surface density of molecular clouds. I

NASA Astrophysics Data System (ADS)

Fischera, Jörg

2014-05-01

The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a composition of a broad distribution around the maximum and a decreasing tail at high mass surface densities. The first component is attributed to the random distribution of gas which is modeled using a log-normal function while the second component is attributed to condensed structures modeled using a simple power-law. The aim of this paper is to provide an analytical model of the PDF of condensed structures which can be used by observers to extract information about the condensations. The condensed structures are considered to be either spheres or cylinders with a truncated radial density profile at cloud radius rcl. The assumed profile is of the form ρ(r) = ρc/ (1 + (r/r0)2)n/ 2 for arbitrary power n where ρc and r0 are the central density and the inner radius, respectively. An implicit function is obtained which either truncates (sphere) or has a pole (cylinder) at maximal mass surface density. The PDF of spherical condensations and the asymptotic PDF of cylinders in the limit of infinite overdensity ρc/ρ(rcl) flattens for steeper density profiles and has a power law asymptote at low and high mass surface densities and a well defined maximum. The power index of the asymptote Σ- γ of the logarithmic PDF (ΣP(Σ)) in the limit of high mass surface densities is given by γ = (n + 1)/(n - 1) - 1 (spheres) or by γ = n/ (n - 1) - 1 (cylinders in the limit of infinite overdensity). Appendices are available in electronic form at http://www.aanda.org
First results from the IllustrisTNG simulations: matter and galaxy clustering

NASA Astrophysics Data System (ADS)

Springel, Volker; Pakmor, Rüdiger; Pillepich, Annalisa; Weinberger, Rainer; Nelson, Dylan; Hernquist, Lars; Vogelsberger, Mark; Genel, Shy; Torrey, Paul; Marinacci, Federico; Naiman, Jill

2018-03-01

Hydrodynamical simulations of galaxy formation have now reached sufficient volume to make precision predictions for clustering on cosmologically relevant scales. Here, we use our new IllustrisTNG simulations to study the non-linear correlation functions and power spectra of baryons, dark matter, galaxies, and haloes over an exceptionally large range of scales. We find that baryonic effects increase the clustering of dark matter on small scales and damp the total matter power spectrum on scales up to k ˜ 10 h Mpc-1 by 20 per cent. The non-linear two-point correlation function of the stellar mass is close to a power-law over a wide range of scales and approximately invariant in time from very high redshift to the present. The two-point correlation function of the simulated galaxies agrees well with Sloan Digital Sky Survey at its mean redshift z ≃ 0.1, both as a function of stellar mass and when split according to galaxy colour, apart from a mild excess in the clustering of red galaxies in the stellar mass range of109-1010 h-2 M⊙. Given this agreement, the TNG simulations can make valuable theoretical predictions for the clustering bias of different galaxy samples. We find that the clustering length of the galaxy autocorrelation function depends strongly on stellar mass and redshift. Its power-law slope γ is nearly invariant with stellar mass, but declines from γ ˜ 1.8 at redshift z = 0 to γ ˜ 1.6 at redshift z ˜ 1, beyond which the slope steepens again. We detect significant scale dependences in the bias of different observational tracers of large-scale structure, extending well into the range of the baryonic acoustic oscillations and causing nominal (yet fortunately correctable) shifts of the acoustic peaks of around ˜ 5 per cent.
Power-law distributions for a trapped ion interacting with a classical buffer gas.

PubMed

DeVoe, Ralph G

2009-02-13

Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment.
The emergence of the galactic stellar mass function from a non-universal IMF in clusters

NASA Astrophysics Data System (ADS)

Dib, Sami; Basu, Shantanu

2018-06-01

We investigate the dependence of a single-generation galactic mass function (SGMF) on variations in the initial stellar mass functions (IMF) of stellar clusters. We show that cluster-to-cluster variations of the IMF lead to a multi-component SGMF where each component in a given mass range can be described by a distinct power-law function. We also show that a dispersion of ≈0.3 M⊙ in the characteristic mass of the IMF, as observed for young Galactic clusters, leads to a low-mass slope of the SGMF that matches the observed Galactic stellar mass function even when the IMFs in the low-mass end of individual clusters are much steeper.
The initial mass function and star formation law in the outer disc of NGC 2915

NASA Astrophysics Data System (ADS)

Bruzzese, S. M.; Meurer, G. R.; Lagos, C. D. P.; Elson, E. C.; Werk, J. K.; Blakeslee, John P.; Ford, H.

2015-02-01

Using Hubble Space Telescope (HST) Advanced Camera for Surveys/Wide Field Camera data we present the photometry and spatial distribution of resolved stellar populations in the outskirts of NGC 2915, a blue compact dwarf with an extended H I disc. These observations reveal an elliptical distribution of red giant branch stars, and a clumpy distribution of main-sequence stars that correlate with the H I gas distribution. We constrain the upper-end initial mass function (IMF) and determine the star formation law (SFL) in this field, using the observed main-sequence stars and an assumed constant star formation rate. Previously published Hα observations of the field, which show one faint H II region, are used to provide further constraints on the IMF. We find that the main-sequence luminosity function analysis alone results in a best-fitting IMF with a power-law slope α = -2.85 and upper-mass limit M_u = 60 M_{⊙}. However, if we assume that all Hα emission is confined to H II regions then the upper-mass limit is restricted to M_u ≲ 20 M_{⊙}. For the luminosity function fit to be correct, we have to discount the Hα observations implying significant diffuse ionized gas or escaping ionizing photons. Combining the HST photometry with H I imaging, we find the SFL has a power-law index N = 1.53 ± 0.21. Applying these results to the entire outer H I disc indicates that it contributes 11-28 per cent of the total recent star formation in NGC 2915, depending on whether the IMF is constant within the disc or varies from the centre to the outer region.
Hydrodynamics-based functional forms of activity metabolism: a case for the power-law polynomial function in animal swimming energetics.

PubMed

Papadopoulos, Anthony

2009-01-01

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.
The γ-ray emission produced by protons that escape from supernova remnant G349.7+0.2

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Li, Hui; Chen, Yang

2016-10-01

G349.7+0.2 is an interacting supernova remnant (SNR) expanding in a dense medium. Recently, a very strong γ-ray source coincident with this SNR has been revealed by Fermi-LAT and H.E.S.S. observations which shows a broken power-law-like spectrum. An escaping-diffusion model, including the power-law and δ-function injection, is applied to this source which can naturally explain the spectral feature in both the GeV and TeV regime. We use the Markov Chain Monte Carlo method to constrain the model parameters and find that the correction factor of slow diffusion around this SNR, χ ˜ 0.01 for power-law injection and χ ˜ 0.1 for δ-function injection, can fit the data best with reasonable molecular cloud mass. This slow diffusion is also consistent with previous results from both phenomenological models and theoretical predication.
A Stack of Cards Rebuilt with Calculus

ERIC Educational Resources Information Center

Kazachkov, Alexander; Kireš, Marián

2017-01-01

Previous work covers building a tower from a stack of homogeneous rectangular plates, each with a maximum shift in displacement. We suggest using plates shaped as curvilinear triangles bounded by segments of power-law functions. The masses of the plates and the position of their center of mass are calculated and measured experimentally after…
Formation of massive, dense cores by cloud-cloud collisions

NASA Astrophysics Data System (ADS)

Takahira, Ken; Shima, Kazuhiro; Habe, Asao; Tasker, Elizabeth J.

2018-03-01

We performed sub-parsec (˜ 0.014 pc) scale simulations of cloud-cloud collisions of two idealized turbulent molecular clouds (MCs) with different masses in the range of (0.76-2.67) × 104 M_{⊙} and with collision speeds of 5-30 km s-1. Those parameters are larger than in Takahira, Tasker, and Habe (2014, ApJ, 792, 63), in which study the colliding system showed a partial gaseous arc morphology that supports the NANTEN observations of objects indicated to be colliding MCs using numerical simulations. Gas clumps with density greater than 10-20 g cm-3 were identified as pre-stellar cores and tracked through the simulation to investigate the effects of the mass of colliding clouds and the collision speeds on the resulting core population. Our results demonstrate that the smaller cloud property is more important for the results of cloud-cloud collisions. The mass function of formed cores can be approximated by a power-law relation with an index γ = -1.6 in slower cloud-cloud collisions (v ˜ 5 km s-1), and is in good agreement with observation of MCs. A faster relative speed increases the number of cores formed in the early stage of collisions and shortens the gas accretion phase of cores in the shocked region, leading to the suppression of core growth. The bending point appears in the high-mass part of the core mass function and the bending point mass decreases with increase in collision speed for the same combination of colliding clouds. The higher-mass part of the core mass function than the bending point mass can be approximated by a power law with γ = -2-3 that is similar to the power index of the massive part of the observed stellar initial mass function. We discuss implications of our results for the massive-star formation in our Galaxy.
Formation of massive, dense cores by cloud-cloud collisions

NASA Astrophysics Data System (ADS)

Takahira, Ken; Shima, Kazuhiro; Habe, Asao; Tasker, Elizabeth J.

2018-05-01

We performed sub-parsec (˜ 0.014 pc) scale simulations of cloud-cloud collisions of two idealized turbulent molecular clouds (MCs) with different masses in the range of (0.76-2.67) × 104 M_{⊙} and with collision speeds of 5-30 km s-1. Those parameters are larger than in Takahira, Tasker, and Habe (2014, ApJ, 792, 63), in which study the colliding system showed a partial gaseous arc morphology that supports the NANTEN observations of objects indicated to be colliding MCs using numerical simulations. Gas clumps with density greater than 10-20 g cm-3 were identified as pre-stellar cores and tracked through the simulation to investigate the effects of the mass of colliding clouds and the collision speeds on the resulting core population. Our results demonstrate that the smaller cloud property is more important for the results of cloud-cloud collisions. The mass function of formed cores can be approximated by a power-law relation with an index γ = -1.6 in slower cloud-cloud collisions (v ˜ 5 km s-1), and is in good agreement with observation of MCs. A faster relative speed increases the number of cores formed in the early stage of collisions and shortens the gas accretion phase of cores in the shocked region, leading to the suppression of core growth. The bending point appears in the high-mass part of the core mass function and the bending point mass decreases with increase in collision speed for the same combination of colliding clouds. The higher-mass part of the core mass function than the bending point mass can be approximated by a power law with γ = -2-3 that is similar to the power index of the massive part of the observed stellar initial mass function. We discuss implications of our results for the massive-star formation in our Galaxy.
Two Regimes of Turbulent Fragmentation and the Stellar Initial Mass Function from Primordial to Present-Day Star Formation

NASA Astrophysics Data System (ADS)

Padoan, Paolo; Nordlund, Åke; Kritsuk, Alexei G.; Norman, Michael L.; Li, Pak Shing

2007-06-01

The Padoan and Nordlund model of the stellar initial mass function (IMF) is derived from low-order statistics of supersonic turbulence, neglecting gravity (e.g., gravitational fragmentation, accretion, and merging). In this work, the predictions of that model are tested using the largest numerical experiments of supersonic hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulence to date (~10003 computational zones) and three different codes (Enzo, Zeus, and the Stagger code). The model predicts a power-law distribution for large masses, related to the turbulence-energy power-spectrum slope and the shock-jump conditions. This power-law mass distribution is confirmed by the numerical experiments. The model also predicts a sharp difference between the HD and MHD regimes, which is recovered in the experiments as well, implying that the magnetic field, even below energy equipartition on the large scale, is a crucial component of the process of turbulent fragmentation. These results suggest that the stellar IMF of primordial stars may differ from that in later epochs of star formation, due to differences in both gas temperature and magnetic field strength. In particular, we find that the IMF of primordial stars born in turbulent clouds may be narrowly peaked around a mass of order 10 Msolar, as long as the column density of such clouds is not much in excess of 1022 cm-2.
A stability analysis of the power-law steady state of marine size spectra.

PubMed

Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J

2011-10-01

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.
Power-law confusion: You say incremental, I say differential

NASA Technical Reports Server (NTRS)

Colwell, Joshua E.

1993-01-01

Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.
Isotopic fractionation studies of uranium and plutonium using porous ion emitters as thermal ionization mass spectrometry sources

DOE PAGES

Baruzzini, Matthew L.; Hall, Howard L.; Spencer, Khalil J.; ...

2018-04-22

Investigations of the isotope fractionation behaviors of plutonium and uranium reference standards were conducted employing platinum and rhenium (Pt/Re) porous ion emitter (PIE) sources, a relatively new thermal ionization mass spectrometry (TIMS) ion source strategy. The suitability of commonly employed, empirically developed mass bias correction laws (i.e., the Linear, Power, and Russell's laws) for correcting such isotope ratio data was also determined. Corrected plutonium isotope ratio data, regardless of mass bias correction strategy, were statistically identical to that of the certificate, however, the process of isotope fractionation behavior of plutonium using the adopted experimental conditions was determined to be bestmore » described by the Power law. Finally, the fractionation behavior of uranium, using the analytical conditions described herein, is also most suitably modeled using the Power law, though Russell's and the Linear law for mass bias correction rendered results that were identical, within uncertainty, to the certificate value.« less
Isotopic fractionation studies of uranium and plutonium using porous ion emitters as thermal ionization mass spectrometry sources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baruzzini, Matthew L.; Hall, Howard L.; Spencer, Khalil J.

Investigations of the isotope fractionation behaviors of plutonium and uranium reference standards were conducted employing platinum and rhenium (Pt/Re) porous ion emitter (PIE) sources, a relatively new thermal ionization mass spectrometry (TIMS) ion source strategy. The suitability of commonly employed, empirically developed mass bias correction laws (i.e., the Linear, Power, and Russell's laws) for correcting such isotope ratio data was also determined. Corrected plutonium isotope ratio data, regardless of mass bias correction strategy, were statistically identical to that of the certificate, however, the process of isotope fractionation behavior of plutonium using the adopted experimental conditions was determined to be bestmore » described by the Power law. Finally, the fractionation behavior of uranium, using the analytical conditions described herein, is also most suitably modeled using the Power law, though Russell's and the Linear law for mass bias correction rendered results that were identical, within uncertainty, to the certificate value.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Erfani, Ehsan; Mitchell, David L.

Here, ice particle mass- and projected area-dimension ( m- D and A- D) power laws are commonly used in the treatment of ice cloud microphysical and optical properties and the remote sensing of ice cloud properties. Although there has long been evidence that a single m- D or A- D power law is often not valid over all ice particle sizes, few studies have addressed this fact. This study develops self-consistent m- D and A- D expressions that are not power laws but can easily be reduced to power laws for the ice particle size (maximum dimension or D) rangemore » of interest, and they are valid over a much larger D range than power laws. This was done by combining ground measurements of individual ice particle m and D formed at temperature T < –20 °C during a cloud seeding field campaign with 2-D stereo (2D-S) and cloud particle imager (CPI) probe measurements of D and A, and estimates of m, in synoptic and anvil ice clouds at similar temperatures. The resulting m- D and A- D expressions are functions of temperature and cloud type (synoptic vs. anvil), and are in good agreement with m- D power laws developed from recent field studies considering the same temperature range (–60 °C < T < –20 °C).« less
A maximum entropy principle for inferring the distribution of 3D plasmoids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lingam, Manasvi; Comisso, Luca

The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of -4/3, -2, -3, and -2, respectively, for smallmore » values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v=|v|, is shown to be flat for v→0, and becomes a power law with an exponent of -7/3 for v→∞. Most of these results are nearly independent of the free parameters involved in this specific problem. In conclusion, a preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.« less
A maximum entropy principle for inferring the distribution of 3D plasmoids

DOE PAGES

Lingam, Manasvi; Comisso, Luca

2018-01-18

The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of -4/3, -2, -3, and -2, respectively, for smallmore » values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v=|v|, is shown to be flat for v→0, and becomes a power law with an exponent of -7/3 for v→∞. Most of these results are nearly independent of the free parameters involved in this specific problem. In conclusion, a preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.« less

The galaxy-wide initial mass function of dwarf late-type to massive early-type galaxies

NASA Astrophysics Data System (ADS)

Weidner, C.; Kroupa, P.; Pflamm-Altenburg, J.; Vazdekis, A.

2013-12-01

Observational studies are showing that the galaxy-wide stellar initial mass function (IMF) is top-heavy in galaxies with high star formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR of a galaxy, it follows that galaxies which have or which formed with SFRs >10 M⊙ yr-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher mass-to-light ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar IMF. For the Milky Way, the IGIMF yields very good agreement with the disc- and the bulge IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a parsec and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index β of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.
Two parametric voice source models and their asymptotic analysis

NASA Astrophysics Data System (ADS)

Leonov, A. S.; Sorokin, V. N.

2014-05-01

The paper studies the asymptotic behavior of the function for the area of the glottis near moments of its opening and closing for two mathematical voice source models. It is shown that in the first model, the asymptotics of the area function obeys a power law with an exponent of no less that 1. Detailed analysis makes it possible to refine these limits depending on the relative sizes of the intervals of a closed and open glottis. This work also studies another parametric model of the area of the glottis, which is based on a simplified physical-geometrical representation of vocal-fold vibration processes. This is a special variant of the well-known two-mass model and contains five parameters: the period of the main tone, equivalent masses on the lower and upper edge of vocal folds, the coefficient of elastic resistance of the lower vocal fold, and the delay time between openings of the upper and lower folds. It is established that the asymptotics of the obtained function for the area of the glottis obey a power law with an exponent of 1 both for opening and closing.
The Core Mass Function in the Massive Protocluster G286.21+0.17 Revealed by ALMA

NASA Astrophysics Data System (ADS)

Cheng, Yu; Tan, Jonathan C.; Liu, Mengyao; Kong, Shuo; Lim, Wanggi; Andersen, Morten; Da Rio, Nicola

2018-02-01

We study the core mass function (CMF) of the massive protocluster G286.21+0.17 with the Atacama Large Millimeter/submillimeter Array via 1.3 mm continuum emission at a resolution of 1.″0 (2500 au). We have mapped a field of 5.‧3 × 5.‧3 centered on the protocluster clump. We measure the CMF in the central region, exploring various core detection algorithms, which give source numbers ranging from 60 to 125, depending on parameter selection. We estimate completeness corrections due to imperfect flux recovery and core identification via artificial core insertion experiments. For masses M ≳ 1 M ⊙, the fiducial dendrogram-identified CMF can be fit with a power law of the form dN/dlog M ∝ M ‑α with α ≃ 1.24 ± 0.17, slightly shallower than, but still consistent with, the index of the Salpeter stellar initial mass function of 1.35. Clumpfind-identified CMFs are significantly shallower with α ≃ 0.64 ± 0.13. While raw CMFs show a peak near 1 M ⊙, completeness-corrected CMFs are consistent with a single power law extending down to ∼0.5 M ⊙, with only a tentative indication of a shallowing of the slope around ∼1 M ⊙. We discuss the implications of these results for star and star cluster formation theories.
Mass functions for globular cluster main sequences based on CCD photometry and stellar models

NASA Astrophysics Data System (ADS)

McClure, Robert D.; Vandenberg, Don A.; Smith, Graeme H.; Fahlman, Gregory G.; Richer, Harvey B.; Hesser, James E.; Harris, William E.; Stetson, Peter B.; Bell, R. A.

1986-08-01

Main-sequence luminosity functions constructed from CCD observations of globular clusters reveal a strong trend in slope with metal abundance. Theoretical luminosity functions constructed from VandenBerg and Bell's (1985) isochrones have been fitted to the observations and reveal a trend between x, the power-law index of the mass function, and metal abundance. The most metal-poor clusters require an index of about x = 2.5, whereas the most metal-rich clusters exhibit an index of x of roughly -0.5. The luminosity functions for two sparse clusters, E3 and Pal 5, are distinct from those of the more massive clusters, in that they show a turndown which is possibly a result of mass loss or tidal disruption.
Use of Mass- and Area-Dimensional Power Laws for Determining Precipitation Particle Terminal Velocities.

NASA Astrophysics Data System (ADS)

Mitchell, David L.

1996-06-01

Based on boundary layer theory and a comparison of empirical power laws relating the Reynolds and Best numbers, it was apparent that the primary variables governing a hydrometeor's terminal velocity were its mass, its area projected to the flow, and its maximum dimension. The dependence of terminal velocities on surface roughness appeared secondary, with surface roughness apparently changing significantly only during phase changes (i.e., ice to liquid). In the theoretical analysis, a new, comprehensive expression for the drag force, which is valid for both inertial and viscous-dominated flow, was derived.A hydrometeor's mass and projected area were simply and accurately represented in terms of its maximum dimension by using dimensional power laws. Hydrometeor terminal velocities were calculated by using mass- and area-dimensional power laws to parameterize the Best number, X. Using a theoretical relationship general for all particle types, the Reynolds number, Re, was then calculated from the Best number. Terminal velocities were calculated from Re.Alternatively, four Re-X power-law expressions were extracted from the theoretical Re-X relationship. These expressions collectively describe the terminal velocities of all ice particle types. These were parameterized using mass- and area-dimensional power laws, yielding four theoretically based power-law expressions predicting fall speeds in terms of ice particle maximum dimension. When parameterized for a given ice particle type, the theoretical fall speed power law can be compared directly with empirical fall speed-dimensional power laws in the literature for the appropriate Re range. This provides a means of comparing theory with observations.Terminal velocities predicted by this method were compared with fall speeds given by empirical fall speed expressions for the same ice particle type, which were curve fits to measured fall speeds. Such comparisons were done for nine types of ice particles. Fall speeds predicted by this method differed from those based on measurements by no more than 20%.The features that distinguish this method of determining fall speeds from others are that it does not represent particles as spheroids, it is general for any ice particle shape and size, it is conceptually and mathematically simple, it appears accurate, and it provides for physical insight. This method also allows fall speeds to be determined from aircraft measurements of ice particle mass and projected area, rather than directly measuring fall speeds. This approach may be useful for ice crystals characterizing cirrus clouds, for which direct fall speed measurements are difficult.
STAR FORMATION LAWS: THE EFFECTS OF GAS CLOUD SAMPLING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Calzetti, D.; Liu, G.; Koda, J., E-mail: calzetti@astro.umass.edu

Recent observational results indicate that the functional shape of the spatially resolved star formation-molecular gas density relation depends on the spatial scale considered. These results may indicate a fundamental role of sampling effects on scales that are typically only a few times larger than those of the largest molecular clouds. To investigate the impact of this effect, we construct simple models for the distribution of molecular clouds in a typical star-forming spiral galaxy and, assuming a power-law relation between star formation rate (SFR) and cloud mass, explore a range of input parameters. We confirm that the slope and the scattermore » of the simulated SFR-molecular gas surface density relation depend on the size of the sub-galactic region considered, due to stochastic sampling of the molecular cloud mass function, and the effect is larger for steeper relations between SFR and molecular gas. There is a general trend for all slope values to tend to {approx}unity for region sizes larger than 1-2 kpc, irrespective of the input SFR-cloud relation. The region size of 1-2 kpc corresponds to the area where the cloud mass function becomes fully sampled. We quantify the effects of selection biases in data tracing the SFR, either as thresholds (i.e., clouds smaller than a given mass value do not form stars) or as backgrounds (e.g., diffuse emission unrelated to current star formation is counted toward the SFR). Apparently discordant observational results are brought into agreement via this simple model, and the comparison of our simulations with data for a few galaxies supports a steep (>1) power-law index between SFR and molecular gas.« less
Analytical time-domain Green’s functions for power-law media

PubMed Central

Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

2008-01-01

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774
The left ventricle as a mechanical engine: from Leonardo da Vinci to the echocardiographic assessment of peak power output-to-left ventricular mass.

PubMed

Dini, Frank L; Guarini, Giacinta; Ballo, Piercarlo; Carluccio, Erberto; Maiello, Maria; Capozza, Paola; Innelli, Pasquale; Rosa, Gian M; Palmiero, Pasquale; Galderisi, Maurizio; Razzolini, Renato; Nodari, Savina

2013-03-01

The interpretation of the heart as a mechanical engine dates back to the teachings of Leonardo da Vinci, who was the first to apply the laws of mechanics to the function of the heart. Similar to any mechanical engine, whose performance is proportional to the power generated with respect to weight, the left ventricle can be viewed as a power generator whose performance can be related to left ventricular mass. Stress echocardiography may provide valuable information on the relationship between cardiac performance and recruited left ventricular mass that may be used in distinguishing between adaptive and maladaptive left ventricular remodeling. Peak power output-to-mass, obtained during exercise or pharmacological stress echocardiography, is a measure that reflects the number of watts that are developed by 100 g of left ventricular mass under maximal stimulation. Power output-to-mass may be calculated as left ventricular power output per 100 g of left ventricular mass: 100× left ventricular power output divided by left ventricular mass (W/100 g). A simplified formula to calculate power output-to-mass is as follows: 0.222 × cardiac output (l/min) × mean blood pressure (mmHg)/left ventricular mass (g). When the integrity of myocardial structure is compromised, a mismatch becomes apparent between maximal cardiac power output and left ventricular mass; when this occurs, a reduction of the peak power output-to-mass index is observed.
Learning curves in highly skilled chess players: a test of the generality of the power law of practice.

PubMed

Howard, Robert W

2014-09-01

The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. Copyright © 2014 Elsevier B.V. All rights reserved.
The Discrepancy between Einstein Mass and Dynamical Mass for SIS and Power-law Mass Models

NASA Astrophysics Data System (ADS)

Li, Rui; Wang, Jiancheng; Shu, Yiping; Xu, Zhaoyi

2018-03-01

We investigate the discrepancy between the two-dimensional projected lensing mass and the dynamical mass for an ensemble of 97 strong gravitational lensing systems discovered by the Sloan Lens ACS Survey, the BOSS Emission-Line Lens Survey (BELLS), and the BELLS for GALaxy-Lyα EmitteR sYstems Survey. We fit the lensing data to obtain the Einstein mass and use the velocity dispersion of the lensing galaxies provided by the Sloan Digital Sky Survey to get the projected dynamical mass within the Einstein radius by assuming the power-law mass approximation. The discrepancy is found to be obvious and quantified by Bayesian analysis. For the singular isothermal sphere mass model, we obtain that the Einstein mass is 20.7% more than the dynamical mass, and the discrepancy increases with the redshift of the lensing galaxies. For the more general power-law mass model, the discrepancy still exists within a 1σ credible region. We suspect the main reason for this discrepancy is mass contamination, including all invisible masses along the line of sight. In addition, the measurement errors and the approximation of the mass models could also contribute to the discrepancy.
Deep luminosity function of the globular cluster M13

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drukier, G.A.; Fahlman, G.G.; Richter, H.B.

The luminosity function in a field of M13 at 14 core radii has been observed to M(V) = +12.0, and new theoretical, low-mass, stellar models appropriate to M13 are used to convert the function to a mass function which extends to M = 0.18 solar, within a factor of two of brown dwarf masses at this metal abundance. As the number of stars observed in each magnitude bin is still increasing at the limit of the data, the presence of stars with masses lower than 0.18 solar is probable. This result sets an upper limit of 0.18 solar mass formore » low-mass cutoffs in dynamical models of M13. No single power law mass function fits all the observations. The trend of the data supports the idea of a steep increase in the slope of the mass function for M less than 0.4 solar. The results imply that the total mass in low-mass stars in M13, and by implication elsewhere, is higher than was previously thought. 26 references.« less
Evidence for Universality in the Initial Planetesimal Mass Function

NASA Astrophysics Data System (ADS)

Simon, Jacob B.; Armitage, Philip J.; Youdin, Andrew N.; Li, Rixin

2017-10-01

Planetesimals may form from the gravitational collapse of dense particle clumps initiated by the streaming instability. We use simulations of aerodynamically coupled gas-particle mixtures to investigate whether the properties of planetesimals formed in this way depend upon the sizes of the particles that participate in the instability. Based on three high-resolution simulations that span a range of dimensionless stopping times 6× {10}-3≤slant τ ≤slant 2, no statistically significant differences in the initial planetesimal mass function are found. The mass functions are fit by a power law, {dN}/{{dM}}p\\propto {M}p-p, with p = 1.5-1.7 and errors of {{Δ }}p≈ 0.1. Comparing the particle density fields prior to collapse, we find that the high-wavenumber power spectra are similarly indistinguishable, though the large-scale geometry of structures induced via the streaming instability is significantly different between all three cases. We interpret the results as evidence for a near-universal slope to the mass function, arising from the small-scale structure of streaming-induced turbulence.
THE STAR FORMATION HISTORIES OF z {approx} 2 DUST-OBSCURED GALAXIES AND SUBMILLIMETER-SELECTED GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bussmann, R. S.; Dey, Arjun; Jannuzi, B. T.

The Spitzer Space Telescope has identified a population of ultraluminous infrared galaxies (ULIRGs) at z {approx} 2 that may play an important role in the evolution of massive galaxies. We measure the stellar masses (M{sub *}) of two populations of Spitzer-selected ULIRGs that have extremely red R - [24] colors (dust-obscured galaxies, or DOGs) and compare our results with submillimeter-selected galaxies (SMGs). One set of 39 DOGs has a local maximum in their mid-infrared (mid-IR) spectral energy distribution (SED) at rest frame 1.6 {mu}m associated with stellar emission ({sup b}ump DOGs{sup )}, while the other set of 51 DOGs havemore » power-law mid-IR SEDs that are typical of obscured active galactic nuclei ({sup p}ower-law DOGs{sup )}. We measure M{sub *} by applying Charlot and Bruzual stellar population synthesis models to broadband photometry in the rest-frame ultraviolet, optical, and near-infrared of each of these populations. Assuming a simple stellar population and a Chabrier initial mass function, we find that power-law DOGs and bump DOGs are on average a factor of 2 and 1.5 more massive than SMGs, respectively (median and inter-quartile M{sub *} values for SMGs, bump DOGs, and power-law DOGs are log(M{sub *}/M{sub Sun }) = 10.42{sup +0.42}{sub -0.36}, 10.62{sup +0.36}{sub -0.32}, and 10.71{sup +0.40}{sub -0.34}, respectively). More realistic star formation histories drawn from two competing theories for the nature of ULIRGs at z {approx} 2 (major merger versus smooth accretion) can increase these mass estimates by up to 0.5 dex. A comparison of our stellar masses with the instantaneous star formation rate (SFR) in these z {approx} 2 ULIRGs provides a preliminary indication supporting high SFRs for a given M{sub *}, a situation that arises more naturally in major mergers than in smooth accretion-powered systems.« less
Growth and form of planetary seedlings: results from a sounding rocket microgravity aggregation experiment.

PubMed

Krause, Maya; Blum, Jürgen

2004-07-09

In a second microgravity experiment on the formation of dust agglomerates by Brownian motion-induced collisions we find that the agglomerates have fractal dimensions as low as 1.4. Because of much better data, we are now able to derive the diffusion constant of the agglomerates as a function of mass, to show that a power law with an exponent of 1.7 describes the temporal evolution of the mean agglomerate mass very well and to prove that the collision cross section is proportional to the geometrical cross section. In addition to that we derived the universal mass-distribution function of the agglomerates.
Size matters: abundance matching, galaxy sizes, and the Tully-Fisher relation in EAGLE

NASA Astrophysics Data System (ADS)

Ferrero, Ismael; Navarro, Julio F.; Abadi, Mario G.; Sales, Laura V.; Bower, Richard G.; Crain, Robert A.; Frenk, Carlos S.; Schaller, Matthieu; Schaye, Joop; Theuns, Tom

2017-02-01

The Tully-Fisher relation (TFR) links the stellar mass of a disc galaxy, Mstr, to its rotation speed: it is well approximated by a power law, shows little scatter, and evolves weakly with redshift. The relation has been interpreted as reflecting the mass-velocity scaling (M ∝ V3) of dark matter haloes, but this interpretation has been called into question by abundance-matching (AM) models, which predict the galaxy-halo mass relation to deviate substantially from a single power law and to evolve rapidly with redshift. We study the TFR of luminous spirals and its relation to AM using the EAGLE set of Λ cold dark matter (ΛCDM) cosmological simulations. Matching both relations requires disc sizes to satisfy constraints given by the concentration of haloes and their response to galaxy assembly. EAGLE galaxies approximately match these constraints and show a tight mass-velocity scaling that compares favourably with the observed TFR. The TFR is degenerate to changes in galaxy formation efficiency and the mass-size relation; simulations that fail to match the galaxy stellar mass function may fit the observed TFR if galaxies follow a different mass-size relation. The small scatter in the simulated TFR results because, at fixed halo mass, galaxy mass and rotation speed correlate strongly, scattering galaxies along the main relation. EAGLE galaxies evolve with lookback time following approximately the prescriptions of AM models and the observed mass-size relation of bright spirals, leading to a weak TFR evolution consistent with observation out to z = 1. ΛCDM models that match both the abundance and size of galaxies as a function of stellar mass have no difficulty reproducing the observed TFR and its evolution.
Relativistic Bessel cylinders

NASA Astrophysics Data System (ADS)

Krisch, J. P.; Glass, E. N.

2014-10-01

A set of cylindrical solutions to Einstein's field equations for power law densities is described. The solutions have a Bessel function contribution to the metric. For matter cylinders regular on axis, the first two solutions are the constant density Gott-Hiscock string and a cylinder with a metric Airy function. All members of this family have the Vilenkin limit to their mass per length. Some examples of Bessel shells and Bessel motion are given.
Light scattering Q-space analysis of irregularly shaped particles

NASA Astrophysics Data System (ADS)

Heinson, Yuli W.; Maughan, Justin B.; Heinson, William R.; Chakrabarti, Amitabha; Sorensen, Christopher M.

2016-01-01

We report Q-space analysis of light scattering phase function data for irregularly shaped dust particles and of theoretical model output to describe them. This analysis involves plotting the scattered intensity versus the magnitude of the scattering wave vector q = (4π/λ)sin(θ/2), where λ is the optical wavelength and θ is the scattering angle, on a double-logarithmic plot. In q-space all the particle shapes studied display a scattering pattern which includes a q-independent forward scattering regime; a crossover, Guinier regime when q is near the inverse size; a power law regime; and an enhanced backscattering regime. Power law exponents show a quasi-universal functionality with the internal coupling parameter ρ'. The absolute value of the exponents start from 4 when ρ' < 1, the diffraction limit, and decreases as ρ' increases until a constant 1.75 ± 0.25 when ρ' ≳ 10. The diffraction limit exponent implies that despite their irregular structures, all the particles studied have mass and surface scaling dimensions of Dm = 3 and Ds = 2, respectively. This is different from fractal aggregates that have a power law equal to the fractal dimension Df because Df = Dm = Ds < 3. Spheres have Dm = 3 and Ds = 2 but do not show a single power law nor the same functionality with ρ'. The results presented here imply that Q-space analysis can differentiate between spheres and these two types of irregularly shaped particles. Furthermore, they are applicable to analysis of the contribution of aerosol radiative forcing to climate change and of aerosol remote sensing data.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Chandar, Rupali; Fall, S. Michael; Whitmore, Bradley C., E-mail: Rupali.Chandar@utoledo.ed, E-mail: fall@stsci.ed, E-mail: whitmore@stsci.ed

We compare the observed bivariate distribution of masses (M) and ages (tau) of star clusters in the Large Magellanic Cloud (LMC) with the predicted distributions g(M, tau) from three idealized models for the disruption of star clusters: (1) sudden mass-dependent disruption, (2) gradual mass-dependent disruption, and (3) gradual mass-independent disruption. The model with mass-independent disruption provides a good, first-order description of these cluster populations, with g(M, tau) {proportional_to} M {sup beta}tau{sup g}amma, beta = -1.8 +- 0.2 and gamma = -0.8 +- 0.2, at least for clusters with ages tau {approx}< 10{sup 9} yr and masses M {approx}> 10{sup 3}more » M{sub sun} (more specifically, tau {approx}< 10{sup 7}(M/10{sup 2} M{sub sun}){sup 1.3} yr). This model predicts that the clusters should have a power-law luminosity function, dN/dL {proportional_to} L {sup -1.8}, in agreement with observations. The first two models, on the other hand, fare poorly when describing the observations, refuting previous claims that mass-dependent disruption of star clusters is observed in the LMC over the studied M-tau domain. Clusters in the SMC can be described by the same g(M, tau) distribution as for the LMC, but with smaller samples and hence larger uncertainties. The successful g(M, tau) model for clusters in the Magellanic Clouds is virtually the same as the one for clusters in the merging Antennae galaxies, but extends the domain of validity to lower masses and to older ages. This indicates that the dominant disruption processes are similar in these very different galaxies over at least tau {approx}< 10{sup 8} yr and possibly tau {approx}< 10{sup 9} yr. The mass functions for young clusters in the LMC are power laws, while that for ancient globular clusters is peaked. We show that the observed shapes of these mass functions are consistent with expectations from the simple evaporation model presented by McLaughlin and Fall.« less
Evolutionary Description of Giant Molecular Cloud Mass Functions on Galactic Disks

NASA Astrophysics Data System (ADS)

Kobayashi, Masato I. N.; Inutsuka, Shu-ichiro; Kobayashi, Hiroshi; Hasegawa, Kenji

2017-02-01

Recent radio observations show that giant molecular cloud (GMC) mass functions noticeably vary across galactic disks. High-resolution magnetohydrodynamics simulations show that multiple episodes of compression are required for creating a molecular cloud in the magnetized interstellar medium. In this article, we formulate the evolution equation for the GMC mass function to reproduce the observed profiles, for which multiple compressions are driven by a network of expanding shells due to H II regions and supernova remnants. We introduce the cloud-cloud collision (CCC) terms in the evolution equation in contrast to previous work (Inutsuka et al.). The computed time evolution suggests that the GMC mass function slope is governed by the ratio of GMC formation timescale to its dispersal timescale, and that the CCC effect is limited only in the massive end of the mass function. In addition, we identify a gas resurrection channel that allows the gas dispersed by massive stars to regenerate GMC populations or to accrete onto pre-existing GMCs. Our results show that almost all of the dispersed gas contributes to the mass growth of pre-existing GMCs in arm regions whereas less than 60% contributes in inter-arm regions. Our results also predict that GMC mass functions have a single power-law exponent in the mass range <105.5 {M}⊙ (where {M}⊙ represents the solar mass), which is well characterized by GMC self-growth and dispersal timescales. Measurement of the GMC mass function slope provides a powerful method to constrain those GMC timescales and the gas resurrecting factor in various environments across galactic disks.
Scaling of Myocardial Mass to Flow and Morphometry of Coronary Arteries

PubMed Central

Choy, Jenny Susana; Kassab, Ghassan S.

2009-01-01

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5±32.7) were used in this study. Various coronary sub-trees of the Left Anterior Descending (LAD), Right Coronary (RCA) and Left Circumflex (LCX) arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) in order to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters and volumetric flow show an approximately 3/4, 3/8 and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease. PMID:18323461

Scaling of myocardial mass to flow and morphometry of coronary arteries.

PubMed

Choy, Jenny Susana; Kassab, Ghassan S

2008-05-01

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5 +/- 32.7) were used in this study. Various coronary subtrees of the left anterior descending, right coronary, and left circumflex arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter, and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters, and volumetric flow show an approximately 3/4, 3/8, and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease.
The Mass Function of Young Star Clusters in the "Antennae" Galaxies.

PubMed

Zhang; Fall

1999-12-20

We determine the mass function of young star clusters in the merging galaxies known as the "Antennae" (NGC 4038/9) from deep images taken with the Wide Field Planetary Camera 2 on the refurbished Hubble Space Telescope. This is accomplished by means of reddening-free parameters and a comparison with stellar population synthesis tracks to estimate the intrinsic luminosity and age, and hence the mass, of each cluster. We find that the mass function of the young star clusters (with ages less, similar160 Myr) is well represented by a power law of the form psi&parl0;M&parr0;~M-2 over the range 104 less, similarM less, similar106 M middle dot in circle. This result may have important implications for our understanding of the origin of globular clusters during the early phases of galactic evolution.
Experiments and Demonstrations in Physics: Bar-Ilan Physics Laboratory (2nd Edition)

NASA Astrophysics Data System (ADS)

Kraftmakher, Yaakov

2014-08-01

The following sections are included: * Data-acquisition systems from PASCO * ScienceWorkshop 750 Interface and DataStudio software * 850 Universal Interface and Capstone software * Mass on spring * Torsional pendulum * Hooke's law * Characteristics of DC source * Digital storage oscilloscope * Charging and discharging a capacitor * Charge and energy stored in a capacitor * Speed of sound in air * Lissajous patterns * I-V characteristics * Light bulb * Short time intervals * Temperature measurements * Oersted's great discovery * Magnetic field measurements * Magnetic force * Magnetic braking * Curie's point I * Electric power in AC circuits * Faraday's law of induction I * Self-inductance and mutual inductance * Electromagnetic screening * LCR circuit I * Coupled LCR circuits * Probability functions * Photometric laws * Kirchhoff's rule for thermal radiation * Malus' law * Infrared radiation * Irradiance and illuminance
The panchromatic Hubble Andromeda Treasury. V. Ages and masses of the year 1 stellar clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fouesneau, Morgan; Johnson, L. Clifton; Weisz, Daniel R.

We present ages and masses for 601 star clusters in M31 from the analysis of the six filter integrated light measurements from near-ultraviolet to near-infrared wavelengths, made as part of the Panchromatic Hubble Andromeda Treasury (PHAT). We derive the ages and masses using a probabilistic technique, which accounts for the effects of stochastic sampling of the stellar initial mass function. Tests on synthetic data show that this method, in conjunction with the exquisite sensitivity of the PHAT observations and their broad wavelength baseline, provides robust age and mass recovery for clusters ranging from ∼10{sup 2} to 2 × 10{sup 6}more » M {sub ☉}. We find that the cluster age distribution is consistent with being uniform over the past 100 Myr, which suggests a weak effect of cluster disruption within M31. The age distribution of older (>100 Myr) clusters falls toward old ages, consistent with a power-law decline of index –1, likely from a combination of fading and disruption of the clusters. We find that the mass distribution of the whole sample can be well described by a single power law with a spectral index of –1.9 ± 0.1 over the range of 10{sup 3}-3 × 10{sup 5} M {sub ☉}. However, if we subdivide the sample by galactocentric radius, we find that the age distributions remain unchanged. However, the mass spectral index varies significantly, showing best-fit values between –2.2 and –1.8, with the shallower slope in the highest star formation intensity regions. We explore the robustness of our study to potential systematics and conclude that the cluster mass function may vary with respect to environment.« less
STARS DO NOT EAT THEIR YOUNG MIGRATING PLANETS: EMPIRICAL CONSTRAINTS ON PLANET MIGRATION HALTING MECHANISMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plavchan, Peter; Bilinski, Christopher

The discovery of ''hot Jupiters'' very close to their parent stars confirmed that Jovian planets migrate inward via several potential mechanisms. We present empirical constraints on planet migration halting mechanisms. We compute model density functions of close-in exoplanets in the orbital semi-major axis-stellar mass plane to represent planet migration that is halted via several mechanisms, including the interior 1:2 resonance with the magnetospheric disk truncation radius, the interior 1:2 resonance with the dust sublimation radius, and several scenarios for tidal halting. The models differ in the predicted power-law dependence of the exoplanet orbital semi-major axis as a function of stellarmore » mass, and thus we also include a power-law model with the exponent as a free parameter. We use a Bayesian analysis to assess the model success in reproducing empirical distributions of confirmed exoplanets and Kepler candidates that orbit interior to 0.1 AU. Our results confirm a correlation of the halting distance with stellar mass. Tidal halting provides the best fit to the empirical distribution of confirmed Jovian exoplanets at a statistically robust level, consistent with the Kozai mechanism and the spin-orbit misalignment of a substantial fraction of hot Jupiters. We can rule out migration halting at the interior 1:2 resonances with the magnetospheric disk truncation radius and the interior 1:2 resonance with the dust disk sublimation radius, a uniform random distribution, and a distribution with no dependence on stellar mass. Note that our results do not rule out Type-II migration, but rather eliminate the role of a circumstellar disk in stopping exoplanet migration. For Kepler candidates, which have a more restricted range in stellar mass compared to confirmed planets, we are unable to discern between the tidal dissipation and magnetospheric disk truncation braking mechanisms at a statistically significant level. The power-law model favors exponents in the range of 0.38-0.9. This is larger than that predicted for tidal halting (0.23-0.33), which suggests that additional physics may be missing in the tidal halting theory.« less
Low-mass stars in globular clusters. III. The mass function of 47 Tucanae.

NASA Astrophysics Data System (ADS)

de Marchi, G.; Paresce, F.

1995-12-01

We have used the WFPC2 on board HST to investigate the stellar population in a field located 4'6 E of the center of the globular cluster 47 Tuc (NGC 104), close to the half-mass radius, through wide band imaging at 606 and 812nm. A total of ~3000 stars are accurately classified by two-color photometry to form a color-magnitude diagram extending down to a limiting magnitude m_814_=~m_I_=~24. A rich cluster main sequence is detected spanning the range from m_814_=~18 through m_814_=~23, where it spreads considerably due to the increasing photometric uncertainty and galaxy contamination. A secondary sequence of objects is also detected, parallel to the main sequence, as expected for a population of binary stars. The measured binary fraction in the range 195%. The main sequence luminosity function obtained from the observed CMD increases with decreasing luminosity following a power-law trend with index α=~0.15 in the range 5
Size-Frequency Distributions of Dust - Size Debris from the Impact Disruption of Chondritic Meteorites

NASA Astrophysics Data System (ADS)

Durda, Daniel D.; Flynn, George J.; Sandel, L. Erica; Strait, Melissa M.

2007-01-01

We present mass-frequency data for fragments from the impact disruption of four chondritic meteorites, extending to masses several orders of magnitude smaller the mass-frequency data that are usually measured in similar impact experiments. Masses of mm- to cm-scale fragments were determined by directly weighing debris collected from the floor of the Ames Vertical Gun Range impact chamber. Masses of sub-mm to dust-size fragments were determined from analysis of foil penetration data. The mass-frequency distributions display a range of morphologies ranging from nearly linear power-law distributions to `broken' power laws with progressively shallower slopes at smaller fragment masses, apparently dependent on the magnitude of the impact specific energy.
Formation of young massive clusters from turbulent molecular clouds

NASA Astrophysics Data System (ADS)

Fujii, Michiko; Portegies Zwart, Simon

2015-08-01

We simulate the formation and evolution of young star clusters using smoothed-particle hydrodynamics (SPH) and direct N-body methods. We start by performing SPH simulations of the giant molecular cloud with a turbulent velocity field, a mass of 10^4 to 10^6 M_sun, and a density between 17 and 1700 cm^-3. We continue the SPH simulations for a free-fall time scale, and analyze the resulting structure of the collapsed cloud. We subsequently replace a density-selected subset of SPH particles with stars. As a consequence, the local star formation efficiency exceeds 30 per cent, whereas globally only a few per cent of the gas is converted to stars. The stellar distribution is very clumpy with typically a dozen bound conglomerates that consist of 100 to 10000 stars. We continue to evolve the stars dynamically using the collisional N-body method, which accurately treats all pairwise interactions, stellar collisions and stellar evolution. We analyze the results of the N-body simulations at 2 Myr and 10 Myr. From dense massive molecular clouds, massive clusters grow via hierarchical merging of smaller clusters. The shape of the cluster mass function that originates from an individual molecular cloud is consistent with a Schechter function with a power-law slope of beta = -1.73 at 2 Myr and beta = -1.67 at 10 Myr, which fits to observed cluster mass function of the Carina region. The superposition of mass functions have a power-law slope of < -2, which fits the observed mass function of star clusters in the Milky Way, M31 and M83. We further find that the mass of the most massive cluster formed in a single molecular cloud with a mass of M_g scales with 6.1 M_g^0.51 which also agrees with recent observation in M51. The molecular clouds which can form massive clusters are much denser than those typical in the Milky Way. The velocity dispersion of such molecular clouds reaches 20 km/s and it is consistent with the relative velocity of the molecular clouds observed near NGC 3603 and Westerlund 2, for which a triggered star formation by cloud-cloud collisions is suggested.
Model selection for identifying power-law scaling.

PubMed

Ton, Robert; Daffertshofer, Andreas

2016-08-01

Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present. Copyright © 2016 Elsevier Inc. All rights reserved.
Evidence for a Constant Initial Mass Function in Early-type Galaxies Based on Their X-Ray Binary Populations

NASA Astrophysics Data System (ADS)

Peacock, Mark B.; Zepf, Stephen E.; Maccarone, Thomas J.; Kundu, Arunav; Gonzalez, Anthony H.; Lehmer, Bret D.; Maraston, Claudia

2014-04-01

A number of recent studies have proposed that the stellar initial mass function (IMF) of early type galaxies varies systematically as a function of galaxy mass, with higher mass galaxies having bottom-heavy IMFs. These bottom-heavy IMFs have more low-mass stars relative to the number of high mass stars, and therefore naturally result in proportionally fewer neutron stars (NSs) and black holes (BHs). In this paper, we specifically predict the variation in the number of BHs and NSs based on the power-law IMF variation required to reproduce the observed mass-to-light ratio trends with galaxy mass. We then test whether such variations are observed by studying the field low-mass X-ray binary (LMXB) populations of nearby early-type galaxies. In these binaries, an NS or BH accretes matter from a low-mass donor star. Their number is therefore expected to scale with the number of BHs and NSs present in a galaxy. We find that the number of LMXBs per K-band light is similar among the galaxies in our sample. These data therefore demonstrate the uniformity of the slope of the IMF from massive stars down to those now dominating the K-band light and are consistent with an invariant IMF. Our results are inconsistent with an IMF which varies from a Kroupa/Chabrier like IMF for low-mass galaxies to a steep power-law IMF (with slope x = 2.8) for high mass galaxies. We discuss how these observations constrain the possible forms of the IMF variations and how future Chandra observations can enable sharper tests of the IMF. Based in part on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA). The scientific results reported in this article are based in part on data obtained from the Chandra Data Archive and observations made by the Chandra X-ray Observatory and published previously in cited articles.
Similarity principles for the biology of pelagic animals

PubMed Central

Barenblatt, G. I.; Monin, A. S.

1983-01-01

A similarity principle is formulated according to which the statistical pattern of the pelagic population is identical in all scales sufficiently large in comparison with the molecular one. From this principle, a power law is obtained analytically for the pelagic animal biomass distribution over the animal sizes. A hypothesis is presented according to which, under fixed external conditions, the oxygen exchange intensity of an animal is governed only by its mass and density and by the specific absorbing capacity of the animal's respiratory organ. From this hypothesis a power law is obtained by the method of dimensional analysis for the exchange intensity mass dependence. The known empirical values of the exponent of this power law are interpreted as an indication that the oxygen-absorbing organs of the animals can be represented as so-called fractal surfaces. In conclusion the biological principle of the decrease in specific exchange intensity with increase in animal mass is discussed. PMID:16593327
Feast and Famine: regulation of black hole growth in low-redshift galaxies

NASA Astrophysics Data System (ADS)

Kauffmann, Guinevere; Heckman, Timothy M.

2009-07-01

We analyse the observed distribution of Eddington ratios (L/LEdd) as a function of supermassive black hole mass for a large sample of nearby galaxies drawn from the Sloan Digital Sky Survey. We demonstrate that there are two distinct regimes of black hole growth in nearby galaxies. The first is associated with galaxies with significant star formation [M*/starformationrate (SFR) ~ a Hubble time] in their central kiloparsec regions, and is characterized by a broad lognormal distribution of accretion rates peaked at a few per cent of the Eddington limit. In this regime, the Eddington ratio distribution is independent of the mass of the black hole and shows little dependence on the central stellar population of the galaxy. The second regime is associated with galaxies with old central stellar populations (M*/SFR >> a Hubble time), and is characterized by a power-law distribution function of Eddington ratios. In this regime, the time-averaged mass accretion rate on to black holes is proportional to the mass of stars in the galaxy bulge, with a constant of proportionality that depends on the mean stellar age of the stars. This result is once again independent of black hole mass. We show that both the slope of the power law and the decrease in the accretion rate on to black holes in old galaxies are consistent with population synthesis model predictions of the decline in stellar mass loss rates as a function of mean stellar age. Our results lead to a very simple picture of black hole growth in the local Universe. If the supply of cold gas in a galaxy bulge is plentiful, the black hole regulates its own growth at a rate that does not further depend on the properties of the interstellar medium. Once the gas runs out, black hole growth is regulated by the rate at which evolved stars lose their mass.
Emergent gravity from a mass deformation in warped spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gherghetta, Tony; Peloso, Marco; Poppitz, Erich

2005-11-15

We consider a deformation of five-dimensional warped gravity with bulk and boundary mass terms to quadratic order in the action. We show that massless zero modes occur for special choices of the masses. The tensor zero mode is a smooth deformation of the Randall-Sundrum graviton wave function and can be localized anywhere in the bulk. There is also a vector zero mode with similar localization properties, which is decoupled from conserved sources at tree level. Interestingly, there are no scalar modes, and the model is ghost-free at the linearized level. When the tensor zero mode is localized near the IRmore » brane, the dual interpretation is a composite graviton describing an emergent (induced) theory of gravity at the IR scale. In this case Newton's law of gravity changes to a new power law below the millimeter scale, with an exponent that can even be irrational.« less
Time-domain comparisons of power law attenuation in causal and noncausal time-fractional wave equations

PubMed Central

Zhao, Xiaofeng; McGough, Robert J.

2016-01-01

The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations. PMID:27250193
VLT-MAD Observations of Trumpler 14

NASA Astrophysics Data System (ADS)

Rochau, B.; Brandner, W.; Stolte, A.; Henning, T.; da Rio, N.; Gennaro, M.; Hormuth, F.; Marchetti, E.; Amico, P.

We present H and KS observations of the young massive cluster Trumpler 14 obtained with the MCAO system VLT-MAD which provides homogeneous Strehl ratios over a large field of view. We derived maximum Strehl ratios of 9.8% and 12.6% with mean Strehl ratios of 6.0% and 5.9% with in H and K_S, respectively, revealing significant improvement of the spatial PSF stability compared to SCAO systems. We detected 2-3 times more sources than comparable seeing-limited observations, and comparison of the colour-magnitude diagram with isochrones reveals a very young cluster that originated in a starburst-like event 1 ± 0.5 Myr ago. We also tentatively detect hints for an older population of 3 Myr. The mass function between 0.25 Msun and 3.2 Msun appears as a broken power law with a change of the power law slope at m_c ˜ 0.53+0.12-0.10 Msun. Shallow power law slopes are found to be Gamma_{PD,PMS1} = ˜ 0.48 ± 0.11 above m_c and Gamma_{PD,PMS2} = 0.68 ± 0.30 below m_c.
The NGC 7742 star cluster luminosity function: a population analysis revisited

NASA Astrophysics Data System (ADS)

de Grijs, Richard; Ma, Chao

2018-02-01

We re-examine the properties of the star cluster population in the circumnuclear starburst ring in the face-on spiral galaxy NGC 7742, whose young cluster mass function has been reported to exhibit significant deviations from the canonical power law. We base our reassessment on the clusters’ luminosities (an observational quantity) rather than their masses (a derived quantity), and confirm conclusively that the galaxy’s starburst-ring clusters—and particularly the youngest subsample, {log}(t {{{yr}}}-1)≤ 7.2—show evidence of a turnover in the cluster luminosity function well above the 90% completeness limit adopted to ensure the reliability of our results. This confirmation emphasizes the unique conundrum posed by this unusual cluster population.
Mixed-power scaling of whole-plant respiration from seedlings to giant trees

PubMed Central

Mori, Shigeta; Yamaji, Keiko; Ishida, Atsushi; Prokushkin, Stanislav G.; Masyagina, Oxana V.; Hagihara, Akio; Hoque, A.T.M. Rafiqul; Suwa, Rempei; Osawa, Akira; Nishizono, Tomohiro; Ueda, Tatsushiro; Kinjo, Masaru; Miyagi, Tsuyoshi; Kajimoto, Takuya; Koike, Takayoshi; Matsuura, Yojiro; Toma, Takeshi; Zyryanova, Olga A.; Abaimov, Anatoly P.; Awaya, Yoshio; Araki, Masatake G.; Kawasaki, Tatsuro; Chiba, Yukihiro; Umari, Marjnah

2010-01-01

The scaling of respiratory metabolism with body mass is one of the most pervasive phenomena in biology. Using a single allometric equation to characterize empirical scaling relationships and to evaluate alternative hypotheses about mechanisms has been controversial. We developed a method to directly measure respiration of 271 whole plants, spanning nine orders of magnitude in body mass, from small seedlings to large trees, and from tropical to boreal ecosystems. Our measurements include the roots, which have often been ignored. Rather than a single power-law relationship, our data are fit by a biphasic, mixed-power function. The allometric exponent varies continuously from 1 in the smallest plants to 3/4 in larger saplings and trees. Therefore, our findings support the recent findings of Reich et al. [Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size, and nitrogen in plants. Nature 439:457–461] and West, Brown, and Enquist [West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122 -126.]. The transition from linear to 3/4-power scaling may indicate fundamental physical and physiological constraints on the allocation of plant biomass between photosynthetic and nonphotosynthetic organs over the course of ontogenetic plant growth. PMID:20080600
Mixed-power scaling of whole-plant respiration from seedlings to giant trees.

PubMed

Mori, Shigeta; Yamaji, Keiko; Ishida, Atsushi; Prokushkin, Stanislav G; Masyagina, Oxana V; Hagihara, Akio; Hoque, A T M Rafiqul; Suwa, Rempei; Osawa, Akira; Nishizono, Tomohiro; Ueda, Tatsushiro; Kinjo, Masaru; Miyagi, Tsuyoshi; Kajimoto, Takuya; Koike, Takayoshi; Matsuura, Yojiro; Toma, Takeshi; Zyryanova, Olga A; Abaimov, Anatoly P; Awaya, Yoshio; Araki, Masatake G; Kawasaki, Tatsuro; Chiba, Yukihiro; Umari, Marjnah

2010-01-26

The scaling of respiratory metabolism with body mass is one of the most pervasive phenomena in biology. Using a single allometric equation to characterize empirical scaling relationships and to evaluate alternative hypotheses about mechanisms has been controversial. We developed a method to directly measure respiration of 271 whole plants, spanning nine orders of magnitude in body mass, from small seedlings to large trees, and from tropical to boreal ecosystems. Our measurements include the roots, which have often been ignored. Rather than a single power-law relationship, our data are fit by a biphasic, mixed-power function. The allometric exponent varies continuously from 1 in the smallest plants to 3/4 in larger saplings and trees. Therefore, our findings support the recent findings of Reich et al. [Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size, and nitrogen in plants. Nature 439:457-461] and West, Brown, and Enquist [West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122 -126.]. The transition from linear to 3/4-power scaling may indicate fundamental physical and physiological constraints on the allocation of plant biomass between photosynthetic and nonphotosynthetic organs over the course of ontogenetic plant growth.
In-plane vibration of FG micro/nano-mass sensor based on nonlocal theory under various thermal loading via differential transformation method

NASA Astrophysics Data System (ADS)

Rahmani, O.; Mohammadi Niaei, A.; Hosseini, S. A. H.; Shojaei, M.

2017-01-01

In the present study, free vibration model of a cantilever functionally graded (FG) nanobeam with an attached mass at tip and under various thermal loading and two types of material distribution is introduced. The vibration performance is considered using nonlocal Euler-Bernoulli beam theory. Two types of thermal loading, namely, uniform and nonlinear temperature rises through the thickness direction are considered. Thermo-mechanical properties of FG nano mass sensor are supposed to vary smoothly and continuously throughout the thickness based on power-law and Mori Tanaka distributions of material properties. Eringen non-local elasticity theory is exploited to describe the size dependency of FG nanobeam. The governing equations of the system with both axial and transverse displacements are derived based on Hamilton's principle and solved utilizing the differential transformation method (DTM) to find the non-dimensional natural frequencies. The results have good agreements with those discussing in the literature. After validation of the present model, the effect of various parameters such as mass and position of the attached nano particle, FG power-law exponent, thermal load type, material distribution type and nonlocal parameter on the frequency of nano sensor are studied. It is shown that the present model produces results of high accuracy, and it can be used as a benchmark in future studies of the free vibration of FG Nano-Mass Sensors.
Numerical modeling of landslides and generated seismic waves: The Bingham Canyon Mine landslides

NASA Astrophysics Data System (ADS)

Miallot, H.; Mangeney, A.; Capdeville, Y.; Hibert, C.

2016-12-01

Landslides are important natural hazards and key erosion processes. They create long period surface waves that can be recorded by regional and global seismic networks. The seismic signals are generated by acceleration/deceleration of the mass sliding over the topography. They consist in a unique and powerful tool to detect, characterize and quantify the landslide dynamics. We investigate here the processes at work during the two massive landslides that struck the Bingham Canyon Mine on the 10th April 2013. We carry a combined analysis of the generated seismic signals and the landslide processes computed with a 3D modeling on a complex topography. Forces computed by broadband seismic waveform inversion are used to constrain the study and particularly the force-source and the bulk dynamic. The source time function are obtained by a 3D model (Shaltop) where rheological parameters can be adjusted. We first investigate the influence of the initial shape of the sliding mass which strongly affects the whole landslide dynamic. We also see that the initial shape of the source mass of the first landslide constrains pretty well the second landslide source mass. We then investigate the effect of a rheological parameter, the frictional angle, that strongly influences the resulted computed seismic source function. We test here numerous friction laws as the frictional Coulomb law and a velocity-weakening friction law. Our results show that the force waveform fitting the observed data is highly variable depending on these different choices.

Updating the MACHO fraction of the Milky Way dark halo with improved mass models

NASA Astrophysics Data System (ADS)

Calcino, Josh; García-Bellido, Juan; Davis, Tamara M.

2018-05-01

Recent interest in primordial black holes as a possible dark matter candidate has motivated the reanalysis of previous methods for constraining massive astrophysical compact objects in the Milky Way halo and beyond. In order to derive these constraints, a model for the dark matter distribution around the Milky Way must be used. Previous microlensing searches have assumed a semi-isothermal density sphere for this task. We show this model is no longer consistent with data from the Milky Way rotation curve, and test two replacement models, namely NFW and power-law. The power-law model is the most flexible as it can break spherical symmetry, and best fits the data. Thus, we recommend the power-law model as a replacement, although it still lacks the flexibility to fully encapsulate all possible shapes of the Milky Way halo. We then use the power-law model to rederive some previous microlensing constraints in the literature, while propagating the primary halo-shape uncertainties through to our final constraints. Our analysis reveals that the microlensing constraints towards the Large Magellanic Cloud weaken somewhat for MACHO masses around 10 M⊙ when this uncertainty is taken into account, but the constraints tighten at lower masses. Exploring some of the simplifying assumptions of previous constraints we also study the effect of wide mass distributions of compact halo objects, as well as the effect of spatial clustering on microlensing constraints. We find that both effects induce a shift in the constraints towards smaller masses, and can effectively remove the microlensing constraints from M ˜ 1 - 10M⊙ for certain MACHO populations.
Thermodynamic and themoeconomic optimization of isothermal endoreversible chemical engine models

NASA Astrophysics Data System (ADS)

Ocampo-García, A.; Barranco-Jiménez, M. A.; Angulo-Brown, F.

2017-12-01

A branch of finite-time thermodynamics (FTT) is the thermoeconomical analysis of simplified power plant models. The most studied models are those of the Curzon-Ahlborn (CA) and Novikov-Chambadal types. In the decade of 90's of the past century, the FTT analysis of thermal engines was extended to chemical engines. In the present paper we made a thermoeconomical analysis of heat engines and chemical engines of the CA and Novikov types. This study is carried out for isothermal endoreversible chemical engine models with a linear mass transfer law and under three different modes of thermodynamic performance (maximum power, maximum ecological function and maximum efficient power).
Black hole mass function from gravitational wave measurements

NASA Astrophysics Data System (ADS)

Kovetz, Ely D.; Cholis, Ilias; Breysse, Patrick C.; Kamionkowski, Marc

2017-05-01

We examine how future gravitational-wave measurements from merging black holes (BHs) can be used to infer the shape of the black-hole mass function, with important implications for the study of star formation and evolution and the properties of binary BHs. We model the mass function as a power law, inherited from the stellar initial mass function, and introduce lower and upper mass cutoff parametrizations in order to probe the minimum and maximum BH masses allowed by stellar evolution, respectively. We initially focus on the heavier BH in each binary, to minimize model dependence. Taking into account the experimental noise, the mass measurement errors and the uncertainty in the redshift dependence of the merger rate, we show that the mass function parameters, as well as the total rate of merger events, can be measured to <10 % accuracy within a few years of advanced LIGO observations at its design sensitivity. This can be used to address important open questions such as the upper limit on the stellar mass which allows for BH formation and to confirm or refute the currently observed mass gap between neutron stars and BHs. In order to glean information on the progenitors of the merging BH binaries, we then advocate the study of the two-dimensional mass distribution to constrain parameters that describe the two-body system, such as the mass ratio between the two BHs, in addition to the merger rate and mass function parameters. We argue that several years of data collection can efficiently probe models of binary formation, and show, as an example, that the hypothesis that some gravitational-wave events may involve primordial black holes can be tested. Finally, we point out that in order to maximize the constraining power of the data, it may be worthwhile to lower the signal-to-noise threshold imposed on each candidate event and amass a larger statistical ensemble of BH mergers.
Universal scaling relations in scale-free structure formation

NASA Astrophysics Data System (ADS)

Guszejnov, Dávid; Hopkins, Philip F.; Grudić, Michael Y.

2018-07-01

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dM ∝ M-2 which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters, and even dark matter haloes. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M-2 and a column density distribution with a power-law tail of dA/dln Σ ∝ Σ-1. In the case where structure formation is controlled by gravity the two-point correlation becomes ξ2D ∝ R-1. Furthermore, structures formed by such processes (e.g. young star clusters, DM haloes) tend to a ρ ∝ R-3 density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation, and detailed `full physics' hydrodynamical simulations. We find that these power laws are good first-order descriptions in all cases.
Universal Scaling Relations in Scale-Free Structure Formation

NASA Astrophysics Data System (ADS)

Guszejnov, Dávid; Hopkins, Philip F.; Grudić, Michael Y.

2018-04-01

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dM∝M-2 which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M-2 and a column density distribution with a power law tail of dA/d lnΣ∝Σ-1. In the case where structure formation is controlled by gravity the two-point correlation becomes ξ2D∝R-1. Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a ρ∝R-3 density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases.
On the determination of age and mass functions of stars in young open star clusters from the analysis of their luminosity functions

NASA Astrophysics Data System (ADS)

Piskunov, A. E.; Belikov, A. N.; Kharchenko, N. V.; Sagar, R.; Subramaniam, A.

2004-04-01

We construct the observed luminosity functions of the remote young open clusters NGC 2383, 2384, 4103, 4755, 7510 and Hogg 15 from CCD observations of them. The observed LFs are corrected for field star contamination determined with the help of a Galactic star count model. In the case of Hogg 15 and NGC 2383 we also consider the additional contamination from neighbouring clusters NGC 4609 and 2384, respectively. These corrections provide a realistic pattern of cluster LF in the vicinity of the main-sequence (MS) turn-on point and at fainter magnitudes reveal the so-called H-feature arising as a result of the transition of the pre-MS phase to the MS, which is dependent on the cluster age. The theoretical LFs are constructed representing a cluster population model with continuous star formation for a short time-scale and a power-law initial mass function (IMF), and these are fitted to the observed LF. As a result, we are able to determine for each cluster a set of parameters describing the cluster population (the age, duration of star formation, IMF slope and percentage of field star contamination). It is found that in spite of the non-monotonic behaviour of observed LFs, cluster IMFs can be described as power-law functions with slopes similar to Salpeter's value. The present main-sequence turn-on cluster ages are several times lower than those derived from the fitting of theoretical isochrones to the turn-off region of the upper main sequences.
Galaxy structure from multiple tracers - III. Radial variations in M87's IMF

NASA Astrophysics Data System (ADS)

Oldham, Lindsay; Auger, Matthew

2018-03-01

We present the first constraints on stellar mass-to-light ratio gradients in an early-type galaxy (ETG) using multiple dynamical tracer populations to model the dark and luminous mass structure simultaneously. We combine the kinematics of the central starlight, two globular cluster populations and satellite galaxies in a Jeans analysis to obtain new constraints on M87's mass structure, employing a flexible mass model which allows for radial gradients in the stellar-mass-to-light ratio. We find that, in the context of our model, a radially declining stellar-mass-to-light ratio is strongly favoured. Modelling the stellar-mass-to-light ratio as following a power law, ϒ⋆ ˜ R-μ, we infer a power-law slope μ = -0.54 ± 0.05; equally, parametrizing the stellar-mass-to-light ratio via a central mismatch parameter relative to a Salpeter initial mass function (IMF), α, and scale radius RM, we find α > 1.48 at 95% confidence and RM = 0.35 ± 0.04 kpc. We use stellar population modelling of high-resolution 11-band HST photometry to show that such a steep gradient cannot be achieved by variations in only the metallicity, age, dust extinction and star formation history if the stellar IMF remains spatially constant. On the other hand, the stellar-mass-to-light ratio gradient that we find is consistent with an IMF whose inner slope changes such that it is Salpeter-like in the central ˜0.5 kpc and becomes Chabrier-like within the stellar effective radius. This adds to recent evidence that the non-universality of the IMF in ETGs may be confined to their core regions, and points towards a picture in which the stars in these central regions may have formed in fundamentally different physical conditions.
Peculiar velocity effect on galaxy correlation functions in nonlinear clustering regime

NASA Astrophysics Data System (ADS)

Matsubara, Takahiko

1994-03-01

We studied the distortion of the apparent distribution of galaxies in redshift space contaminated by the peculiar velocity effect. Specifically we obtained the expressions for N-point correlation functions in redshift space with given functional form for velocity distribution f(v) and evaluated two- and three-point correlation functions quantitatively. The effect of velocity correlations is also discussed. When the two-point correlation function in real space has a power-law form, Xir(r) is proportional to r(-gamma), the redshift-space counterpart on small scales also has a power-law form but with an increased power-law index: Xis(s) is proportional to s(1-gamma). When the three-point correlation function has the hierarchical form and the two-point correlation function has the power-law form in real space, the hierarchical form of the three-point correlation function is almost preserved in redshift space. The above analytic results are compared with the direct analysis based on N-body simulation data for cold dark matter models. Implications on the hierarchical clustering ansatz are discussed in detail.
Power-law tails and non-Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory

NASA Astrophysics Data System (ADS)

Chakraborty, Ahana; Sensarma, Rajdeep

2018-03-01

The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.
Understanding star formation in molecular clouds. I. Effects of line-of-sight contamination on the column density structure

NASA Astrophysics Data System (ADS)

Schneider, N.; Ossenkopf, V.; Csengeri, T.; Klessen, R. S.; Federrath, C.; Tremblin, P.; Girichidis, P.; Bontemps, S.; André, Ph.

2015-03-01

Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud- and star-formation (SF) studies. With the Herschel satellite it is now possible to precisely determine the column density from dust emission, which is the best tracer of the bulk of material in molecular clouds. However, line-of-sight (LOS) contamination from fore- or background clouds can lead to overestimating the dust emission of molecular clouds, in particular for distant clouds. This implies values that are too high for column density and mass, which can potentially lead to an incorrect physical interpretation of the column density probability distribution function (PDF). In this paper, we use observations and simulations to demonstrate how LOS contamination affects the PDF. We apply a first-order approximation (removing a constant level) to the molecular clouds of Auriga and Maddalena (low-mass star-forming), and Carina and NGC 3603 (both high-mass SF regions). In perfect agreement with the simulations, we find that the PDFs become broader, the peak shifts to lower column densities, and the power-law tail of the PDF for higher column densities flattens after correction. All corrected PDFs have a lognormal part for low column densities with a peak at Av ~ 2 mag, a deviation point (DP) from the lognormal at Av(DP) ~ 4-5 mag, and a power-law tail for higher column densities. Assuming an equivalent spherical density distribution ρ ∝ r- α, the slopes of the power-law tails correspond to αPDF = 1.8, 1.75, and 2.5 for Auriga, Carina, and NGC 3603. These numbers agree within the uncertainties with the values of α ≈ 1.5,1.8, and 2.5 determined from the slope γ (with α = 1-γ) obtained from the radial column density profiles (N ∝ rγ). While α ~ 1.5-2 is consistent with a structure dominated by collapse (local free-fall collapse of individual cores and clumps and global collapse), the higher value of α > 2 for NGC 3603 requires a physical process that leads to additional compression (e.g., expanding ionization fronts). From the small sample of our study, we find that clouds forming only low-mass stars and those also forming high-mass stars have slightly different values for their average column density (1.8 × 1021 cm-2 vs. 3.0 × 1021 cm-2), and they display differences in the overall column density structure. Massive clouds assemble more gas in smaller cloud volumes than low-mass SF ones. However, for both cloud types, the transition of the PDF from lognormal shape into power-law tail is found at the same column density (at Av ~ 4-5 mag). Low-mass and high-mass SF clouds then have the same low column density distribution, most likely dominated by supersonic turbulence. At higher column densities, collapse and external pressure can form the power-law tail. The relative importance of the twoprocesses can vary between clouds and thus lead to the observed differences in PDF and column density structure. Appendices are available in electronic form at http://www.aanda.orgHerschel maps as FITS files are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/575/A79
A Submillimeter Continuum Survey of Local Dust-obscured Galaxies

NASA Astrophysics Data System (ADS)

Lee, Jong Chul; Hwang, Ho Seong; Lee, Gwang-Ho

2016-12-01

We conduct a 350 μm dust continuum emission survey of 17 dust-obscured galaxies (DOGs) at z = 0.05-0.08 with the Caltech Submillimeter Observatory (CSO). We detect 14 DOGs with S 350 μm = 114-650 mJy and signal-to-noise > 3. By including two additional DOGs with submillimeter data in the literature, we are able to study dust content for a sample of 16 local DOGs, which consist of 12 bump and four power-law types. We determine their physical parameters with a two-component modified blackbody function model. The derived dust temperatures are in the range 57-122 K and 22-35 K for the warm and cold dust components, respectively. The total dust mass and the mass fraction of the warm dust component are 3-34 × 107 M ⊙ and 0.03%-2.52%, respectively. We compare these results with those of other submillimeter-detected infrared luminous galaxies. The bump DOGs, the majority of the DOG sample, show similar distributions of dust temperatures and total dust mass to the comparison sample. The power-law DOGs show a hint of smaller dust masses than other samples, but need to be tested with a larger sample. These findings support that the reason DOGs show heavy dust obscuration is not an overall amount of dust content, but probably the spatial distribution of dust therein.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Conroy, Charlie; Van Dokkum, Pieter G.; Villaume, Alexa

It is now well-established that the stellar initial mass function (IMF) can be determined from the absorption line spectra of old stellar systems, and this has been used to measure the IMF and its variation across the early-type galaxy population. Previous work focused on measuring the slope of the IMF over one or more stellar mass intervals, implicitly assuming that this is a good description of the IMF and that the IMF has a universal low-mass cutoff. In this work we consider more flexible IMFs, including two-component power laws with a variable low-mass cutoff and a general non-parametric model. Wemore » demonstrate with mock spectra that the detailed shape of the IMF can be accurately recovered as long as the data quality is high (S/N ≳ 300 Å{sup −1}) and cover a wide wavelength range (0.4–1.0 μ m). We apply these flexible IMF models to a high S/N spectrum of the center of the massive elliptical galaxy NGC 1407. Fitting the spectrum with non-parametric IMFs, we find that the IMF in the center shows a continuous rise extending toward the hydrogen-burning limit, with a behavior that is well-approximated by a power law with an index of −2.7. These results provide strong evidence for the existence of extreme (super-Salpeter) IMFs in the cores of massive galaxies.« less
Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential, Soma Membrane Current and Single-Neuron Contribution to the EEG

PubMed Central

Pettersen, Klas H.; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T.

2014-01-01

Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation. PMID:25393030
Power laws from linear neuronal cable theory: power spectral densities of the soma potential, soma membrane current and single-neuron contribution to the EEG.

PubMed

Pettersen, Klas H; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T

2014-11-01

Power laws, that is, power spectral densities (PSDs) exhibiting 1/f(α) behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency 1/f(α) power laws with power-law exponents analytically identified as α∞(I) = 1/2 for the soma membrane current, α∞(p) = 3/2 for the current-dipole moment, and α∞(V) = 2 for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink (1/f) noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how 1/f(α) power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.
X-ray and SZ constraints on the properties of hot CGM

NASA Astrophysics Data System (ADS)

Singh, Priyanka; Majumdar, Subhabrata; Nath, Biman B.; Silk, Joseph

2018-05-01

We use observations of stacked X-ray luminosity and Sunyaev-Zel'dovich (SZ) signal from a cosmological sample of ˜80, 000 and 104,000 massive galaxies, respectively, with 1012.6 ≲ M500 ≲ 1013M⊙ and mean redshift, z¯ ˜ 0.1 - 0.14 to constrain the hot Circumgalactic Medium (CGM) density and temperature. The X-ray luminosities constrain the density and hot CGM mass, while the SZ signal helps in breaking the density-temperature degeneracy. We consider a simple power-law density distribution (ne∝r-3β) as well as a hydrostatic hot halo model, with the gas assumed to be isothermal in both cases. The datasets are best described by the mean hot CGM profile ∝r-1.2, which is shallower than an NFW profile. For halo virial mass ˜1012 - 1013M⊙, the hot CGM contains ˜ 20 - 30% of galactic baryonic mass for the power-law model and 4 - 11% for the hydrostatic halo model, within the virial radii. For the power-law model, the hot CGM profile broadly agrees with observations of the Milky Way. The mean hot CGM mass is comparable to or larger than the mass contained in other phases of the CGM for L* galaxies.
Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

NASA Astrophysics Data System (ADS)

Schneider, Peter; Sluse, Dominique

2013-11-01

The light travel time differences in strong gravitational lensing systems allows an independent determination of the Hubble constant. This method has been successfully applied to several lens systems. The formally most precise measurements are, however, in tension with the recent determination of H0 from the Planck satellite for a spatially flat six-parameters ΛCDM cosmology. We reconsider the uncertainties of the method, concerning the mass profile of the lens galaxies, and show that the formal precision relies on the assumption that the mass profile is a perfect power law. Simple analytical arguments and numerical experiments reveal that mass-sheet like transformations yield significant freedom in choosing the mass profile, even when exquisite Einstein rings are observed. Furthermore, the characterization of the environment of the lens does not break that degeneracy which is not physically linked to extrinsic convergence. We present an illustrative example where the multiple imaging properties of a composite (baryons + dark matter) lens can be extremely well reproduced by a power-law model having the same velocity dispersion, but with predictions for the Hubble constant that deviate by ~20%. Hence we conclude that the impact of degeneracies between parametrized models have been underestimated in current H0 measurements from lensing, and need to be carefully reconsidered.
Mass-Mobility Characterization of Flame-made ZrO2 Aerosols: Primary Particle Diameter & Extent of Aggregation

PubMed Central

Eggersdorfer, M.L.; Gröhn, A.J.; Sorensen, C.M.; McMurry, P.H.; Pratsinis, S.E.

2013-01-01

Gas-borne nanoparticles undergoing coagulation and sintering form irregular or fractal-like structures affecting their transport, light scattering, effective surface area and density. Here, zirconia (ZrO2) nanoparticles are generated by scalable spray combustion, and their mobility diameter and mass are obtained nearly in-situ by differential mobility analyzer (DMA) and aerosol particle mass (APM) measurements. Using these data, the density of ZrO2 and a power law between mobility and primary particle diameters, the structure of fractal-like particles is determined (mass-mobility exponent, prefactor and average number and surface area mean diameter of primary particles, dva). The dva determined by DMA-APM measurements and this power law is in good agreement with the dva obtained by ex-situ nitrogen adsorption and microscopic analysis. Using this combination of measurements and above power law, the effect of flame spray process parameters (e.g. precursor solution and oxygen flow rate as well as zirconium concentration) on fractal-like particle structure characteristics is investigated in detail. This reveals that predominantly agglomerates (physically-bonded particles) and aggregates (chemically- or sinter-bonded particles) of nanoparticles are formed at low and high particle concentrations, respectively. PMID:22959835
Microlensing of an extended source by a power-law mass distribution

NASA Astrophysics Data System (ADS)

Congdon, Arthur B.; Keeton, Charles R.; Osmer, S. J.

2007-03-01

Microlensing promises to be a powerful tool for studying distant galaxies and quasars. As the data and models improve, there are systematic effects that need to be explored. Quasar continuum and broad-line regions may respond differently to microlensing due to their different sizes; to understand this effect, we study microlensing of finite sources by a mass function of stars. We find that microlensing is insensitive to the slope of the mass function but does depend on the mass range. For negative-parity images, diluting the stellar population with dark matter increases the magnification dispersion for small sources and decreases it for large sources. This implies that the quasar continuum and broad-line regions may experience very different microlensing in negative-parity lensed images. We confirm earlier conclusions that the surface brightness profile and geometry of the source have little effect on microlensing. Finally, we consider non-circular sources. We show that elliptical sources that are aligned with the direction of shear have larger magnification dispersions than sources with perpendicular alignment, an effect that becomes more prominent as the ellipticity increases. Elongated sources can lead to more rapid variability than circular sources, which raises the prospect of using microlensing to probe source shape.
Power law behavior of the isotope yield distributions in the multifragmentation regime of heavy ion reactions

NASA Astrophysics Data System (ADS)

Huang, M.; Wada, R.; Chen, Z.; Keutgen, T.; Kowalski, S.; Hagel, K.; Barbui, M.; Bonasera, A.; Bottosso, C.; Materna, T.; Natowitz, J. B.; Qin, L.; Rodrigues, M. R. D.; Sahu, P. K.; Schmidt, K. J.; Wang, J.

2010-11-01

Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, asym/T, extracted in previous work and that of the pairing term, ap/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I=N-Z value, the corrected yields of isotopes relative to the yield of C12 show a power law distribution Y(N,Z)/Y(12C)~A-τ in the mass range 1⩽A⩽30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted τ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be τprim=2.4±0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.
Near-infrared reddening of extra-galactic giant molecular clouds in a face-on geometry

NASA Astrophysics Data System (ADS)

Kainulainen, J.; Juvela, M.; Alves, J.

2008-04-01

Aims: We describe the near-infrared reddening signature of giant molecular clouds (GMCs) in external galaxies. In particular, we examine the EJ-H and EH-K color excesses and the effective extinction law observed in discrete GMC regions. We also study the effect of the relative scale height of the GMC distribution to the color excesses, and to the observed mass function of GMCs when the masses are derived using color excess as a linear estimator of mass. Methods: We performed Monte Carlo radiative transfer simulations with 3D models of stellar radiation and clumpy dust distributions, resembling a face-on geometry. The scattered light is included in the models, and near-infrared color maps were calculated from the simulated data. We performed the simulations with different scale heights of GMCs and compared the color excesses and attenuation of light in different geometries. We extracted GMCs from the simulated color maps and compared the mass functions to the input mass functions. Results: The effective near-infrared reddening law, i.e. the ratio EJ-H/EH-K, has a value close to unity in GMC regions. The ratio depends significantly on the relative scale height of GMCs, ξ, and for ξ values 0.1...0.75, we find the typical ratios of 0.6...1.1. The effective extinction law turns out to be very flat in GMC regions. We find the ratios of apparent extinctions of AH^a/AKa = 1.35...1.55 and AJ^a/AHa = 1.15. The effect of the scattered flux on the effective reddening law, as well as on the effective extinction law, is significant. Regarding the GMC mass function, we find no correlation between the input and observed slopes of the mass functions. Instead, the observed slope reflects the parameter ξ and the dynamical range of the mass function. As the observed slope depends on the geometric parameters, which are not known, it is not possible to constrain the slope of the mass function using this technique. We estimate that only a fraction of 10...20% of the total mass of GMCs is recovered, if the observed color excess values are transformed to masses using the Galactic reddening law. In the case of individual clouds, the fraction can vary between ~0...50%.

Power-law modeling based on least-squares minimization criteria.

PubMed

Hernández-Bermejo, B; Fairén, V; Sorribas, A

1999-10-01

The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system.
Physics of chewing in terrestrial mammals.

PubMed

Virot, Emmanuel; Ma, Grace; Clanet, Christophe; Jung, Sunghwan

2017-03-07

Previous studies on chewing frequency across animal species have focused on finding a single universal scaling law. Controversy between the different models has been aroused without elucidating the variations in chewing frequency. In the present study we show that vigorous chewing is limited by the maximum force of muscle, so that the upper chewing frequency scales as the -1/3 power of body mass for large animals and as a constant frequency for small animals. On the other hand, gentle chewing to mix food uniformly without excess of saliva describes the lower limit of chewing frequency, scaling approximately as the -1/6 power of body mass. These physical constraints frame the -1/4 power law classically inferred from allometry of animal metabolic rates. All of our experimental data stay within these physical boundaries over six orders of magnitude of body mass regardless of food types.
Physics of chewing in terrestrial mammals

NASA Astrophysics Data System (ADS)

Virot, Emmanuel; Ma, Grace; Clanet, Christophe; Jung, Sunghwan

2017-03-01

Previous studies on chewing frequency across animal species have focused on finding a single universal scaling law. Controversy between the different models has been aroused without elucidating the variations in chewing frequency. In the present study we show that vigorous chewing is limited by the maximum force of muscle, so that the upper chewing frequency scales as the -1/3 power of body mass for large animals and as a constant frequency for small animals. On the other hand, gentle chewing to mix food uniformly without excess of saliva describes the lower limit of chewing frequency, scaling approximately as the -1/6 power of body mass. These physical constraints frame the -1/4 power law classically inferred from allometry of animal metabolic rates. All of our experimental data stay within these physical boundaries over six orders of magnitude of body mass regardless of food types.
A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.
STAR FORMATION IN TURBULENT MOLECULAR CLOUDS WITH COLLIDING FLOW

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsumoto, Tomoaki; Dobashi, Kazuhito; Shimoikura, Tomomi, E-mail: matsu@hosei.ac.jp

2015-03-10

Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin filamentary clouds with a sub-parsec width. The colliding flow accumulates the filamentary clouds into a sheet cloud and promotes active star formation for initially high-density clouds. Clouds with a colliding flow exhibit a finer filamentary network than clouds without a colliding flow. The probability distribution functions (PDFs) for the density and column density can be fitted by lognormal functions for clouds without colliding flow. When the initial turbulence ismore » weak, the column density PDF has a power-law wing at high column densities. The colliding flow considerably deforms the PDF, such that the PDF exhibits a double peak. The stellar mass distributions reproduced here are consistent with the classical initial mass function with a power-law index of –1.35 when the initial clouds have a high density. The distribution of stellar velocities agrees with the gas velocity distribution, which can be fitted by Gaussian functions for clouds without colliding flow. For clouds with colliding flow, the velocity dispersion of gas tends to be larger than the stellar velocity dispersion. The signatures of colliding flows and turbulence appear in channel maps reconstructed from the simulation data. Clouds without colliding flow exhibit a cloud-scale velocity shear due to the turbulence. In contrast, clouds with colliding flow show a prominent anti-correlated distribution of thin filaments between the different velocity channels, suggesting collisions between the filamentary clouds.« less
A power-law coupled three-form dark energy model

NASA Astrophysics Data System (ADS)

Yao, Yan-Hong; Yan, Yang-Jie; Meng, Xin-He

2018-02-01

We consider a field theory model of coupled dark energy which treats dark energy as a three-form field and dark matter as a spinor field. By assuming the effective mass of dark matter as a power-law function of the three-form field and neglecting the potential term of dark energy, we obtain three solutions of the autonomous system of evolution equations, including a de Sitter attractor, a tracking solution and an approximate solution. To understand the strength of the coupling, we confront the model with the latest Type Ia Supernova, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation observations, with the conclusion that the combination of these three databases marginalized over the present dark matter density parameter Ω _{m0} and the present three-form field κ X0 gives stringent constraints on the coupling constant, - 0.017< λ <0.047 (2σ confidence level), by which we present the model's applicable parameter range.
Power law scaling in synchronization of brain signals depends on cognitive load.

PubMed

Tinker, Jesse; Velazquez, Jose Luis Perez

2014-01-01

As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors.
Collisional evolution - an analytical study for the nonsteady-state mass distribution

NASA Astrophysics Data System (ADS)

Martins, R. Vieira

1999-05-01

To study the collisional evolution of asteroidal groups we can use an analytical solutionfor the self-similar collision cascades. This solution is suitable to study the steady-state massdistribution of the collisional fragmentation. However, out of the steady-state conditions, thissolution is not satisfactory for some values of the collisional parameters. In fact, for some valuesfor the exponent of the mass distribution power law of an asteroidal group and its relation to theexponent of the function which describes how rocks break we arrive at singular points for theequation which describes the collisional evolution. These singularities appear since someapproximations are usually made in the laborious evaluation of many integrals that appear in theanalytical calculations. They concern the cutoff for the smallest and the largest bodies. Thesesingularities set some restrictions to the study of the analytical solution for the collisionalequation. To overcome these singularities we performed an algebraic computationconsidering the smallest and the largest bodies and we obtained the analytical expressions for theintegrals that describe the collisional evolution without restriction on the parameters. However,the new distribution is more sensitive to the values of the collisional parameters. In particular thesteady-state solution for the differential mass distribution has exponents slightly different from11⧸6 for the usual parameters in the Asteroid Belt. The sensitivity of this distribution with respectto the parameters is analyzed for the usual values in the asteroidal groups. With anexpression for the mass distribution without singularities, we can evaluate also its time evolution.We arrive at an analytical expression given by a power series of terms constituted by a smallparameter multiplied by the mass to an exponent, which depends on the initial power lawdistribution. This expression is a formal solution for the equation which describes the collisionalevolution. Furthermore, the first-order term for this solution is the time rate of the distribution atthe initial time. In particular the solution shows the fundamental importance played by theexponent of the power law initial condition in the evolution of the system.
THE STELLAR INITIAL MASS FUNCTION OF ULTRA-FAINT DWARF GALAXIES: EVIDENCE FOR IMF VARIATIONS WITH GALACTIC ENVIRONMENT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geha, Marla; Brown, Thomas M.; Tumlinson, Jason

2013-07-01

We present constraints on the stellar initial mass function (IMF) in two ultra-faint dwarf (UFD) galaxies, Hercules and Leo IV, based on deep Hubble Space Telescope Advanced Camera for Surveys imaging. The Hercules and Leo IV galaxies are extremely low luminosity (M{sub V} = -6.2, -5.5), metal-poor (([Fe/H]) = -2.4, -2.5) systems that have old stellar populations (>11 Gyr). Because they have long relaxation times, we can directly measure the low-mass stellar IMF by counting stars below the main-sequence turnoff without correcting for dynamical evolution. Over the stellar mass range probed by our data, 0.52-0.77 M{sub Sun }, the IMFmore » is best fit by a power-law slope of {alpha}= 1.2{sub -0.5}{sup +0.4} for Hercules and {alpha} = 1.3 {+-} 0.8 for Leo IV. For Hercules, the IMF slope is more shallow than a Salpeter ({alpha} = 2.35) IMF at the 5.8{sigma} level, and a Kroupa ({alpha} = 2.3 above 0.5 M{sub Sun }) IMF slope at 5.4{sigma} level. We simultaneously fit for the binary fraction, f{sub binary}, finding f{sub binary}= 0.47{sup +0.16}{sub -0.14} for Hercules, and 0.47{sup +0.37}{sub -0.17} for Leo IV. The UFD binary fractions are consistent with that inferred for Milky Way stars in the same mass range, despite very different metallicities. In contrast, the IMF slopes in the UFDs are shallower than other galactic environments. In the mass range 0.5-0.8 M{sub Sun }, we see a trend across the handful of galaxies with directly measured IMFs such that the power-law slopes become shallower (more bottom-light) with decreasing galactic velocity dispersion and metallicity. This trend is qualitatively consistent with results in elliptical galaxies inferred via indirect methods and is direct evidence for IMF variations with galactic environment.« less
Mean Occupation Function of High-redshift Quasars from the Planck Cluster Catalog

NASA Astrophysics Data System (ADS)

Chakraborty, Priyanka; Chatterjee, Suchetana; Dutta, Alankar; Myers, Adam D.

2018-06-01

We characterize the distribution of quasars within dark matter halos using a direct measurement technique for the first time at redshifts as high as z ∼ 1. Using the Planck Sunyaev-Zeldovich (SZ) catalog for galaxy groups and the Sloan Digital Sky Survey (SDSS) DR12 quasar data set, we assign host clusters/groups to the quasars and make a measurement of the mean number of quasars within dark matter halos as a function of halo mass. We find that a simple power-law fit of {log}< N> =(2.11+/- 0.01) {log}(M)-(32.77+/- 0.11) can be used to model the quasar fraction in dark matter halos. This suggests that the quasar fraction increases monotonically as a function of halo mass even to redshifts as high as z ∼ 1.
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.

PubMed

Teka, Wondimu; Stockton, David; Santamaria, Fidel

2016-03-01

We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.
Galaxy and Mass Assembly (GAMA): the star formation rate dependence of the stellar initial mass function

NASA Astrophysics Data System (ADS)

Gunawardhana, M. L. P.; Hopkins, A. M.; Sharp, R. G.; Brough, S.; Taylor, E.; Bland-Hawthorn, J.; Maraston, C.; Tuffs, R. J.; Popescu, C. C.; Wijesinghe, D.; Jones, D. H.; Croom, S.; Sadler, E.; Wilkins, S.; Driver, S. P.; Liske, J.; Norberg, P.; Baldry, I. K.; Bamford, S. P.; Loveday, J.; Peacock, J. A.; Robotham, A. S. G.; Zucker, D. B.; Parker, Q. A.; Conselice, C. J.; Cameron, E.; Frenk, C. S.; Hill, D. T.; Kelvin, L. S.; Kuijken, K.; Madore, B. F.; Nichol, B.; Parkinson, H. R.; Pimbblet, K. A.; Prescott, M.; Sutherland, W. J.; Thomas, D.; van Kampen, E.

2011-08-01

The stellar initial mass function (IMF) describes the distribution in stellar masses produced from a burst of star formation. For more than 50 yr, the implicit assumption underpinning most areas of research involving the IMF has been that it is universal, regardless of time and environment. We measure the high-mass IMF slope for a sample of low-to-moderate redshift galaxies from the Galaxy and Mass Assembly survey. The large range in luminosities and galaxy masses of the sample permits the exploration of underlying IMF dependencies. A strong IMF-star formation rate dependency is discovered, which shows that highly star-forming galaxies form proportionally more massive stars (they have IMFs with flatter power-law slopes) than galaxies with low star formation rates. This has a significant impact on a wide variety of galaxy evolution studies, all of which rely on assumptions about the slope of the IMF. Our result is supported by, and provides an explanation for, the results of numerous recent explorations suggesting a variation of or evolution in the IMF.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

NASA Technical Reports Server (NTRS)

Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

2015-01-01

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices

NASA Astrophysics Data System (ADS)

Lillo, F.

2007-02-01

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons.
Determination of the spectral dependence of reduced scattering and quantitative second-harmonic generation imaging for detection of fibrillary changes in ovarian cancer

NASA Astrophysics Data System (ADS)

Campbell, Kirby R.; Tilbury, Karissa B.; Campagnola, Paul J.

2015-03-01

Here, we examine ovarian cancer extracellular matrix (ECM) modification by measuring the wavelength dependence of optical scattering measurements and quantitative second-harmonic generation (SHG) imaging metrics in the range of 800-1100 nm in order to determine fibrillary changes in ex vivo normal ovary, type I, and type II ovarian cancer. Mass fractals of the collagen fiber structure is analyzed based on a power law correlation function using spectral dependence measurements of the reduced scattering coefficient μs' where the mass fractal dimension is related to the power. Values of μs' are measured using independent methods of determining the values of μs and g by on-axis attenuation measurements using the Beer-Lambert Law and by fitting the angular distribution of scattering to the Henyey-Greenstein phase function, respectively. Quantitativespectral SHG imaging on the same tissues determines FSHG/BSHG creation ratios related to size and harmonophore distributions. Both techniques probe fibril packing order, but the optical scattering probes structures of sizes from about 50-2000 nm where SHG imaging - although only able to resolve individual fibers - builds contrast from the assembly of fibrils. Our findings suggest that type I ovarian tumor structure has the most ordered collagen fibers followed by normal ovary then type II tumors showing the least order.
Rotation-limited growth of three-dimensional body-centered-cubic crystals

NASA Astrophysics Data System (ADS)

Tarp, Jens M.; Mathiesen, Joachim

2015-07-01

According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered-cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe, as a function of the quenching depth, a crossover between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescence through rotation and alignment of the lattices of neighboring grains. We show that the grain rotation per volume change of a grain follows a power law with an exponent of -1.25 . The scaling exponent is consistent with theoretical considerations based on the conservation of dislocations.
First results from the IllustrisTNG simulations: the stellar mass content of groups and clusters of galaxies

NASA Astrophysics Data System (ADS)

Pillepich, Annalisa; Nelson, Dylan; Hernquist, Lars; Springel, Volker; Pakmor, Rüdiger; Torrey, Paul; Weinberger, Rainer; Genel, Shy; Naiman, Jill P.; Marinacci, Federico; Vogelsberger, Mark

2018-03-01

The IllustrisTNG project is a new suite of cosmological magnetohydrodynamical simulations of galaxy formation performed with the AREPO code and updated models for feedback physics. Here, we introduce the first two simulations of the series, TNG100 and TNG300, and quantify the stellar mass content of about 4000 massive galaxy groups and clusters (1013 ≤ M200c/M⊙ ≤ 1015) at recent times (z ≤ 1). The richest clusters have half of their total stellar mass bound to satellite galaxies, with the other half being associated with the central galaxy and the diffuse intracluster light. Haloes more massive than about 5 × 1014 M⊙ have more diffuse stellar mass outside 100 kpc than within 100 kpc, with power-law slopes of the radial mass density distribution as shallow as the dark matter's ( - 3.5 ≲ α3D ≲ -3). Total halo mass is a very good predictor of stellar mass, and vice versa: at z = 0, the 3D stellar mass measured within 30 kpc scales as ∝(M500c)0.49 with a ˜0.12 dex scatter. This is possibly too steep in comparison to the available observational constraints, even though the abundance of The Next Generation less-massive galaxies ( ≲ 1011 M⊙ in stars) is in good agreement with the measured galaxy stellar mass functions at recent epochs. The 3D sizes of massive galaxies fall too on a tight (˜0.16 dex scatter) power-law relation with halo mass, with r^stars_0.5 ∝ (M_200c)^{0.53}. Even more fundamentally, halo mass alone is a good predictor for the whole stellar mass profiles beyond the inner few kiloparsecs, and we show how on average these can be precisely recovered given a single-mass measurement of the galaxy or its halo.
Characterization of fish sauce aroma-impact compounds using GC-MS, SPME-Osme-GCO, and Stevens' power law exponents.

PubMed

Pham, A J; Schilling, M W; Yoon, Y; Kamadia, V V; Marshall, D L

2008-05-01

The objectives of this study were to characterize volatile compounds and to determine the characteristic aromas associated with impact compounds in 4 fish sauces using solid-phase micro-extraction, gas chromatography-mass spectrometry, Osme, and gas chromatography olfactometry (SPME-Osme-GCO) coupled with Stevens' Power Law. Compounds were separated using GCMS and GCO and were identified with the mass spectral database, aroma perceived at the sniffing port, retention indices, and verification of compounds by authentic standards in the GCMS and GCO. Aromas that were isolated and present in all 4 fish sauce samples at all concentrations included fishy (trimethylamine), pungent and dirty socks (combination of butanoic, pentanoic, hexanoic, and heptanoic acids), cooked rice and buttery popcorn (2,6-dimethyl pyrazine), and sweet and cotton candy (benzaldehyde). All fish sauces contained the same aromas as determined by GCO and GCMS (verified using authentic standard compounds), but the odor intensity associated with each compound or group of compounds was variable for different fish sauce samples. Stevens' Power Law exponents were also determined using this analytical technique, but exponents were not consistent for the same compounds that were found in all fish sauces. Stevens' Power Law exponents ranged from 0.14 to 0.37, 0.24 to 0.34, 0.09 to 0.21, and 0.10 to 0.35 for dirty socks, fishy, buttery popcorn, and sweet aromas, respectively. This demonstrates that there is variability in Stevens' Power Law exponents for odorants within fish sauce samples.
ON THE IMF IN A TRIGGERED STAR FORMATION CONTEXT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Tingtao; Huang, Chelsea X.; Lin, D. N. C.

2015-07-20

The origin of the stellar initial mass function (IMF) is a fundamental issue in the theory of star formation. It is generally fit with a composite power law. Some clues on the progenitors can be found in dense starless cores that have a core mass function (CMF) with a similar shape. In the low-mass end, these mass functions increase with mass, albeit the sample may be somewhat incomplete; in the high-mass end, the mass functions decrease with mass. There is an offset in the turn-over mass between the two mass distributions. The stellar mass for the IMF peak is lowermore » than the corresponding core mass for the CMF peak in the Pipe Nebula by about a factor of three. Smaller offsets are found between the IMF and the CMFs in other nebulae. We suggest that the offset is likely induced during a starburst episode of global star formation which is triggered by the formation of a few O/B stars in the multi-phase media, which naturally emerged through the onset of thermal instability in the cloud-core formation process. We consider the scenario that the ignition of a few massive stars photoionizes the warm medium between the cores, increases the external pressure, reduces their Bonnor–Ebert mass, and triggers the collapse of some previously stable cores. We quantitatively reproduce the IMF in the low-mass end with the assumption of additional rotational fragmentation.« less
Turbulent Equilibria for Charged Particles in Space

NASA Astrophysics Data System (ADS)

Yoon, Peter

2017-04-01

The solar wind electron distribution function is apparently composed of several components including non-thermal tail population. The electron distribution that contains energetic tail feature is well fitted with the kappa distribution function. The solar wind protons also possess quasi power-law tail distribution function that is well fitted with an inverse power law model. The present paper discusses the latest theoretical development regarding the dynamical steady-state solution of electrons and Langmuir turbulence that are in turbulent equilibrium. According to such a theory, the Maxwellian and kappa distribution functions for the electrons emerge as the only two possible solution that satisfy the steady-state weak turbulence plasma kinetic equation. For the proton inverse power-law tail problem, a similar turbulent equilibrium solution can be conceived of, but instead of high-frequency Langmuir fluctuation, the theory involves low-frequency kinetic Alfvenic turbulence. The steady-state solution of the self-consistent proton kinetic equation and wave kinetic equation for Alfvenic waves can be found in order to obtain a self-consistent solution for the inverse power law tail distribution function.

The Surface Density Distribution in the Solar Nebula

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2004-01-01

The commonly used minimum mass power law representation of the pre-solar nebula is reanalyzed using a new cumulative-mass-model. This model predicts a smoother surface density approximation compared with methods based on direct computation of surface density. The density is quantified using two independent analytical formulations. First, a best-fit transcendental function is applied directly to the basic planetary data. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the solar nebula data. The latter model is shown to be a good approximation to the finite-size early Solar Nebula, and by extension to other extra solar protoplanetary disks.
The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function. [galaxy distribution

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1979-01-01

The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.
The young star cluster population of M51 with LEGUS - I. A comprehensive study of cluster formation and evolution

NASA Astrophysics Data System (ADS)

Messa, M.; Adamo, A.; Östlin, G.; Calzetti, D.; Grasha, K.; Grebel, E. K.; Shabani, F.; Chandar, R.; Dale, D. A.; Dobbs, C. L.; Elmegreen, B. G.; Fumagalli, M.; Gouliermis, D. A.; Kim, H.; Smith, L. J.; Thilker, D. A.; Tosi, M.; Ubeda, L.; Walterbos, R.; Whitmore, B. C.; Fedorenko, K.; Mahadevan, S.; Andrews, J. E.; Bright, S. N.; Cook, D. O.; Kahre, L.; Nair, P.; Pellerin, A.; Ryon, J. E.; Ahmad, S. D.; Beale, L. P.; Brown, K.; Clarkson, D. A.; Guidarelli, G. C.; Parziale, R.; Turner, J.; Weber, M.

2018-01-01

Recently acquired WFC3 UV (F275W and F336W) imaging mosaics under the Legacy Extragalactic UV Survey (LEGUS), combined with archival ACS data of M51, are used to study the young star cluster (YSC) population of this interacting system. Our newly extracted source catalogue contains 2834 cluster candidates, morphologically classified to be compact and uniform in colour, for which ages, masses and extinction are derived. In this first work we study the main properties of the YSC population of the whole galaxy, considering a mass-limited sample. Both luminosity and mass functions follow a power-law shape with slope -2, but at high luminosities and masses a dearth of sources is observed. The analysis of the mass function suggests that it is best fitted by a Schechter function with slope -2 and a truncation mass at 1.00 ± 0.12 × 105 M⊙. Through Monte Carlo simulations, we confirm this result and link the shape of the luminosity function to the presence of a truncation in the mass function. A mass limited age function analysis, between 10 and 200 Myr, suggests that the cluster population is undergoing only moderate disruption. We observe little variation in the shape of the mass function at masses above 1 × 104 M⊙ over this age range. The fraction of star formation happening in the form of bound clusters in M51 is ∼ 20 per cent in the age range 10-100 Myr and little variation is observed over the whole range from 1 to 200 Myr.
Temporal dependence of transient dark counts in an avalanche photodiode: A solution for power-law behavior of afterpulsing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akiba, M., E-mail: akiba@nict.go.jp; Tsujino, K.

This paper offers a theoretical explanation of the temperature and temporal dependencies of transient dark count rates (DCRs) measured for a linear-mode silicon avalanche photodiode (APD) and the dependencies of afterpulsing that were measured in Geiger-mode Si and InGaAs/InP APDs. The temporal dependencies exhibit power-law behavior, at least to some extent. For the transient DCR, the value of the DCR for a given time period increases with decreases in temperature, while the power-law behavior remains unchanged. The transient DCR is attributed to electron emissions from traps in the multiplication layer of the APD with a high electric field, and itsmore » temporal dependence is explained by a continuous change in the electron emission rate as a function of the electric field strength. The electron emission rate is calculated using a quantum model for phonon-assisted tunnel emission. We applied the theory to the temporal dependence of afterpulsing that was measured for Si and InGaAs/InP APDs. The power-law temporal dependence is attributed to the power-law function of the electron emission rate from the traps as a function of their position across the p–n junction of the APD. Deviations from the power-law temporal dependence can be derived from the upper and lower limits of the electric field strength.« less
Variability Selected Low-Luminosity Active Galactic Nuclei in the 4 Ms Chandra Deep Field-South

NASA Technical Reports Server (NTRS)

Young, M.; Brandt, W. N.; Xue, Y. Q.; Paolillo, D. M.; Alexander, F. E.; Bauer, F. E.; Lehmer, B. D.; Luo, B.; Shemmer, O.; Schneider, D. P.;

2012-01-01

The 4 Ms Chandra Deep Field-South (CDF-S) and other deep X-ray surveys have been highly effective at selecting active galactic nuclei (AGN). However, cosmologically distant low-luminosity AGN (LLAGN) have remained a challenge to identify due to significant contribution from the host galaxy. We identify long-term X ray variability (approx. month years, observed frame) in 20 of 92 CDF-S galaxies spanning redshifts approx equals 00.8 - 1.02 that do not meet other AGN selection criteria. We show that the observed variability cannot be explained by X-ray binary populations or ultraluminous X-ray sources, so the variability is most likely caused by accretion onto a supermassive black hole. The variable galaxies are not heavily obscured in general, with a stacked effective power-law photon index of Gamma(sub Stack) approx equals 1.93 +/- 0.13, and arc therefore likely LLAGN. The LLAGN tend to lie it factor of approx equal 6-89 below the extrapolated linear variability-luminosity relation measured for luminous AGN. This may he explained by their lower accretion rates. Variability-independent black-hole mass and accretion-rate estimates for variable galaxies show that they sample a significantly different black hole mass-accretion-rate space, with masses a factor of 2.4 lower and accretion rates a factor of 22.5 lower than variable luminous AGNs at the same redshift. We find that an empirical model based on a universal broken power-law power spectral density function, where the break frequency depends on SMBH mass and accretion rate, roughly reproduces the shape, but not the normalization, of the variability-luminosity trends measured for variable galaxies and more luminous AGNs.

A SUBMILLIMETER CONTINUUM SURVEY OF LOCAL DUST-OBSCURED GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Jong Chul; Hwang, Ho Seong; Lee, Gwang-Ho, E-mail: jclee@kasi.re.kr

We conduct a 350 μ m dust continuum emission survey of 17 dust-obscured galaxies (DOGs) at z = 0.05–0.08 with the Caltech Submillimeter Observatory (CSO). We detect 14 DOGs with S{sub 350μm} = 114–650 mJy and signal-to-noise > 3. By including two additional DOGs with submillimeter data in the literature, we are able to study dust content for a sample of 16 local DOGs, which consist of 12 bump and four power-law types. We determine their physical parameters with a two-component modified blackbody function model. The derived dust temperatures are in the range 57–122 K and 22–35 K for themore » warm and cold dust components, respectively. The total dust mass and the mass fraction of the warm dust component are 3–34 × 10{sup 7} M {sub ⊙} and 0.03%–2.52%, respectively. We compare these results with those of other submillimeter-detected infrared luminous galaxies. The bump DOGs, the majority of the DOG sample, show similar distributions of dust temperatures and total dust mass to the comparison sample. The power-law DOGs show a hint of smaller dust masses than other samples, but need to be tested with a larger sample. These findings support that the reason DOGs show heavy dust obscuration is not an overall amount of dust content, but probably the spatial distribution of dust therein.« less
Collisional evolution - an analytical study for the non steady-state mass distribution.

NASA Astrophysics Data System (ADS)

Vieira Martins, R.

1999-05-01

To study the collisional evolution of asteroidal groups one can use an analytical solution for the self-similar collision cascades. This solution is suitable to study the steady-state mass distribution of the collisional fragmentation. However, out of the steady-state conditions, this solution is not satisfactory for some values of the collisional parameters. In fact, for some values for the exponent of the mass distribution power law of an asteroidal group and its relation to the exponent of the function which describes "how rocks break" the author arrives at singular points for the equation which describes the collisional evolution. These singularities appear since some approximations are usually made in the laborious evaluation of many integrals that appear in the analytical calculations. They concern the cutoff for the smallest and the largest bodies. These singularities set some restrictions to the study of the analytical solution for the collisional equation. To overcome these singularities the author performed an algebraic computation considering the smallest and the largest bodies and he obtained the analytical expressions for the integrals that describe the collisional evolution without restriction on the parameters. However, the new distribution is more sensitive to the values of the collisional parameters. In particular the steady-state solution for the differential mass distribution has exponents slightly different from 11/6 for the usual parameters in the asteroid belt. The sensitivity of this distribution with respect to the parameters is analyzed for the usual values in the asteroidal groups. With an expression for the mass distribution without singularities, one can evaluate also its time evolution. The author arrives at an analytical expression given by a power series of terms constituted by a small parameter multiplied by the mass to an exponent, which depends on the initial power law distribution. This expression is a formal solution for the equation which describes the collisional evolution.
A generalization of the power law distribution with nonlinear exponent

NASA Astrophysics Data System (ADS)

Prieto, Faustino; Sarabia, José María

2017-01-01

The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

NASA Astrophysics Data System (ADS)

Fang, Tiegang

2014-05-01

In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.
The scaling relationship between baryonic mass and stellar disc size in morphologically late-type galaxies

NASA Astrophysics Data System (ADS)

Wu, Po-Feng

2018-02-01

Here I report the scaling relationship between the baryonic mass and scale-length of stellar discs for ∼1000 morphologically late-type galaxies. The baryonic mass-size relationship is a single power law R_\\ast ∝ M_b^{0.38} across ∼3 orders of magnitude in baryonic mass. The scatter in size at fixed baryonic mass is nearly constant and there are no outliers. The baryonic mass-size relationship provides a more fundamental description of the structure of the disc than the stellar mass-size relationship. The slope and the scatter of the stellar mass-size relationship can be understood in the context of the baryonic mass-size relationship. For gas-rich galaxies, the stars are no longer a good tracer for the baryons. High-baryonic-mass, gas-rich galaxies appear to be much larger at fixed stellar mass because most of the baryonic content is gas. The stellar mass-size relationship thus deviates from the power-law baryonic relationship, and the scatter increases at the low-stellar-mass end. These extremely gas-rich low-mass galaxies can be classified as ultra-diffuse galaxies based on the structure.
Evidence for an Intermediate Mass Black Hole in NGC 5408 X-1

NASA Technical Reports Server (NTRS)

Strohmayer, Tod E.; Mushotzky, Richard F.

2009-01-01

We report the discovery with XMM-Newton of correlated spectral and timing behavior in the ultraluminous X-ray source (ULX) NGC 5408 X-1. An approx. 100 ksec pointing with XMM/Newton obtained in January, 2008 reveals a strong 10 mHz QPO in the > 1 keV flux, as well as flat-topped, band limited noise breaking to a power law. The energy spectrum is again dominated by two components, a 0.16 keV thermal disk and a power-law with an index of approx. 2.5. These new measurements, combined with results from our previous January 2006 pointing in which we first detected QPOs, show for the first time in a ULX a pattern of spectral and temporal correlations strongly analogous to that seen in Galactic black hole sources, but at much higher X-ray luminosity and longer characteristic time-scales. We find that the QPO frequency is proportional to the inferred disk flux, while the QPO and broad-band noise amplitude (root mean squared, rms) are inversely proportional to the disk flux. Assuming that QPO frequency scales inversely with black hole mass at a given power-law spectral index we derive mass estimates using the observed QPO frequency - spectral index relations from five stellar-mass black hole systems with dynamical mass constraints. The results from all sources are consistent with a mass range for NGC 5408 X-1 from 1000 - 9000 Stellar mass. We argue that these are conservative limits, and a more likely range is from 2000 - 5000 Stellar mass. Moreover, the recent relation from Gierlinski et al. that relates black hole mass to the strength of variability at high frequencies (above the break in the power spectrum), and the variability plane results of McHardy et al. and Koerding et al., are also suggestive of such a. high mass for NGC 5408 X-1. Importantly, none of the above estimates appears consistent with a black hole mass less than approx. 1000 Stellar mass for NGC 5408 X-1. We argue that these new findings strongly support the conclusion that NGC 5408 X-1 harbors an intermediate mass black hole.
Spectral Modeling of the EGRET 3EG Gamma Ray Sources Near the Galactic Plane

NASA Technical Reports Server (NTRS)

Bertsch, D. L.; Hartman, R. C.; Hunter, S. D.; Thompson, D. J.; Lin, Y. C.; Kniffen, D. A.; Kanbach, G.; Mayer-Hasselwander, H. A.; Reimer, O.; Sreekumar, P.

1999-01-01

The third EGRET catalog lists 84 sources within 10 deg of the Galactic Plane. Five of these are well-known spin-powered pulsars, 2 and possibly 3 others are blazars, and the remaining 74 are classified as unidentified, although 6 of these are likely to be artifacts of nearby strong sources. Several of the remaining 68 unidentified sources have been noted as having positional agreement with supernovae remnants and OB associations. Others may be radio-quiet pulsars like Geminga, and still others may belong to a totally new class of sources. The question of the energy spectral distributions of these sources is an important clue to their identification. In this paper, the spectra of the sources within 10 deg of Galactic Plane are fit with three different functional forms; a single power law, two power laws, and a power law with an exponential cutoff. Where possible, the best fit is selected with statistical tests. Twelve, and possibly an additional 5 sources, are found to have spectra that are fit by a breaking power law or by the power law with exponential cutoff function.
A DEEP CHANDRA OBSERVATION OF THE WOLF-RAYET + BLACK HOLE BINARY NGC 300 X-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Binder, B.; Williams, B. F.; Anderson, S. F.

We have obtained a 63 ks Chandra ACIS-I observation of the Wolf-Rayet + black hole binary NGC 300 X-1. We measure rapid low-amplitude variability in the 0.35-8 keV light curve. The power density spectrum has a power-law index {gamma} = 1.02 {+-} 0.15 consistent with an accreting black hole in a steep power-law state. When compared to previous studies of NGC 300 X-1 performed with XMM-Newton, we find the source at the low end of the previously measured 0.3-10 keV luminosity. The spectrum of NGC 300 X-1 is dominated by a power law ({Gamma} = 2.0 {+-} 0.3) with amore » contribution at low energies by a thermal component. We estimate the 0.3-10 keV luminosity to be 2.6{sup +0.8}{sub -1.0} Multiplication-Sign 10{sup 38} erg s{sup -1}. The timing and spectroscopic properties of NGC 300 X-1 are consistent with being in a steep power-law state, similar to earlier observations performed with XMM-Newton. We additionally compare our observations to known high-mass X-ray binaries and ultraluminous X-ray sources, and find the properties of NGC 300 X-1 are most consistent with black hole high-mass X-ray binaries.« less
Saving Moore’s Law Down To 1 nm Channels With Anisotropic Effective Mass

NASA Astrophysics Data System (ADS)

Ilatikhameneh, Hesameddin; Ameen, Tarek; Novakovic, Bozidar; Tan, Yaohua; Klimeck, Gerhard; Rahman, Rajib

2016-08-01

Scaling transistors’ dimensions has been the thrust for the semiconductor industry in the last four decades. However, scaling channel lengths beyond 10 nm has become exceptionally challenging due to the direct tunneling between source and drain which degrades gate control, switching functionality, and worsens power dissipation. Fortunately, the emergence of novel classes of materials with exotic properties in recent times has opened up new avenues in device design. Here, we show that by using channel materials with an anisotropic effective mass, the channel can be scaled down to 1 nm and still provide an excellent switching performance in phosphorene nanoribbon MOSFETs. To solve power consumption challenge besides dimension scaling in conventional transistors, a novel tunnel transistor is proposed which takes advantage of anisotropic mass in both ON- and OFF-state of the operation. Full-band atomistic quantum transport simulations of phosphorene nanoribbon MOSFETs and TFETs based on the new design have been performed as a proof.
The relation of turbulence to diffusion in open-channel flows

USGS Publications Warehouse

Keefer, Thomas N.

1971-01-01

The exponent in the power-law equation describing the decay of scalar quantities downstream of a jet is a linear function of the shear velocity of the channel. The length of the core region of a jet is a power-law function of the jet strength with the exponent depending on boundary roughness.
Space-to-Space Power Beaming Enabling High Performance Rapid Geocentric Orbit Transfer

NASA Technical Reports Server (NTRS)

Dankanich, John W.; Vassallo, Corinne; Tadge, Megan

2015-01-01

The use of electric propulsion is more prevalent than ever, with industry pursuing all electric orbit transfers. Electric propulsion provides high mass utilization through efficient propellant transfer. However, the transfer times become detrimental as the delta V transitions from near-impulsive to low-thrust. Increasing power and therefore thrust has diminishing returns as the increasing mass of the power system limits the potential acceleration of the spacecraft. By using space-to-space power beaming, the power system can be decoupled from the spacecraft and allow significantly higher spacecraft alpha (W/kg) and therefore enable significantly higher accelerations while maintaining high performance. This project assesses the efficacy of space-to-space power beaming to enable rapid orbit transfer while maintaining high mass utilization. Concept assessment requires integrated techniques for low-thrust orbit transfer steering laws, efficient large-scale rectenna systems, and satellite constellation configuration optimization. This project includes the development of an integrated tool with implementation of IPOPT, Q-Law, and power-beaming models. The results highlight the viability of the concept, limits and paths to infusion, and comparison to state-of-the-art capabilities. The results indicate the viability of power beaming for what may be the only approach for achieving the desired transit times with high specific impulse.
The Causal Connection Between Disc and Power-Law Variability in Hard State Black Hole X-Ray Binaries

NASA Technical Reports Server (NTRS)

Uttley, P.; Wilkinson, T.; Cassatella, P.; Wilms, J.; Pottschimdt, K.; Hanke, M.; Boeck, M.

2010-01-01

We use the XMM-Newton EPIC-pn instrument in timing mode to extend spectral time-lag studies of hard state black hole X-ray binaries into the soft X-ray band. \\Ve show that variations of the disc blackbody emission substantially lead variations in the power-law emission, by tenths of a second on variability time-scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time-delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time-scales less than a second the disc lags the power-law variations by a few ms, consistent with the disc variations being dominated by X-ray heating by the power-law, with the short lag corresponding to the light-travel time between the power-law emitting region and the disc. Our results indicate that instabilities in the accretion disc are responsible for continuum variability on time-scales of seconds or longer and probably also on shorter time-scales.
Fundamental Properties of Co-moving Stars Observed by Gaia

NASA Astrophysics Data System (ADS)

Bochanski, John J.; Faherty, Jacqueline K.; Gagné, Jonathan; Nelson, Olivia; Coker, Kristina; Smithka, Iliya; Desir, Deion; Vasquez, Chelsea

2018-04-01

We have estimated fundamental parameters for a sample of co-moving stars observed by Gaia and identified by Oh et al. We matched the Gaia observations to the 2MASS and Wide-Field Infrared Survey Explorer catalogs and fit MIST isochrones to the data, deriving estimates of the mass, radius, [Fe/H], age, distance, and extinction to 9754 stars in the original sample of 10606 stars. We verify these estimates by comparing our new results to previous analyses of nearby stars, examining fiducial cluster properties, and estimating the power-law slope of the local present-day mass function. A comparison to previous studies suggests that our mass estimates are robust, while metallicity and age estimates are increasingly uncertain. We use our calculated masses to examine the properties of binaries in the sample and show that separation of the pairs dominates the observed binding energies and expected lifetimes.
Convection Heat and Mass Transfer in a Power Law Fluid with Non Constant Relaxation Time Past a Vertical Porous Plate in the Presence of Thermo and Thermal Diffusion

NASA Astrophysics Data System (ADS)

Olajuwon, B. I.; Oyelakin, I. S.

2012-12-01

The paper investigates convection heat and mass transfer in power law fluid flow with non relaxation time past a vertical porous plate in presence of a chemical reaction, heat generation, thermo diffu- sion and thermal diffusion. The non - linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration profiles for pseudo plastic fluids and for different values of parameters governing the prob- lem. The skin friction, heat transfer and mass transfer rates are presented numerically in tabular form. The results show that these parameters have significant effects on the flow, heat transfer and mass transfer.
Hydrodynamics of a cold one-dimensional fluid: the problem of strong shock waves

NASA Astrophysics Data System (ADS)

Hurtado, Pablo I.

2005-03-01

We study a shock wave induced by an infinitely massive piston propagating into a one-dimensional cold gas. The cold gas is modelled as a collection of hard rods which are initially at rest, so the temperature is zero. Most of our results are based on simulations of a gas of rods with binary mass distribution, and we partcularly focus on the case of spatially alternating masses. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches, e.g., the flow-field profiles relax algebraically toward their equilibrium values. In addition, most relevant observables characterizing local thermodynamic equilibrium and equipartition decay as a power law of the distance to the shock layer. The exponents of these power laws depend non-monotonously on the mass ratio. Similar interesting dependences on the mass ratio also characterize the shock width, density and temperature overshoots, etc.

Critical fluctuations of the proton density in A+A collisions at 158A GeV

DOE PAGES

Anticic, T.; Baatar, B.; Bartke, J.; ...

2015-12-12

Here, we look for fluctuations expected for the QCD critical point using an intermittency analysis in the transverse momentum phase space of protons produced around midrapidity in the 12.5 % most central C+C, Si+Si and Pb+Pb collisions at the maximum SPS energy of 158A GeV. We find evidence of power-law fluctuations for the Si+Si data. The fitted power-law exponent Φ 2=0.96 +0.38 –0.25 (stat.) ± 0.16 (syst.) is consistent with the value expected for critical fluctuations. Power-law fluctuations had previously also been observed in low-mass π +π – pairs in the same Si+Si collisions.
Increasing power-law range in avalanche amplitude and energy distributions

NASA Astrophysics Data System (ADS)

Navas-Portella, Víctor; Serra, Isabel; Corral, Álvaro; Vives, Eduard

2018-02-01

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.
Increasing power-law range in avalanche amplitude and energy distributions.

PubMed

Navas-Portella, Víctor; Serra, Isabel; Corral, Álvaro; Vives, Eduard

2018-02-01

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.
Effects of film growth kinetics on grain coarsening and grain shape.

PubMed

Reis, F D A Aarão

2017-04-01

We study models of grain nucleation and coarsening during the deposition of a thin film using numerical simulations and scaling approaches. The incorporation of new particles in the film is determined by lattice growth models in three different universality classes, with no effect of the grain structure. The first model of grain coarsening is similar to that proposed by Saito and Omura [Phys. Rev. E 84, 021601 (2011)PLEEE81539-375510.1103/PhysRevE.84.021601], in which nucleation occurs only at the substrate, and the grain boundary evolution at the film surface is determined by a probabilistic competition of neighboring grains. The surface grain density has a power-law decay, with an exponent related to the dynamical exponent of the underlying growth kinetics, and the average radius of gyration scales with the film thickness with the same exponent. This model is extended by allowing nucleation of new grains during the deposition, with constant but small rates. The surface grain density crosses over from the initial power law decay to a saturation; at the crossover, the time, grain mass, and surface grain density are estimated as a function of the nucleation rate. The distributions of grain mass, height, and radius of gyration show remarkable power law decays, similar to other systems with coarsening and particle injection, with exponents also related to the dynamical exponent. The scaling of the radius of gyration with the height h relative to the base of the grain show clearly different exponents in growth dominated by surface tension and growth dominated by surface diffusion; thus it may be interesting for investigating the effects of kinetic roughening on grain morphology. In growth dominated by surface diffusion, the increase of grain size with temperature is observed.
The necessity of feedback physics in setting the peak of the initial mass function

NASA Astrophysics Data System (ADS)

Guszejnov, Dávid; Krumholz, Mark R.; Hopkins, Philip F.

2016-05-01

A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initial mass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, self-gravitating, isothermal turbulence are scale-free, and do not predict any characteristic mass. In this paper we show that, although an isothermal self-gravitating flow does produce a CMF with a mass scale imposed by the initial conditions, this scale changes as the parent cloud evolves. In addition, the cores that form undergo further fragmentation and after sufficient time forget about their initial conditions, yielding a scale-free pure power-law distribution dN/dM ∝ M-2 for the stellar IMF. We show that this problem can be alleviated by introducing additional physics that provides a termination scale for the cascade. Our candidate for such physics is a simple model for stellar radiation feedback. Radiative heating, powered by accretion on to forming stars, arrests the fragmentation cascade and imposes a characteristic mass scale that is nearly independent of the time-evolution or initial conditions in the star-forming cloud, and that agrees well with the peak of the observed IMF. In contrast, models that introduce a stiff equation of state for denser clouds but that do not explicitly include the effects of feedback do not yield an invariant IMF.
Observational constraints on varying neutrino-mass cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geng, Chao-Qiang; Lee, Chung-Chi; Myrzakulov, R.

We consider generic models of quintessence and we investigate the influence of massive neutrino matter with field-dependent masses on the matter power spectrum. In case of minimally coupled neutrino matter, we examine the effect in tracker models with inverse power-law and double exponential potentials. We present detailed investigations for the scaling field with a steep exponential potential, non-minimally coupled to massive neutrino matter, and we derive constraints on field-dependent neutrino masses from the observational data.
Kinematics of Globular Cluster: new Perspectives of Energy Equipartition from N-body Simulations

NASA Astrophysics Data System (ADS)

Kim, Hyunwoo; Pasquato, Mario; Yoon, Suk-jin

2018-01-01

Globular clusters (GCs) evolve dynamically through gravitational two-body interactions between stars. We investigated the evolution towards energy equipartition in GCs using direct n-body simulations in NBODY6. If a GC reaches full energy equipartition, the velocity dispersion as a function of stars’ mass becomes a power law with exponent -1/2. However, our n-body simulations never reach full equipartition, which is similar to Trenti & van de Marel (2013) results. Instead we found that in simulations with a shallow mass spectrum the best fit exponent becomes positive slightly before core collapse time. This inversion is a new result, which can be used as a kinematic predictor of core collapse. We are currently exploring applications of this inversion indicator to the detection of intermediate mass black holes.
On the theory of behavioral mechanics.

PubMed

Dzendolet, E

1999-12-01

The Theory of Behavioral Mechanics is the behavioral analogue of Newton's laws of motion, with the rate of responding in operant conditioning corresponding to physical velocity. In an earlier work, the basic relation between rate of responding and sessions under two FI schedules and over a range of commonly used session values had been shown to be a power function. Using that basic relation, functions for behavioral acceleration, mass, and momentum are derived here. Data from other laboratories also support the applicability of a power function to VI schedules. A particular numerical value is introduced here to be the standard reference value for the behavioral force under the VI-60-s schedule. This reference allows numerical values to be calculated for the behavioral mass and momentum of individual animals. A comparison of the numerical values of the momenta of two animals can be used to evaluate their relative resistances to change, e.g., to extinction, which is itself viewed as a continuously changing behavioral force being imposed on the animal. This overall numerical approach allows behavioral force-values to be assigned to various experimental conditions such as the evaluation of the behavioral force of a medication dosage.
Limits on the power-law mass and luminosity density profiles of elliptical galaxies from gravitational lensing systems

NASA Astrophysics Data System (ADS)

Cao, Shuo; Biesiada, Marek; Yao, Meng; Zhu, Zong-Hong

2016-09-01

We use 118 strong gravitational lenses observed by the SLACS, BOSS emission-line lens survey (BELLS), LSD and SL2S surveys to constrain the total mass profile and the profile of luminosity density of stars (light tracers) in elliptical galaxies up to redshift z ˜ 1. Assuming power-law density profiles for the total mass density, ρ = ρ0(r/r0)-α, and luminosity density, ν = ν0(r/r0)-δ, we investigate the power-law index and its first derivative with respect to the redshift. Using Monte Carlo simulations of the posterior likelihood taking the Planck's best-fitting cosmology as a prior, we find γ = 2.132 ± 0.055 with a mild trend ∂γ/∂zl = -0.067 ± 0.119 when α = δ = γ, suggesting that the total density profile of massive galaxies could have become slightly steeper over cosmic time. Furthermore, similar analyses performed on sub-samples defined by different lens redshifts and velocity dispersions indicate the need of treating low-, intermediate- and high-mass galaxies separately. Allowing δ to be a free parameter, we obtain α = 2.070 ± 0.031, ∂α/∂zl = -0.121 ± 0.078 and δ = 2.710 ± 0.143. The model in which mass traces light is rejected at >95 per cent confidence, and our analysis robustly indicates the presence of dark matter in the form of a mass component that is differently spatially extended than the light. In this case, intermediate-mass elliptical galaxies (200 km s-1 <σap ≤ 300 km s-1) show the best consistency with the singular isothermal sphere as an effective model of galactic lenses.
Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

Karsh, P. K.; Mukhopadhyay, T.; Dey, S.

2018-03-01

This paper presents the stochastic natural frequency analysis of functionally graded plates by applying artificial neural network (ANN) approach. Latin hypercube sampling is utilised to train the ANN model. The proposed algorithm for stochastic natural frequency analysis of FGM plates is validated and verified with original finite element method and Monte Carlo simulation (MCS). The combined stochastic variation of input parameters such as, elastic modulus, shear modulus, Poisson ratio, and mass density are considered. Power law is applied to distribute the material properties across the thickness. The present ANN model reduces the sample size and computationally found efficient as compared to conventional Monte Carlo simulation.
Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses

NASA Technical Reports Server (NTRS)

Wijers, Ralph A. M. J.; Lubin, Lori M.

1994-01-01

We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.
A characterization of persistence at short times in the WFC3/IR detector

NASA Astrophysics Data System (ADS)

Gennaro, M.; Bajaj, V.; Long, K.

2018-05-01

Persistence in the WFC3/IR detector appears to decay as a power law as a function of time elapsed since the end of a stimulus. In this report we study departures from the power law at times shorter than a few hundreds seconds after the stimulus. In order to have better short-time cadence, we use the Multiaccum (.ima) files, which trace the accumulated charge in the pixels as function of time, rather than the final pipeline products (.flt files), which instead report the electron rate estimated via a linear fit to the accumulated charge vs. time relation. We note that at short times after the stimulus, the absolute change in persistence is the strongest, thus a linear fit to the accumulated signal (the .flt values) can be a poor representation of the strongly varying persistence signal. The already observed power-law decay of the persistence signal, still holds at shorter times, with typical values of the power law index, gamma in [-0.8,-1] for stimuli that saturate the WFC3 pixels. To a good degree of approximation, a single power law is a good fit to the persistence signal decay from 100 to 5000 seconds. We also detect a tapering-off in the power-law decay at increasingly shorter times. This change in behavior is of the order of Delta Gamma 0.02 - 0.05 when comparing power-law fits performed to the persistence signal from 0 up to 250 seconds and from 0 up to 4000 seconds after the stimulus, indicating that persistence decays slightly more rapidly as time progresses. Our results may suggest that for even shorter times, not probed by our study, the WFC3 persistence signal might deviate from a single power-law model.
The VIMOS Public Extragalactic Redshift Survey (VIPERS) . Luminosity and stellar mass dependence of galaxy clustering at 0.5 < z < 1.1

NASA Astrophysics Data System (ADS)

Marulli, F.; Bolzonella, M.; Branchini, E.; Davidzon, I.; de la Torre, S.; Granett, B. R.; Guzzo, L.; Iovino, A.; Moscardini, L.; Pollo, A.; Abbas, U.; Adami, C.; Arnouts, S.; Bel, J.; Bottini, D.; Cappi, A.; Coupon, J.; Cucciati, O.; De Lucia, G.; Fritz, A.; Franzetti, P.; Fumana, M.; Garilli, B.; Ilbert, O.; Krywult, J.; Le Brun, V.; Le Fèvre, O.; Maccagni, D.; Małek, K.; McCracken, H. J.; Paioro, L.; Polletta, M.; Schlagenhaufer, H.; Scodeggio, M.; Tasca, L. A. M.; Tojeiro, R.; Vergani, D.; Zanichelli, A.; Burden, A.; Di Porto, C.; Marchetti, A.; Marinoni, C.; Mellier, Y.; Nichol, R. C.; Peacock, J. A.; Percival, W. J.; Phleps, S.; Wolk, M.; Zamorani, G.

2013-09-01

Aims: We investigate the dependence of galaxy clustering on luminosity and stellar mass in the redshift range 0.5 < z < 1.1, using the first ~ 55 000 redshifts from the VIMOS Public Extragalactic Redshift Survey (VIPERS). Methods: We measured the redshift-space two-point correlation functions (2PCF), ξ(s) and ξ(rp,π) , and the projected correlation function, wp(rp), in samples covering different ranges of B-band absolute magnitudes and stellar masses. We considered both threshold and binned galaxy samples, with median B-band absolute magnitudes - 21.6 ≲ MB - 5log (h) ≲ - 19.5 and median stellar masses 9.8 ≲ log (M⋆ [h-2 M⊙]) ≲ 10.7. We assessed the real-space clustering in the data from the projected correlation function, which we model as a power law in the range 0.2 < rp [h-1 Mpc ] < 20. Finally, we estimated the galaxy bias as a function of luminosity, stellar mass, and redshift, assuming a flat Λ cold dark matter model to derive the dark matter 2PCF. Results: We provide the best-fit parameters of the power-law model assumed for the real-space 2PCF - the correlation length, r0, and the slope, γ - as well as the linear bias parameter, as a function of the B-band absolute magnitude, stellar mass, and redshift. We confirm and provide the tightest constraints on the dependence of clustering on luminosity at 0.5 < z < 1.1. We prove the complexity of comparing the clustering dependence on stellar mass from samples that are originally flux-limited and discuss the possible origin of the observed discrepancies. Overall, our measurements provide stronger constraints on galaxy formation models, which are now required to match, in addition to local observations, the clustering evolution measured by VIPERS galaxies between z = 0.5 and z = 1.1 for a broad range of luminosities and stellar masses. Based on observations collected at the European Southern Observatory, Paranal, Chile, under programmes 182.A-0886 (LP) at the Very Large Telescope, and also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. The VIPERS web site is http://vipers.inaf.it/
A statistical model of aggregate fragmentation

NASA Astrophysics Data System (ADS)

Spahn, F.; Vieira Neto, E.; Guimarães, A. H. F.; Gorban, A. N.; Brilliantov, N. V.

2014-01-01

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process—a crack moves against the stress gradient while dissipating energy during its growth. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small- and intermediate-size fragments obeys a power law, F(m)∝m-3/2, in agreement with experimental observations. We develop an analytical theory which explains the detected power law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that one observed in experiments.
X-Ray Spectra from MHD Simulations of Accreting Black Holes

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy D.; Noble, Scott C.; Krolik, Julian H.

2011-01-01

We present new global calculations of X-ray spectra from fully relativistic magneto-hydrodynamic (MHO) simulations of black hole (BH) accretion disks. With a self consistent radiative transfer code including Compton scattering and returning radiation, we can reproduce the predominant spectral features seen in decades of X-ray observations of stellar-mass BHs: a broad thermal peak around 1 keV, power-law continuum up to >100 keV, and a relativistically broadened iron fluorescent line. By varying the mass accretion rate, different spectral states naturally emerge: thermal-dominant, steep power-law, and low/hard. In addition to the spectral features, we briefly discuss applications to X-ray timing and polarization.
Power-law decay of the spatial correlation function in exciton-polariton condensates

PubMed Central

Roumpos, Georgios; Lohse, Michael; Nitsche, Wolfgang H.; Keeling, Jonathan; Szymańska, Marzena Hanna; Littlewood, Peter B.; Löffler, Andreas; Höfling, Sven; Worschech, Lukas; Forchel, Alfred; Yamamoto, Yoshihisa

2012-01-01

We create a large exciton-polariton condensate and employ a Michelson interferometer setup to characterize the short- and long-distance behavior of the first order spatial correlation function. Our experimental results show distinct features of both the two-dimensional and nonequilibrium characters of the condensate. We find that the gaussian short-distance decay is followed by a power-law decay at longer distances, as expected for a two-dimensional condensate. The exponent of the power law is measured in the range 0.9–1.2, larger than is possible in equilibrium. We compare the experimental results to a theoretical model to understand the features required to observe a power law and to clarify the influence of external noise on spatial coherence in nonequilibrium phase transitions. Our results indicate that Berezinskii–Kosterlitz–Thouless-like phase order survives in open-dissipative systems. PMID:22496595
Development of procedures for calculating stiffness and damping properties of elastomers in engineering applications. Part 2: Elastomer characteristics at constant temperature

NASA Technical Reports Server (NTRS)

Gupta, P. K.; Tessarzik, J. M.; Cziglenyi, L.

1974-01-01

Dynamic properties of a commerical polybutadiene compound were determined at a constant temperature of 32 C by a forced-vibration resonant mass type of apparatus. The constant thermal state of the elastomer was ensured by keeping the ambient temperature constant and by limiting the power dissipation in the specimen. Experiments were performed with both compression and shear specimens at several preloads (nominal strain varying from 0 to 5 percent), and the results are reported in terms of a complex stiffness as a function of frequency. Very weak frequency dependence is observed and a simple power law type of correlation is shown to represent the data well. Variations in the complex stiffness as a function of preload are also found to be small for both compression and shear specimens.
The cluster galaxy circular velocity function

NASA Astrophysics Data System (ADS)

Desai, V.; Dalcanton, J. J.; Mayer, L.; Reed, D.; Quinn, T.; Governato, F.

2004-06-01

We present galaxy circular velocity functions (GCVFs) for 34 low-redshift (z<~ 0.15) clusters identified in the Sloan Digital Sky Survey (SDSS), for 15 clusters drawn from dark matter simulations of hierarchical structure growth in a ΛCDM cosmology, and for ~22 000 SDSS field galaxies. We find that the simulations successfully reproduce the shape, amplitude and scatter in the observed distribution of cluster galaxy circular velocities. The power-law slope of the observed cluster GCVF is ~-2.4, independent of cluster velocity dispersion. The average slope of the simulated GCVFs is somewhat steeper, although formally consistent given the errors. We find that the effects of baryons on galaxy rotation curves is to flatten the simulated cluster GCVF into better agreement with observations. The cumulative GCVFs of the simulated clusters are very similar across a wide range of cluster masses, provided individual subhalo circular velocities are scaled by the circular velocities of the parent cluster. The scatter is consistent with that measured in the cumulative, scaled observed cluster GCVF. Finally, the observed field GCVF deviates significantly from a power law, being flatter than the cluster GCVF at circular velocities less than 200 km s-1.
Measurements of dielectron production in Au + Au collisions at s N N = 200 GeV from the STAR experiment

DOE PAGES

Adamczyk, L.; Adkins, J. K.; Agakishiev, G.; ...

2015-08-24

We report on measurements of dielectron (e⁺e⁻) production in Au+Au collisions at a center-of-mass energy of 200 GeV per nucleon-nucleon pair using the STAR detector at RHIC. Systematic measurements of the dielectron yield as a function of transverse momentum (p T) and collision centrality show an enhancement compared to a cocktail simulation of hadronic sources in the low invariant-mass region (M ee < 1GeV/c 2). This enhancement cannot be reproduced by the ρ-meson vacuum spectral function. In minimum-bias collisions, in the invariant-mass range of 0.30 – 0.76GeV/c², integrated over the full p T acceptance, the enhancement factor is 1.76±0.06(stat.)±0.26(sys.)±0.29(cocktail). Themore » enhancement factor exhibits weak centrality and p T dependence in STAR's accessible kinematic regions, while the excess yield in this invariant-mass region as a function of the number of participating nucleons follows a power-law shape with a power of 1.44±0.10. Models that assume an in-medium broadening of the ρ-meson spectral function consistently describe the observed excess in these measurements. In addition, we report on measurements of ω- and Φ-meson production through their e⁺e⁻ decay channel. These measurements show good agreement with Tsallis blast-wave model predictions, as well as, in the case of the Φ meson, results through its K⁺K⁻ decay channel. In the intermediate invariant-mass region (1.1 < M ee < 3GeV/c²), we investigate the spectral shapes from different collision centralities. Physics implications for possible in-medium modification of charmed hadron production and other physics sources are discussed.« less
Extracting functionally feedforward networks from a population of spiking neurons

PubMed Central

Vincent, Kathleen; Tauskela, Joseph S.; Thivierge, Jean-Philippe

2012-01-01

Neuronal avalanches are a ubiquitous form of activity characterized by spontaneous bursts whose size distribution follows a power-law. Recent theoretical models have replicated power-law avalanches by assuming the presence of functionally feedforward connections (FFCs) in the underlying dynamics of the system. Accordingly, avalanches are generated by a feedforward chain of activation that persists despite being embedded in a larger, massively recurrent circuit. However, it is unclear to what extent networks of living neurons that exhibit power-law avalanches rely on FFCs. Here, we employed a computational approach to reconstruct the functional connectivity of cultured cortical neurons plated on multielectrode arrays (MEAs) and investigated whether pharmacologically induced alterations in avalanche dynamics are accompanied by changes in FFCs. This approach begins by extracting a functional network of directed links between pairs of neurons, and then evaluates the strength of FFCs using Schur decomposition. In a first step, we examined the ability of this approach to extract FFCs from simulated spiking neurons. The strength of FFCs obtained in strictly feedforward networks diminished monotonically as links were gradually rewired at random. Next, we estimated the FFCs of spontaneously active cortical neuron cultures in the presence of either a control medium, a GABAA receptor antagonist (PTX), or an AMPA receptor antagonist combined with an NMDA receptor antagonist (APV/DNQX). The distribution of avalanche sizes in these cultures was modulated by this pharmacology, with a shallower power-law under PTX (due to the prominence of larger avalanches) and a steeper power-law under APV/DNQX (due to avalanches recruiting fewer neurons) relative to control cultures. The strength of FFCs increased in networks after application of PTX, consistent with an amplification of feedforward activity during avalanches. Conversely, FFCs decreased after application of APV/DNQX, consistent with fading feedforward activation. The observed alterations in FFCs provide experimental support for recent theoretical work linking power-law avalanches to the feedforward organization of functional connections in local neuronal circuits. PMID:23091458

Extracting functionally feedforward networks from a population of spiking neurons.

PubMed

Vincent, Kathleen; Tauskela, Joseph S; Thivierge, Jean-Philippe

2012-01-01

Neuronal avalanches are a ubiquitous form of activity characterized by spontaneous bursts whose size distribution follows a power-law. Recent theoretical models have replicated power-law avalanches by assuming the presence of functionally feedforward connections (FFCs) in the underlying dynamics of the system. Accordingly, avalanches are generated by a feedforward chain of activation that persists despite being embedded in a larger, massively recurrent circuit. However, it is unclear to what extent networks of living neurons that exhibit power-law avalanches rely on FFCs. Here, we employed a computational approach to reconstruct the functional connectivity of cultured cortical neurons plated on multielectrode arrays (MEAs) and investigated whether pharmacologically induced alterations in avalanche dynamics are accompanied by changes in FFCs. This approach begins by extracting a functional network of directed links between pairs of neurons, and then evaluates the strength of FFCs using Schur decomposition. In a first step, we examined the ability of this approach to extract FFCs from simulated spiking neurons. The strength of FFCs obtained in strictly feedforward networks diminished monotonically as links were gradually rewired at random. Next, we estimated the FFCs of spontaneously active cortical neuron cultures in the presence of either a control medium, a GABA(A) receptor antagonist (PTX), or an AMPA receptor antagonist combined with an NMDA receptor antagonist (APV/DNQX). The distribution of avalanche sizes in these cultures was modulated by this pharmacology, with a shallower power-law under PTX (due to the prominence of larger avalanches) and a steeper power-law under APV/DNQX (due to avalanches recruiting fewer neurons) relative to control cultures. The strength of FFCs increased in networks after application of PTX, consistent with an amplification of feedforward activity during avalanches. Conversely, FFCs decreased after application of APV/DNQX, consistent with fading feedforward activation. The observed alterations in FFCs provide experimental support for recent theoretical work linking power-law avalanches to the feedforward organization of functional connections in local neuronal circuits.
Scale-similar clustering of heavy particles in the inertial range of turbulence

NASA Astrophysics Data System (ADS)

Ariki, Taketo; Yoshida, Kyo; Matsuda, Keigo; Yoshimatsu, Katsunori

2018-03-01

Heavy particle clustering in turbulence is discussed from both phenomenological and analytical points of view, where the -4 /3 power law of the pair-correlation function is obtained in the inertial range. A closure theory explains the power law in terms of the balance between turbulence mixing and preferential-concentration mechanism. The obtained -4 /3 power law is supported by a direct numerical simulation of particle-laden turbulence.
A New Paradigm for Gamma Ray Bursts: Long Term Accretion Rate Modulation by an External Accretion Disk

NASA Technical Reports Server (NTRS)

Cannizzo, John; Gehrels, Neil

2009-01-01

We present a new way of looking at the very long term evolution of GRBs in which the disk of material surrounding the putative black hole powering the GRB jet modulates the mass flow, and hence the efficacy of the process that extracts rotational energy from the black hole and inner accretion disk. The pre-Swift paradigm of achromatic, shallow-to-steep "breaks" in the long term GRB light curves has not been borne out by detailed Swift data amassed in the past several years. We argue that, given the initial existence of a fall-back disk near the progenitor, an unavoidable consequence will be the formation of an "external disk" whose outer edge continually moves to larger radii due to angular momentum transport and lack of a confining torque. The mass reservoir at large radii moves outward with time and gives a natural power law decay to the GRB light curves. In this model, the different canonical power law decay segments in the GRB identified by Zhang et al. and Nousek et al. represent different physical states of the accretion disk. We identify a physical disk state with each power law segment.
The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies

NASA Astrophysics Data System (ADS)

El-Badry, Kareem; Weisz, Daniel R.; Quataert, Eliot

2017-06-01

We use Monte Carlo simulations to explore the statistical challenges of constraining the characteristic mass (mc) and width (σ) of a lognormal sub-solar initial mass function (IMF) in Local Group dwarf galaxies using direct star counts. For a typical Milky Way (MW) satellite (MV = -8), jointly constraining mc and σ to a precision of ≲ 20 per cent requires that observations be complete to ≲ 0.2 M⊙, if the IMF is similar to the MW IMF. A similar statistical precision can be obtained if observations are only complete down to 0.4 M⊙, but this requires measurement of nearly 100× more stars, and thus, a significantly more massive satellite (MV ˜ -12). In the absence of sufficiently deep data to constrain the low-mass turnover, it is common practice to fit a single-sloped power law to the low-mass IMF, or to fit mc for a lognormal while holding σ fixed. We show that the former approximation leads to best-fitting power-law slopes that vary with the mass range observed and can largely explain existing claims of low-mass IMF variations in MW satellites, even if satellite galaxies have the same IMF as the MW. In addition, fixing σ during fitting leads to substantially underestimated uncertainties in the recovered value of mc (by a factor of ˜4 for typical observations). If the IMFs of nearby dwarf galaxies are lognormal and do vary, observations must reach down to ˜mc in order to robustly detect these variations. The high-sensitivity, near-infrared capabilities of the James Webb Space Telescope and Wide-Field Infrared Survey Telescope have the potential to dramatically improve constraints on the low-mass IMF. We present an efficient observational strategy for using these facilities to measure the IMFs of Local Group dwarf galaxies.
A Universal Break in the Planet-to-star Mass-ratio Function of Kepler MKG Stars

NASA Astrophysics Data System (ADS)

Pascucci, Ilaria; Mulders, Gijs D.; Gould, Andrew; Fernandes, Rachel

2018-04-01

We follow the microlensing approach and quantify the occurrence of Kepler exoplanets as a function of planet-to-star mass ratio, q, rather than planet radius or mass. For planets with radii ∼1–6 R ⊕ and periods <100 days, we find that, except for a normalization factor, the occurrence rate versus q can be described by the same broken power law with a break at ∼3 × 10‑5 independent of host type for hosts below 1 M ⊙. These findings indicate that the planet-to-star mass ratio is a more fundamental quantity in planet formation than planet mass. We then compare our results to those from microlensing for which the overwhelming majority satisfies the M host < 1 M ⊙ criterion. The break in q for the microlensing planet population, which mostly probes the region outside the snowline, is ∼3–10 times higher than that inferred from Kepler. Thus, the most common planet inside the snowline is ∼3–10 times less massive than the one outside. With rocky planets interior to gaseous planets, the solar system broadly follows the combined mass-ratio function inferred from Kepler and microlensing. However, the exoplanet population has a less extreme radial distribution of planetary masses than the solar system. Establishing whether the mass-ratio function beyond the snowline is also host type independent will be crucial to build a comprehensive theory of planet formation.
Halo density profiles and baryon physics

NASA Astrophysics Data System (ADS)

Del Popolo, A.; Li, Xi-Guo

2017-08-01

The radial dependence of the pseudo phase-space density, ρ( r)/ σ 3( r) is studied. We find that the pseudo phase-space density for halos consisting both of dark matter and baryons is approximately a power-law only down to 0.1% of the virial radius while it has a non-power law behavior below the quoted scale, with inner profiles changing with mass. Halos consisting just of dark matter, as the one in dark matter only simulations, are characterized by an approximately power-law behavior. The results argue against universality of the pseudo phase-space density, when the baryons effect are included, and as a consequence argue against universality of density profiles constituted by dark matter and baryons as also discussed in [1].
AGN host galaxy mass function in COSMOS. Is AGN feedback responsible for the mass-quenching of galaxies?

NASA Astrophysics Data System (ADS)

Bongiorno, A.; Schulze, A.; Merloni, A.; Zamorani, G.; Ilbert, O.; La Franca, F.; Peng, Y.; Piconcelli, E.; Mainieri, V.; Silverman, J. D.; Brusa, M.; Fiore, F.; Salvato, M.; Scoville, N.

2016-04-01

We investigate the role of supermassive black holes in the global context of galaxy evolution by measuring the host galaxy stellar mass function (HGMF) and the specific accretion rate, that is, λSAR, the distribution function (SARDF), up to z ~ 2.5 with ~1000 X-ray selected AGN from XMM-COSMOS. Using a maximum likelihood approach, we jointly fit the stellar mass function and specific accretion rate distribution function, with the X-ray luminosity function as an additional constraint. Our best-fit model characterizes the SARDF as a double power-law with mass-dependent but redshift-independent break, whose low λSAR slope flattens with increasing redshift while the normalization increases. This implies that for a given stellar mass, higher λSAR objects have a peak in their space density at earlier epoch than the lower λSAR objects, following and mimicking the well-known AGN cosmic downsizing as observed in the AGN luminosity function. The mass function of active galaxies is described by a Schechter function with an almost constant M∗⋆ and a low-mass slope α that flattens with redshift. Compared to the stellar mass function, we find that the HGMF has a similar shape and that up to log (M⋆/M⊙) ~ 11.5, the ratio of AGN host galaxies to star-forming galaxies is basically constant (~10%). Finally, the comparison of the AGN HGMF for different luminosity and specific accretion rate subclasses with a previously published phenomenological model prediction for the "transient" population, which are galaxies in the process of being mass-quenched, reveals that low-luminosity AGN do not appear to be able to contribute significantly to the quenching and that at least at high masses, that is, M⋆ > 1010.7 M⊙, feedback from luminous AGN (log Lbol ≳ 46 [erg/s]) may be responsible for the quenching of star formation in the host galaxy.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1975-01-01

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
The NANOGrav Nine-Year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background

NASA Technical Reports Server (NTRS)

Arzoumanian, Z.; Brazier, A.; Burke-Spolaor, S.; Chamberlin, S. J.; Chatterjee, S.; Christy, B.; Cordes, J. M.; Cornish, N. J.; Crowter, K.; Demorest, P. B.;

2016-01-01

We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. Well-tested Bayesian techniques are used to set upper limits on the dimensionless strain amplitude (at a frequency of 1 yr(exp -1) for a GWB from supermassive black hole binaries of A(sub gw) less than 1.5 x 10(exp -15). We also parameterize the GWB spectrum with a broken power-law model by placing priors on the strain amplitude derived from simulations of Sesana and McWilliams et al. Using Bayesian model selection we find that the data favor a broken power law to a pure power law with odds ratios of 2.2 and 22 to one for the Sesana and McWilliams prior models, respectively. Using the broken power-law analysis we construct posterior distributions on environmental factors that drive the binary to the GW-driven regime including the stellar mass density for stellar-scattering, mass accretion rate for circumbinary disk interaction, and orbital eccentricity for eccentric binaries, marking the first time that the shape of the GWB spectrum has been used to make astrophysical inferences. Returning to a power-law model, we place stringent limits on the energy density of relic GWs, OMEGA(sub gw) (f) h squared less than 4.2 x 10(exp -10). Our limit on the cosmic string GWB, OMEGA(sub gw) (f) h squared less than 2.2 x 10(exp -10), translates to a conservative limit on the cosmic string tension with G mu less than 3.3 x 10(exp -8), a factor of four better than the joint Planck and high-l‚ cosmic microwave background data from other experiments.

ALMA OBSERVATIONS OF THE DEBRIS DISK AROUND THE YOUNG SOLAR ANALOG HD 107146

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ricci, L.; Carpenter, J. M.; Fu, B.

We present the Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations at a wavelength of 1.25 mm of the debris disk surrounding the ∼100 Myr old solar analog HD 107146. The continuum emission extends from about 30 to 150 AU from the central star with a decrease in the surface brightness at intermediate radii. We analyze the ALMA interferometric visibilities using debris disk models with radial profiles for the dust surface density parameterized as (1) a single power law, (2) a single power law with a gap, and (3) a double power law. We find that models with a gap of radial widthmore » ∼8 AU at a distance of ∼80 AU from the central star, as well as double power-law models with a dip in the dust surface density at ∼70 AU provide significantly better fits to the ALMA data than single power-law models. We discuss possible scenarios for the origin of the HD 107146 debris disk using models of planetesimal belts in which the formation of Pluto-sized objects trigger disruptive collisions of large bodies, as well as models that consider the interaction of a planetary system with a planetesimal belt and spatial variation of the dust opacity across the disk. If future observations with higher angular resolution and sensitivity confirm the fully depleted gap structure discussed here, a planet with a mass of approximately a few Earth masses in a nearly circular orbit at ∼80 AU from the central star would be a possible explanation for the presence of the gap.« less
Statistical analysis of quiet stance sway in 2-D

PubMed Central

DiZio, Paul; Lackner, James R.

2014-01-01

Subjects exposed to a rotating environment that perturbs their postural sway show adaptive changes in their voluntary spatially directed postural motion to restore accurate movement paths but do not exhibit any obvious learning during passive stance. We have found, however, that a variable known to characterize the degree of stochasticity in quiet stance can also reveal subtle learning phenomena in passive stance. We extended Chow and Collins (Phys Rev E 52(1):909–912, 1995) one-dimensional pinned-polymer model (PPM) to two dimensions (2-D) and then evaluated the model’s ability to make analytical predictions for 2-D quiet stance. To test the model, we tracked center of mass and centers of foot pressures, and compared and contrasted stance sway for the anterior–posterior versus medio-lateral directions before, during, and after exposure to rotation at 10 rpm. Sway of the body during rotation generated Coriolis forces that acted perpendicular to the direction of sway. We found significant adaptive changes for three characteristic features of the mean square displacement (MSD) function: the exponent of the power law defined at short time scales, the proportionality constant of the power law, and the saturation plateau value defined at longer time scales. The exponent of the power law of MSD at a short time scale lies within the bounds predicted by the 2-D PPM. The change in MSD during exposure to rotation also had a power-law exponent in the range predicted by the theoretical model. We discuss the Coriolis force paradigm for studying postural and movement control and the applicability of the PPM model in 2-D for studying postural adaptation. PMID:24477760
The young star cluster population of M51 with LEGUS - II. Testing environmental dependences

NASA Astrophysics Data System (ADS)

Messa, Matteo; Adamo, A.; Calzetti, D.; Reina-Campos, M.; Colombo, D.; Schinnerer, E.; Chandar, R.; Dale, D. A.; Gouliermis, D. A.; Grasha, K.; Grebel, E. K.; Elmegreen, B. G.; Fumagalli, M.; Johnson, K. E.; Kruijssen, J. M. D.; Östlin, G.; Shabani, F.; Smith, L. J.; Whitmore, B. C.

2018-06-01

It has recently been established that the properties of young star clusters (YSCs) can vary as a function of the galactic environment in which they are found. We use the cluster catalogue produced by the Legacy Extragalactic UV Survey (LEGUS) collaboration to investigate cluster properties in the spiral galaxy M51. We analyse the cluster population as a function of galactocentric distance and in arm and inter-arm regions. The cluster mass function exhibits a similar shape at all radial bins, described by a power law with a slope close to -2 and an exponential truncation around 105 M⊙. While the mass functions of the YSCs in the spiral arm and inter-arm regions have similar truncation masses, the inter-arm region mass function has a significantly steeper slope than the one in the arm region, a trend that is also observed in the giant molecular cloud mass function and predicted by simulations. The age distribution of clusters is dependent on the region considered, and is consistent with rapid disruption only in dense regions, while little disruption is observed at large galactocentric distances and in the inter-arm region. The fraction of stars forming in clusters does not show radial variations, despite the drop in the H2 surface density measured as a function of galactocentric distance. We suggest that the higher disruption rate observed in the inner part of the galaxy is likely at the origin of the observed flat cluster formation efficiency radial profile.
Dynamical Formation Signatures of Black Hole Binaries in the First Detected Mergers by LIGO

NASA Astrophysics Data System (ADS)

O'Leary, Ryan M.; Meiron, Yohai; Kocsis, Bence

2016-06-01

The dynamical formation of stellar-mass black hole-black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M tot roughly as \\propto {M}{{tot}}β , with β ≳ 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO’s greater sensitivity to massive black hole binaries with M tot ≲ 80 {M}⊙ . We find that for power-law BH mass functions dN/dM ∝ M -α with α ≤ 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about ˜5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries.
The Arches Cluster Out to its Tidal Radius: Dynamical Mass Segregation and the Effect of the Extinction Law on the - Lar Mass Function

NASA Astrophysics Data System (ADS)

Habibi, Maryam; Stolte, Andrea; Brandner, Wolfgang; Hussman, Benjamin

2013-07-01

The Galactic Center is the most active site of star formation in the Milky Way Galaxy, where particularly high-mass stars have formed very recently and are still forming today. However, since we are looking at the Galactic Center through the Galactic disk, knowledge of extinction is crucial to study this region. The Arches cluster is a young, massive starburst cluster near the Galactic Center. We observed the Arches cluster out to its tidal radius using Ks-band imaging obtained with NAOS/CONICA at the VLT combined with Subaro/Cisco J-band data to gain a full understanding of the cluster mass distribution. We show that the determination of the mass of the most massive star in the Arches cluster, which had been used in previous studies to establish an upper-mass limit for the star formation process in the Milky Way, strongly depends on the assumed slope of the extinction law. Assuming the two regimes of widely used infrared extinction laws, we show that the difference can reach up to 30% for individually derived stellar masses and ∆AKs˜1 magnitude in acquired Ks-band extinction, while the present mass function slope changes by ˜0.17 dex. The present-day mass function slope derived assuming the Nishiyama et al. (2009) extinction law increases from a flat slope of α-Nishi = 1.50 ± 0.35 in the core (r<0.2 pc) to α-Nishi = 2.21±0.27 in the intermediate annulus (0.2
Experimental validation of convection-diffusion discretisation scheme employed for computational modelling of biological mass transport

PubMed Central

2010-01-01

Background The finite volume solver Fluent (Lebanon, NH, USA) is a computational fluid dynamics software employed to analyse biological mass-transport in the vasculature. A principal consideration for computational modelling of blood-side mass-transport is convection-diffusion discretisation scheme selection. Due to numerous discretisation schemes available when developing a mass-transport numerical model, the results obtained should either be validated against benchmark theoretical solutions or experimentally obtained results. Methods An idealised aneurysm model was selected for the experimental and computational mass-transport analysis of species concentration due to its well-defined recirculation region within the aneurysmal sac, allowing species concentration to vary slowly with time. The experimental results were obtained from fluid samples extracted from a glass aneurysm model, using the direct spectrophometric concentration measurement technique. The computational analysis was conducted using the four convection-diffusion discretisation schemes available to the Fluent user, including the First-Order Upwind, the Power Law, the Second-Order Upwind and the Quadratic Upstream Interpolation for Convective Kinetics (QUICK) schemes. The fluid has a diffusivity of 3.125 × 10-10 m2/s in water, resulting in a Peclet number of 2,560,000, indicating strongly convection-dominated flow. Results The discretisation scheme applied to the solution of the convection-diffusion equation, for blood-side mass-transport within the vasculature, has a significant influence on the resultant species concentration field. The First-Order Upwind and the Power Law schemes produce similar results. The Second-Order Upwind and QUICK schemes also correlate well but differ considerably from the concentration contour plots of the First-Order Upwind and Power Law schemes. The computational results were then compared to the experimental findings. An average error of 140% and 116% was demonstrated between the experimental results and those obtained from the First-Order Upwind and Power Law schemes, respectively. However, both the Second-Order upwind and QUICK schemes accurately predict species concentration under high Peclet number, convection-dominated flow conditions. Conclusion Convection-diffusion discretisation scheme selection has a strong influence on resultant species concentration fields, as determined by CFD. Furthermore, either the Second-Order or QUICK discretisation schemes should be implemented when numerically modelling convection-dominated mass-transport conditions. Finally, care should be taken not to utilize computationally inexpensive discretisation schemes at the cost of accuracy in resultant species concentration. PMID:20642816
Gas and Dust Structures of the Protoplanetary Disk around HD 142527

NASA Astrophysics Data System (ADS)

Momose, M.; Muto, T.; Hanawa, T.; Fukagawa, M.; Tsukagoshi, T.; Saigo, K.; Kataoka, A.; Nomura, H.; Takeuchi, T.; Akiyama, E.; Ohashi, N.; Fujiwara, H.; Shibai, H.; Kitamura, Y.; Inutsuka, S.; Kobayashi, H.; Honda, M.; Aso, Y.; Takahashi, S. Z.

2015-12-01

HD142527 is a Herbig Fe star accompanied by a disk with ring-like structure. We derive the distributions of dust and gas separately by model fitting and discuss the spatial variation of gas-to-dust mass ratio in the disk. The radial distribution of dust is well approximated by a Gaussian function, while the gas is roughly followed by a power-law distribution between 110 and 400 AU in radius, which is significantly more extended than dust. G/d may reach the order of unity at the northern peak.
Lighting the dark molecular gas and a Bok globule

NASA Astrophysics Data System (ADS)

Togi, Aditya G.

Stars are the building blocks of galaxies. The gas present in galaxies is the primary fuel for star formation. Galaxy evolution depends on the amount of gas present in the interstellar medium (ISM). Stars are born mainly from molecular gas in the GMCs. Robust knowledge of the molecular hydrogen H2 gas distribution is necessary to understand star formation in galaxies. Since H2 is not readily observable in the cold interstellar medium (ISM), the molecular gas content has traditionally been inferred using indirect tracers like carbon-monoxide (CO), dust emission, gamma ray interactions, and star formation efficiency. Physical processes resulting in enhancement and reduction of these indirect tracers can result in misleading estimates of molecular gas masses. My dissertation work is based on devising a new temperature power law distribution model for H2, a direct tracer, to calculate the total molecular gas mass in galaxies. The model parameters are estimated using mid infrared (MIR) H2 rotational line fluxes obtained from IRS-Spitzer (Infrared Spectrograph-Spitzer) instrument and the model is extrapolated to a suitable lower temperature to recover the total molecular gas mass. The power law model is able to recover the dark molecular gas, undetected by CO, in galaxies at metallicity as low as one-tenth of our Milky Way value. I have applied the power law model in U/LIRGs and shocks of Stephan's Quintet to understand molecular gas properties, where shocks play an important role in exciting H2. Comparing the molecular gas content derived through our power law model can be useful in studying the application of our model in mergers. The parameters derived by our model is useful in understanding variation in molecular gas properties in shock regions of Stephan's Quintet. Low mass stars are formed in small isolated dense cores known as Bok globules. Multiple star formation events are seen in a Bok globule. In my thesis I also studied a Bok globule, B207, and determined the physical properties and future evolutionary stage of the cloud. My thesis spans studying ISM properties in galaxies from kpc to sub-pc scales. Using the power law model in the coming era of James Webb Space Telescope (JWST) with the high sensitivity MIR Instrument (MIRI) spectrograph we will be able to understand the properties of molecular gas at low and high redshifts.
Models of fragmentation with composite power laws

NASA Astrophysics Data System (ADS)

Tavassoli, Z.; Rodgers, G. J.

1999-06-01

Some models for binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the first model we assume a fixed rate of fragmentation for the largest fragment and two different rates of fragmentation in the two regions of sizes above and below the transition size. The model is solved exactly in the long time limit to reveal stable time-invariant solutions for the fragment size and mass distributions. These solutions exhibit composite power law behaviours; power laws with two different exponents for fragments in smaller and larger regions. A special case of the model with no fragmentation in the smaller size region is also examined. Another model is also introduced which have three regions of fragment sizes with different rates of fragmentation. The similarities between the stable distributions in our models and composite power law distributions from experimental work on shock fragmentation of long thin glass rods and thick clay plates are discussed.
Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method

NASA Astrophysics Data System (ADS)

Wei, H. L.; Billings, S. A.

2009-09-01

Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.
An animal-to-human scaling law for blast-induced traumatic brain injury risk assessment.

PubMed

Jean, Aurélie; Nyein, Michelle K; Zheng, James Q; Moore, David F; Joannopoulos, John D; Radovitzky, Raúl

2014-10-28

Despite recent efforts to understand blast effects on the human brain, there are still no widely accepted injury criteria for humans. Recent animal studies have resulted in important advances in the understanding of brain injury due to intense dynamic loads. However, the applicability of animal brain injury results to humans remains uncertain. Here, we use advanced computational models to derive a scaling law relating blast wave intensity to the mechanical response of brain tissue across species. Detailed simulations of blast effects on the brain are conducted for different mammals using image-based biofidelic models. The intensity of the stress waves computed for different external blast conditions is compared across species. It is found that mass scaling, which successfully estimates blast tolerance of the thorax, fails to capture the brain mechanical response to blast across mammals. Instead, we show that an appropriate scaling variable must account for the mass of protective tissues relative to the brain, as well as their acoustic impedance. Peak stresses transmitted to the brain tissue by the blast are then shown to be a power function of the scaling parameter for a range of blast conditions relevant to TBI. In particular, it is found that human brain vulnerability to blast is higher than for any other mammalian species, which is in distinct contrast to previously proposed scaling laws based on body or brain mass. An application of the scaling law to recent experiments on rabbits furnishes the first physics-based injury estimate for blast-induced TBI in humans.

Strong gravitational lensing and the stellar IMF of early-type galaxies

NASA Astrophysics Data System (ADS)

Leier, Dominik; Ferreras, Ignacio; Saha, Prasenjit; Charlot, Stéphane; Bruzual, Gustavo; La Barbera, Francesco

2016-07-01

Systematic variations of the initial mass function (IMF) in early-type galaxies, and their connection with possible drivers such as velocity dispersion or metallicity, have been much debated in recent years. Strong lensing over galaxy scales combined with photometric and spectroscopic data provides a powerful method to constrain the stellar mass-to-light ratio and hence the functional form of the IMF. We combine photometric and spectroscopic constraints from the latest set of population synthesis models of Charlot & Bruzual, including a varying IMF, with a non-parametric analysis of the lens masses of 18 ETGs from the SLACS survey, with velocity dispersions in the range 200-300 km s-1. We find that very bottom-heavy IMFs are excluded. However, the upper limit to the bimodal IMF slope (μ ≲ 2.2, accounting for a dark matter fraction of 20-30 per cent, where μ = 1.3 corresponds to a Kroupa-like IMF) is compatible at the 1σ level with constraints imposed by gravity-sensitive line strengths. A two-segment power-law parametrization of the IMF (Salpeter-like for high masses) is more constrained (Γ ≲ 1.5, where Γ is the power index at low masses) but requires a dark matter contribution of ≳25 per cent to reconcile the results with a Salpeter IMF. For a standard Milky Way-like IMF to be applicable, a significant dark matter contribution is required within 1Re. Our results reveal a large range of allowed IMF slopes, which, when interpreted as intrinsic scatter in the IMF properties of ETGs, could explain the recent results of Smith et al., who find Milky Way-like IMF normalizations in a few massive lensing ETGs.
Explanation of power law behavior of autoregressive conditional duration processes based on the random multiplicative process

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2004-04-01

Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
Explanation of power law behavior of autoregressive conditional duration processes based on the random multiplicative process.

PubMed

Sato, Aki-Hiro

2004-04-01

Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
The power laws of nanoscale forces in ambient conditions

NASA Astrophysics Data System (ADS)

Chiesa, Matteo; Santos, Sergio; Lai, Chia-Yun

Power laws are ubiquitous in the physical sciences and indispensable to qualitatively and quantitatively describe physical phenomena. A nanoscale force law that accurately describes the phenomena observed in ambient conditions at several nm or fractions of a nm above a surface however is still lacking. Here we report a power law derived from experimental data and describing the interaction between an atomic force microscope AFM tip modelled as a sphere and a surface in ambient conditions. By employing a graphite surface as a model system the resulting effective power is found to be a function of the tip radius and the distance. The data suggest a nano to mesoscale transition in the power law that results in relative agreement with the distance-dependencies predicted by the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only
Star formation in the outskirts of DDO 154: A top-light IMF in a nearly dormant disc

NASA Astrophysics Data System (ADS)

Watts, Adam B.; Meurer, Gerhardt R.; Lagos, Claudia D. P.; Bruzzese, Sarah M.; Kroupa, Pavel; Jerabkova, Tereza

2018-04-01

We present optical photometry of Hubble Space Telescope (HST) ACS/WFC data of the resolved stellar populations in the outer disc of the dwarf irregular galaxy DDO 154. The photometry reveals that young main sequence stars are almost absent from the outermost HI disc. Instead, most are clustered near the main stellar component of the galaxy. We constrain the stellar initial mass function (IMF) by comparing the luminosity function of the main sequence stars to simulated stellar populations assuming a constant star formation rate over the dynamical timescale. The best-fitting IMF is deficient in high mass stars compared to a canonical Kroupa IMF, with a best-fit slope α = -2.45 and upper mass limit MU = 16 M⊙. This top-light IMF is consistent with predictions of the Integrated Galaxy-wide IMF theory. Combining the HST images with HI data from The HI Nearby Galaxy Survey Treasury (THINGS) we determine the star formation law (SFL) in the outer disc. The fit has a power law exponent N = 2.92 ± 0.22 and zero point A = 4.47 ± 0.65 × 10-7 M⊙ yr-1 kpc-2. This is depressed compared to the Kennicutt-Schmidt Star Formation Law, but consistent with weak star formation observed in diffuse HI environments. Extrapolating the SFL over the outer disc implies that there could be significant star formation occurring that is not detectable in Hα. Last, we determine the Toomre stability parameter Q of the outer disc of DDO 154 using the THINGS HI rotation curve and velocity dispersion map. 72% of the HI in our field has Q ≤ 4 and this incorporates 96% of the observed MS stars. Hence 28% of the HI in the field is largely dormant.
Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steffen, J. H.; Baumbaugh, A.; Chou, A. S.

2010-12-31

We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
A self-consistent high- and low-frequency scattering model for cirrus

NASA Astrophysics Data System (ADS)

Baran, Anthony J.; Cotton, Richard; Havemann, Stephan; C.-Labonnote, Laurent; Marenco, Franco

2013-05-01

This paper demonstrates that an ensemble model of cirrus ice crystals that follows observed mass-dimensional power laws can predict the scattering properties of cirrus across the electromagnetic spectrum, without the need for tailor made scattering models for particular regions of the spectrum. The ensemble model predicts a mass-dimensional power law of the following form, mass ∝ D2 (where D is the maximum dimension of the ice crystal). This same mass-dimensional power law is applied across the spectrum to predict the particle size distribution (PSD) using a moment estimation parameterization of the PSD. The PSD parameterization predicts the original PSD, using in-situ estimates (bulk measurements) of the ice water content (IWC) and measurements of the in-cloud temperature; the measurements were obtained from a number of mid-latitude cirrus cases, which occurred over the U.K. during the winter and spring of 2010. It is demonstrated that the ensemble model predicts lidar backscatter estimates, at 0.355 μm, of the volume extinction coefficient and total solar optical depth to within current experimental uncertainties, hyperspectral brightness temperature measurements of the terrestrial region (800 cm-1 - 1200 cm-1) to generally well within ±1 K in the window regions, and the 35 GHz radar reflectivity to within ±2 dBZ. Therefore, for simulation of satellite radiances within general circulation models, and retrieval of cirrus properties, scattering models, which are demonstrated to be physically consistent across the electromagnetic spectrum, should be preferred.
Correction to the Beer-Lambert-Bouguer law for optical absorption.

PubMed

Abitan, Haim; Bohr, Henrik; Buchhave, Preben

2008-10-10

The Beer-Lambert-Bouguer absorption law, known as Beer's law for absorption in an optical medium, is precise only at power densities lower than a few kW. At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission. In previous models that considered those processes, an analytical expression for the absorption law could not be obtained. We show here that by utilizing the Lambert W-function, the two-level energy rate equation model is solved analytically, and this leads into a general absorption law that is exact because it accounts for absorption as well as stimulated and spontaneous emission. The general absorption law reduces to Beer's law at low power densities. A criterion for its application is given along with experimental examples. (c) 2008 Optical Society of America
Beta Function Quintessence Cosmological Parameters and Fundamental Constants I: Power and Inverse Power Law Dark Energy Potentials

NASA Astrophysics Data System (ADS)

Thompson, Rodger I.

2018-04-01

This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar ϕ with respect to the natural log of the scale factor a, β (φ )=d φ /d ln (a). Once the beta function is specified, modulo a boundary condition, the evolution of the scalar ϕ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated "beta potential" is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are that are not calculable using only the model action. As an example this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that ΛCDM is part of the family of quintessence cosmology power law potentials with a power of zero.
Beta function quintessence cosmological parameters and fundamental constants - I. Power and inverse power law dark energy potentials

NASA Astrophysics Data System (ADS)

Thompson, Rodger I.

2018-07-01

This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar φ with respect to the natural log of the scale factor a, β (φ)=d φ/d ln (a). Once the beta function is specified, modulo a boundary condition, the evolution of the scalar φ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated `beta potential' is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are not calculable using only the model action. As an example, this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that Λ cold dark matter is part of the family of quintessence cosmology power-law potentials with a power of zero.
Vibration suppression of planar truss structures utilizing uniform damping control

NASA Technical Reports Server (NTRS)

Andersen, G. C.; Silverberg, L. M.

1986-01-01

A variety of methods has been devised for vibrational control of a structure using both passive and active controls. Presented in this paper is a relatively new method for vibration suppression, uniform damping control. This method consists of implementing a control law which tends to dampen each vibrational mode of the structure at the same desirable exponential rate. The unique aspects of this method are that the control law is not explicitly dependent on the structural stiffness, the control forces are directly proportional to the distribution of the structural mass, and the control law is natural and decentralized. The control law was applied to a flexible planar truss structure and the various aspects of implementation of the control law examined are: actuator/sensor number, placement, and the impact of the actuator/sensor number and placement on the necessary control 'power' requirements such as peak power loads, total power requirements, etc. Also examined are the effects of using a limited number of active members in terms of the vibrational performance when compared with the 'ideal' distributed control law.
The Mass Distribution of Stellar-mass Black Holes

NASA Astrophysics Data System (ADS)

Farr, Will M.; Sravan, Niharika; Cantrell, Andrew; Kreidberg, Laura; Bailyn, Charles D.; Mandel, Ilya; Kalogera, Vicky

2011-11-01

We perform a Bayesian analysis of the mass distribution of stellar-mass black holes using the observed masses of 15 low-mass X-ray binary systems undergoing Roche lobe overflow and 5 high-mass, wind-fed X-ray binary systems. Using Markov Chain Monte Carlo calculations, we model the mass distribution both parametrically—as a power law, exponential, Gaussian, combination of two Gaussians, or log-normal distribution—and non-parametrically—as histograms with varying numbers of bins. We provide confidence bounds on the shape of the mass distribution in the context of each model and compare the models with each other by calculating their relative Bayesian evidence as supported by the measurements, taking into account the number of degrees of freedom of each model. The mass distribution of the low-mass systems is best fit by a power law, while the distribution of the combined sample is best fit by the exponential model. This difference indicates that the low-mass subsample is not consistent with being drawn from the distribution of the combined population. We examine the existence of a "gap" between the most massive neutron stars and the least massive black holes by considering the value, M 1%, of the 1% quantile from each black hole mass distribution as the lower bound of black hole masses. Our analysis generates posterior distributions for M 1%; the best model (the power law) fitted to the low-mass systems has a distribution of lower bounds with M 1%>4.3 M sun with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M 1%>4.5 M sun with 90% confidence. We conclude that our sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the lower bound on black hole masses. Our results on the low-mass sample are in qualitative agreement with those of Ozel et al., although our broad model selection analysis more reliably reveals the best-fit quantitative description of the underlying mass distribution. The results on the combined sample of low- and high-mass systems are in qualitative agreement with Fryer & Kalogera, although the presence of a mass gap remains theoretically unexplained.
Low-Energy Impacts onto Lunar Regolith Simulant

NASA Astrophysics Data System (ADS)

Seward, Laura M.; Colwell, J.; Mellon, M.; Stemm, B.

2012-10-01

Low-Energy Impacts onto Lunar Regolith Simulant Laura M. Seward1, Joshua E. Colwell1, Michael T. Mellon2, and Bradley A. Stemm1, 1Department of Physics, University of Central Florida, Orlando, Florida, 2Southwest Research Institute, Boulder, Colorado. Impacts and cratering in space play important roles in the formation and evolution of planetary bodies. Low-velocity impacts and disturbances to planetary regolith are also a consequence of manned and robotic exploration of planetary bodies such as the Moon, Mars, and asteroids. We are conducting a program of laboratory experiments to study low-velocity impacts of 1 to 5 m/s into JSC-1 lunar regolith simulant, JSC-Mars-1 Martian regolith simulant, and silica targets under 1 g. We use direct measurement of ejecta mass and high-resolution video tracking of ejecta particle trajectories to derive ejecta mass velocity distributions. Additionally, we conduct similar experiments under microgravity conditions in a laboratory drop tower and on parabolic aircraft with velocities as low as 10 cm/s. We wish to characterize and understand the collision parameters that control the outcome of low-velocity impacts into regolith, including impact velocity, impactor mass, target shape and size distribution, regolith depth, target relative density, and crater depth, and to experimentally determine the functional dependencies of the outcomes of low-velocity collisions (ejecta mass and ejecta velocities) on the controlling parameters of the collision. We present results from our ongoing study showing the positive correlation between impact energy and ejecta mass. The total ejecta mass is also dependent on the packing density (porosity) of the regolith. We find that ejecta mass velocity fits a power-law or broken power-law distribution. Our goal is to understand the physics of ejecta production and regolith compaction in low-energy impacts and experimentally validate predictive models for dust flow and deposition. We will present our results from one-g and microgravity impact experiments.
Mass distribution of orbiting man-made space debris

NASA Technical Reports Server (NTRS)

Bess, T. D.

1975-01-01

Three ways of producing space debris were considered, and data were analyzed to determine mass distributions for man-made space debris. Hypervelocity (3.0 to 4.5 km/sec) projectile impact with a spacecraft wall, high intensity explosions and low intensity explosions were studied. For hypervelocity projectile impact of a spacecraft wall, the number of fragments fits a power law. The number of fragments for both high intensity and low intensity explosions fits an exponential law. However, the number of fragments produced by low intensity explosions is much lower than the number of fragments produced by high intensity explosions. Fragment masses down to 10 to the -7 power gram were produced from hypervelocity impact, but the smallest fragment mass resulting from an explosion appeared to be about 10 mg. Velocities of fragments resulting from hypervelocity impact were about 10 m/sec, and those from low intensity explosions were about 100 m/sec. Velocities of fragments from high intensity explosions were about 3 km/sec.
Mapping the core mass function to the initial mass function

NASA Astrophysics Data System (ADS)

Guszejnov, Dávid; Hopkins, Philip F.

2015-07-01

It has been shown that fragmentation within self-gravitating, turbulent molecular clouds (`turbulent fragmentation') can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the initial mass function (IMF). First, a high-mass power-law scaling very close to the Salpeter slope, which is a generic consequence of the scale-free nature of turbulence and self-gravity. We predict the IMF slope (-2.3) is slightly steeper than the CMF slope (-2.1), owing to the slower collapse and easier fragmentation of large cores. Secondly, a turnover mass, which is set by a combination of the CMF turnover mass (a couple solar masses, determined by the `sonic scale' of galactic turbulence, and so weakly dependent on galaxy properties), and the equation of state (EOS). A `soft' EOS with polytropic index γ < 1.0 predicts that the IMF slope becomes `shallow' below the sonic scale, but fails to produce the full turnover observed. An EOS, which becomes `stiff' at sufficiently low surface densities Σgas ˜ 5000 M⊙ pc-2, and/or models, where each collapsing core is able to heat and effectively stiffen the EOS of a modest mass (˜0.02 M⊙) of surrounding gas, are able to reproduce the observed turnover. Such features are likely a consequence of more detailed chemistry and radiative feedback.
Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

NASA Technical Reports Server (NTRS)

Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye

1998-01-01

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.
A WEAK LENSING STUDY OF X-RAY GROUPS IN THE COSMOS SURVEY: FORM AND EVOLUTION OF THE MASS-LUMINOSITY RELATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leauthaud, Alexie; Finoguenov, Alexis; Cappelluti, Nico

2010-01-20

Measurements of X-ray scaling laws are critical for improving cosmological constraints derived with the halo mass function and for understanding the physical processes that govern the heating and cooling of the intracluster medium. In this paper, we use a sample of 206 X-ray-selected galaxy groups to investigate the scaling relation between X-ray luminosity (L{sub X}) and halo mass (M{sub 200}) where M{sub 200} is derived via stacked weak gravitational lensing. This work draws upon a broad array of multi-wavelength COSMOS observations including 1.64 degrees{sup 2} of contiguous imaging with the Advanced Camera for Surveys to a limiting magnitude of I{submore » F814W} = 26.5 and deep XMM-Newton/Chandra imaging to a limiting flux of 1.0 x 10{sup -15} erg cm{sup -2} s{sup -1} in the 0.5-2 keV band. The combined depth of these two data sets allows us to probe the lensing signals of X-ray-detected structures at both higher redshifts and lower masses than previously explored. Weak lensing profiles and halo masses are derived for nine sub-samples, narrowly binned in luminosity and redshift. The COSMOS data alone are well fit by a power law, M{sub 200} propor to (L{sub X}){sup a}lpha, with a slope of alpha = 0.66 +- 0.14. These results significantly extend the dynamic range for which the halo masses of X-ray-selected structures have been measured with weak gravitational lensing. As a result, tight constraints are obtained for the slope of the M-L{sub X} relation. The combination of our group data with previously published cluster data demonstrates that the M-L{sub X} relation is well described by a single power law, alpha = 0.64 +- 0.03, over two decades in mass, M{sub 200} approx 10{sup 13.5}-10{sup 15.5} h {sup -1}{sub 72} M{sub sun}. These results are inconsistent at the 3.7sigma level with the self-similar prediction of alpha = 0.75. We examine the redshift dependence of the M-L{sub X} relation and find little evidence for evolution beyond the rate predicted by self-similarity from z approx 0.25 to z approx 0.8.« less
Concentric layered Hermite scatterers

NASA Astrophysics Data System (ADS)

Astheimer, Jeffrey P.; Parker, Kevin J.

2018-05-01

The long wavelength limit of scattering from spheres has a rich history in optics, electromagnetics, and acoustics. Recently it was shown that a common integral kernel pertains to formulations of weak spherical scatterers in both acoustics and electromagnetic regimes. Furthermore, the relationship between backscattered amplitude and wavenumber k was shown to follow power laws higher than the Rayleigh scattering k2 power law, when the inhomogeneity had a material composition that conformed to a Gaussian weighted Hermite polynomial. Although this class of scatterers, called Hermite scatterers, are plausible, it may be simpler to manufacture scatterers with a core surrounded by one or more layers. In this case the inhomogeneous material property conforms to a piecewise continuous constant function. We demonstrate that the necessary and sufficient conditions for supra-Rayleigh scattering power laws in this case can be stated simply by considering moments of the inhomogeneous function and its spatial transform. This development opens an additional path for construction of, and use of scatterers with unique power law behavior.
Power law tails in phylogenetic systems.

PubMed

Qin, Chongli; Colwell, Lucy J

2018-01-23

Covariance analysis of protein sequence alignments uses coevolving pairs of sequence positions to predict features of protein structure and function. However, current methods ignore the phylogenetic relationships between sequences, potentially corrupting the identification of covarying positions. Here, we use random matrix theory to demonstrate the existence of a power law tail that distinguishes the spectrum of covariance caused by phylogeny from that caused by structural interactions. The power law is essentially independent of the phylogenetic tree topology, depending on just two parameters-the sequence length and the average branch length. We demonstrate that these power law tails are ubiquitous in the large protein sequence alignments used to predict contacts in 3D structure, as predicted by our theory. This suggests that to decouple phylogenetic effects from the interactions between sequence distal sites that control biological function, it is necessary to remove or down-weight the eigenvectors of the covariance matrix with largest eigenvalues. We confirm that truncating these eigenvectors improves contact prediction.
Power-law viscous materials for analogue experiments: New data on the rheology of highly-filled silicone polymers

NASA Astrophysics Data System (ADS)

Boutelier, D.; Schrank, C.; Cruden, A.

2008-03-01

The selection of appropriate analogue materials is a central consideration in the design of realistic physical models. We investigate the rheology of highly-filled silicone polymers in order to find materials with a power-law strain-rate softening rheology suitable for modelling rock deformation by dislocation creep and report the rheological properties of the materials as functions of the filler content. The mixtures exhibit strain-rate softening behaviour but with increasing amounts of filler become strain-dependent. For the strain-independent viscous materials, flow laws are presented while for strain-dependent materials the relative importance of strain and strain rate softening/hardening is reported. If the stress or strain rate is above a threshold value some highly-filled silicone polymers may be considered linear visco-elastic (strain independent) and power-law strain-rate softening. The power-law exponent can be raised from 1 to ˜3 by using mixtures of high-viscosity silicone and plasticine. However, the need for high shear strain rates to obtain the power-law rheology imposes some restrictions on the usage of such materials for geodynamic modelling. Two simple shear experiments are presented that use Newtonian and power-law strain-rate softening materials. The results demonstrate how materials with power-law rheology result in better strain localization in analogue experiments.

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski's Coagulation Equation with Inverse Power Law Kernels

NASA Astrophysics Data System (ADS)

Laurençot, Philippe

2018-03-01

Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel K is given by K(x,x_*)=2(x x_*)^{-α } , (x,x_*)\\in (0,∞)^2 , for some α >0.
Effects of variability of X-ray binaries on the X-ray luminosity functions of Milky Way

NASA Astrophysics Data System (ADS)

Islam, Nazma; Paul, Biswajit

2016-08-01

The X-ray luminosity functions of galaxies have become a useful tool for population studies of X-ray binaries in them. The availability of long term light-curves of X-ray binaries with the All Sky X-ray Monitors opens up the possibility of constructing X-ray luminosity functions, by also including the intensity variation effects of the galactic X-ray binaries. We have constructed multiple realizations of the X-ray luminosity functions (XLFs) of Milky Way, using the long term light-curves of sources obtained in the 2-10 keV energy band with the RXTE-ASM. The observed spread seen in the value of slope of both HMXB and LMXB XLFs are due to inclusion of variable luminosities of X-ray binaries in construction of these XLFs as well as finite sample effects. XLFs constructed for galactic HMXBs in the luminosity range 1036-1039 erg/sec is described by a power-law model with a mean power-law index of -0.48 and a spread due to variability of HMXBs as 0.19. XLFs constructed for galactic LMXBs in the luminosity range 1036-1039 erg/sec has a shape of cut-off power-law with mean power-law index of -0.31 and a spread due to variability of LMXBs as 0.07.
Power-law ansatz in complex systems: Excessive loss of information.

PubMed

Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming

2015-12-01

The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring.
The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2005-01-01

The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.
Nonlinear GARCH model and 1 / f noise

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Duality in Power-Law Localization in Disordered One-Dimensional Systems

NASA Astrophysics Data System (ADS)

Deng, X.; Kravtsov, V. E.; Shlyapnikov, G. V.; Santos, L.

2018-03-01

The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1 /ra . For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of a >0 . Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops (a <1 ) and short-range hops (a >1 ), in which the wave function amplitude falls off algebraically with the same power γ from the localization center.
A statistical physics view of pitch fluctuations in the classical music from Bach to Chopin: evidence for scaling.

PubMed

Liu, Lu; Wei, Jianrong; Zhang, Huishu; Xin, Jianhong; Huang, Jiping

2013-01-01

Because classical music has greatly affected our life and culture in its long history, it has attracted extensive attention from researchers to understand laws behind it. Based on statistical physics, here we use a different method to investigate classical music, namely, by analyzing cumulative distribution functions (CDFs) and autocorrelation functions of pitch fluctuations in compositions. We analyze 1,876 compositions of five representative classical music composers across 164 years from Bach, to Mozart, to Beethoven, to Mendelsohn, and to Chopin. We report that the biggest pitch fluctuations of a composer gradually increase as time evolves from Bach time to Mendelsohn/Chopin time. In particular, for the compositions of a composer, the positive and negative tails of a CDF of pitch fluctuations are distributed not only in power laws (with the scale-free property), but also in symmetry (namely, the probability of a treble following a bass and that of a bass following a treble are basically the same for each composer). The power-law exponent decreases as time elapses. Further, we also calculate the autocorrelation function of the pitch fluctuation. The autocorrelation function shows a power-law distribution for each composer. Especially, the power-law exponents vary with the composers, indicating their different levels of long-range correlation of notes. This work not only suggests a way to understand and develop music from a viewpoint of statistical physics, but also enriches the realm of traditional statistical physics by analyzing music.
Similarity of Turbulent Energy Scale Budget Equation of a Round Turbulent Jet

NASA Astrophysics Data System (ADS)

Sadeghi, Hamed; Lavoie, Philippe; Pollard, Andrew

2014-11-01

A novel extension to the similarity-based form of the transport equation for the second-order velocity structure function of <(δq) 2 > along the jet centreline (see Danaila et al., 2004) has been obtained. This new self-similar equation has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. According to this equation, the normalized third-order structure function can be uniquely determined when the normalized second-order structure function, the power-law exponent of and the decay rate constants of and are available. In addition, on the basis of the current similarity analysis, the similarity assumptions in combination with power-law decay of mean velocity (U ~(x -x0) - 1) are strong enough to imply power-law decay of fluctuations ( ~(x -x0) m). The similarity solutions are then tested against new experimental data, which were taken along the centreline of a round jet at ReD = 50 , 000 . For the present set of initial conditions, exhibits a power-law behaviour with m = - 1 . 83 . This work was supported by grants from NSERC (Canada).
Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.
Spatially associated clump populations in Rosette from CO and dust maps

NASA Astrophysics Data System (ADS)

Veltchev, Todor V.; Ossenkopf-Okada, Volker; Stanchev, Orlin; Schneider, Nicola; Donkov, Sava; Klessen, Ralf S.

2018-04-01

Spatial association of clumps from different tracers turns out to be a valuable tool to determine the physical properties of molecular clouds. It provides a reliable estimate for the X-factors, serves to trace the density of clumps seen in column densities only, and allows one to measure the velocity dispersion of clumps identified in dust emission. We study the spatial association between clump populations, extracted by use of the GAUSSCLUMPS technique from 12CO (1-0), 13CO (1-0) line maps and Herschel dust-emission maps of the star-forming region Rosette, and analyse their physical properties. All CO clumps that overlap with another CO or dust counterpart are found to be gravitationally bound and located in the massive star-forming filaments of the molecular cloud. They obey a single mass-size relation M_cl∝ R_cl^γ with γ ≃ 3 (implying constant mean density) and display virtually no velocity-size relation. We interpret their population as low-density structures formed through compression by converging flows and still not evolved under the influence of self-gravity. The high-mass parts of their clump mass functions are fitted by a power law dN_cl/d log M_cl∝ M_cl^{Γ } and display a nearly Salpeter slope Γ ˜ -1.3. On the other hand, clumps extracted from the dust-emission map exhibit a shallower mass-size relation with γ = 2.5 and mass functions with very steep slopes Γ ˜ -2.3 even if associated with CO clumps. They trace density peaks of the associated CO clumps at scales of a few tenths of pc where no single density scaling law should be expected.
The Importance of Physical Models for Deriving Dust Masses and Grain Size Distributions in Supernova Ejecta. I. Radiatively Heated Dust in the Crab Nebula

NASA Technical Reports Server (NTRS)

Temim, Tea; Dwek, Eli

2013-01-01

Recent far-infrared (IR) observations of supernova remnants (SNRs) have revealed significantly large amounts of newly condensed dust in their ejecta, comparable to the total mass of available refractory elements. The dust masses derived from these observations assume that all the grains of a given species radiate at the same temperature, regardless of the dust heating mechanism or grain radius. In this paper, we derive the dust mass in the ejecta of the Crab Nebula, using a physical model for the heating and radiation from the dust. We adopt a power-law distribution of grain sizes and two different dust compositions (silicates and amorphous carbon), and calculate the heating rate of each dust grain by the radiation from the pulsar wind nebula. We find that the grains attain a continuous range of temperatures, depending on their size and composition. The total mass derived from the best-fit models to the observed IR spectrum is 0.019-0.13 Solar Mass, depending on the assumed grain composition. We find that the power-law size distribution of dust grains is characterized by a power-law index of 3.5-4.0 and a maximum grain size larger than 0.1 micron. The grain sizes and composition are consistent with what is expected for dust grains formed in a Type IIP supernova (SN). Our derived dust mass is at least a factor of two less than the mass reported in previous studies of the Crab Nebula that assumed more simplified two-temperature models. These models also require a larger mass of refractory elements to be locked up in dust than was likely available in the ejecta. The results of this study show that a physical model resulting in a realistic distribution of dust temperatures can constrain the dust properties and affect the derived dust masses. Our study may also have important implications for deriving grain properties and mass estimates in other SNRs and for the ultimate question of whether SNe are major sources of dust in the Galactic interstellar medium and in external galaxies.
Mass Incarceration and the Making of Citizens

ERIC Educational Resources Information Center

Justice, Benjamin

2014-01-01

Like laws for formal education, laws for crime and punishment shape the relationship between the citizen and the state. They could, in fact, be equally powerful in building or breaking the civic spirit. In the past three decades, a revolution has occurred in the United States that is as insidious as it is unprecedented: the rise of the American…
Power Laws are Disguised Boltzmann Laws

NASA Astrophysics Data System (ADS)

Richmond, Peter; Solomon, Sorin

Using a previously introduced model on generalized Lotka-Volterra dynamics together with some recent results for the solution of generalized Langevin equations, we derive analytically the equilibrium mean field solution for the probability distribution of wealth and show that it has two characteristic regimes. For large values of wealth, it takes the form of a Pareto style power law. For small values of wealth, w<=wm, the distribution function tends sharply to zero. The origin of this law lies in the random multiplicative process built into the model. Whilst such results have been known since the time of Gibrat, the present framework allows for a stable power law in an arbitrary and irregular global dynamics, so long as the market is ``fair'', i.e., there is no net advantage to any particular group or individual. We further show that the dynamics of relative wealth is independent of the specific nature of the agent interactions and exhibits a universal character even though the total wealth may follow an arbitrary and complicated dynamics. In developing the theory, we draw parallels with conventional thermodynamics and derive for the system some new relations for the ``thermodynamics'' associated with the Generalized Lotka-Volterra type of stochastic dynamics. The power law that arises in the distribution function is identified with new additional logarithmic terms in the familiar Boltzmann distribution function for the system. These are a direct consequence of the multiplicative stochastic dynamics and are absent for the usual additive stochastic processes.
The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. I. The Role of Self-gravity

NASA Astrophysics Data System (ADS)

Simon, Jacob B.; Armitage, Philip J.; Li, Rixin; Youdin, Andrew N.

2016-05-01

We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for the Athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self-gravitating solid particles. Upon employment of our algorithm to planetesimal formation simulations, we find that (when a direct comparison is possible) the Athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques. In particular, the gravitational collapse of streaming-initiated clumps leads to an initial planetesimal mass function that is well-represented by a power law, {dN}/{{dM}}p\\propto {M}p-p, with p≃ 1.6+/- 0.1, which equates to a differential size distribution of {dN}/{{dR}}p\\propto {R}p-q, with q≃ 2.8+/- 0.1. We find no significant trends with resolution from a convergence study of up to 5123 grid zones and {N}{{par}}≈ 1.5× {10}8 particles. Likewise, the power-law slope appears indifferent to changes in the relative strength of self-gravity and tidal shear, and to the time when (for reasons of numerical economy) self-gravity is turned on, though the strength of these claims is limited by small number statistics. For a typically assumed radial distribution of minimum mass solar nebula solids (assumed here to have dimensionless stopping time τ =0.3), our results support the hypothesis that bodies on the scale of large asteroids or Kuiper Belt Objects could have formed as the high-mass tail of a primordial planetesimal population.
DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K., E-mail: lzhao@fit.edu

2016-04-10

A double power law or a power law with exponential rollover at a few to tens of MeV nucleon{sup −1} of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochasticmore » approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon{sup −1} is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.« less
Properties of Dust Obscured Galaxies in the Nep-Deep Field

NASA Astrophysics Data System (ADS)

Oi, Nagisa; Matsuhara, Hideo; Pearson, Chris; Buat, Veronique; Burgarella, Denis; Malkan, Matt; Miyaji, Takamitsu; AKARI-NEP Team

2017-03-01

We selected 47 DOGs at z∼1.5 using optical R (or r^{'}), AKARI 18 μm, and 24 μm color in the AKARI North Ecliptic Pole (NEP) Deep survey field. Using the colors among 3, 4, 7, and 9μm, we classified them into 3 groups; bump DOGs (23 sources), power-law DOGs (16 sources), and unknown DOGs (8 sources). We built spectral energy distributions (SEDs) with optical to far-infrared photometric data and investigated their properties using SED fitting method. We found that AGN activity such as a AGN contribution to the infrared luminosity and a Chandra detection rate for bump and power-law DOGs are significantly different, while stellar component properties like a stellar mass and a star-formation rate are similar to each other. A specific star-formation rate range of power-law DOGs is slightly higher than that of bump DOGs with wide overlap. Herschel/PACS detection rates are almost the same between bump and power-law DOGs. On the other hand SPIRE detection rates show large differences between bump and power-law DOGs. These results might be explained by differences in dust temperatures. Both groups of DOGs host hot and/or warm dust (∼ 50 Kelvin), and many bump DOGs contain cooler dust (≤ 30 Kelvin)
OGLE-2017-BLG-1434Lb: Eighth q<1×10-4 Mass-Ratio Microlens Planet Confirms Turnover in Planet Mass-Ratio Function

NASA Astrophysics Data System (ADS)

Udalski, A.; Ryu, Y.-H.; Sajadian, S.; Gould, A.; Mrǎłz, P.; Poleski, R.; Szymański, M. K.; Skowron, J.; Soszyński, I.; Kozłowski, S.; Pietrukowicz, P.; Ulaczyk, K.; Pawlak, M.; Rybicki, K.; Iwanek, P.; Albrow, M. D.; Chung, S.-J.; Han, C.; Hwang, K.-H.; Jung, Y., K.; Shin, I.-G.; Shvartzvald, Y.; Yee, J. C.; Zang, W.; Zhu, W.; Cha, S.-M.; Kim, D.-J.; Kim, H.-W.; Kim, S.-L.; Lee, C.-U.; Lee, D.-J.; Lee, Y.; Park, B.-G.; Pogge, R. W.; Bozza, V.; Dominik, M.; Helling, C.; Hundertmark, M.; Jørgensen, U. G.; Longa-Peña, P.; Lowry, S.; Burgdorf, M.; Campbell-White, J.; Ciceri, S.; Evans, D.; Figuera Jaimes, R.; Fujii, Y. I.; Haikala, L. K.; Henning, T.; Hinse, T. C.; Mancini, L.; Peixinho, N.; Rahvar, S.; Rabus, M.; Skottfelt, J.; Snodgrass, C.; Southworth, J.; von Essen, C.

2018-03-01

We report the discovery of a cold Super-Earth planet (mp=4.4±0.5 M⊙) orbiting a low-mass (M=0.23±0.03) M⊙ dwarf at projected separation a⊥=1.18±0.10 a.u., i.e., about 1.9 times the distance the snow line. The system is quite nearby for a microlensing planet, DL=0.86±0.09 kpc. Indeed, it was the large lens-source relative parallax πrel=1.0 mas (combined with the low mass M) that gave rise to the large, and thus well-measured, "microlens parallax" πE∝(πrel/M)1/2 that enabled these precise measurements. OGLE-2017-BLG-1434Lb is the eighth microlensing planet with planet-host mass ratio q<1×10-4. We apply a new planet-detection sensitivity method, which is a variant of "V/Vmax", to seven of these eight planets to derive the mass-ratio function in this regime. We find dN/d lnq ∝ qp, with p=1.05+0.78-0.68, which confirms the "turnover" in the mass function found by Suzuki et al. relative to the power law of opposite sign n=-0.93±0.13 at higher mass ratios q≳2×10-4. We combine our result with that of Suzuki et al. to obtain p=0.73+0.42-0.34.
Stochastic ontogenetic growth model

NASA Astrophysics Data System (ADS)

West, B. J.; West, D.

2012-02-01

An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
A CONNECTION BETWEEN PLASMA CONDITIONS NEAR BLACK HOLE EVENT HORIZONS AND OUTFLOW PROPERTIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koljonen, K. I. I.; Russell, D. M.; Bernardini, F.

Accreting black holes are responsible for producing the fastest, most powerful outflows of matter in the universe. The formation process of powerful jets close to black holes is poorly understood, and the conditions leading to jet formation are currently hotly debated. In this paper, we report an unambiguous empirical correlation between the properties of the plasma close to the black hole and the particle acceleration properties within jets launched from the central regions of accreting stellar-mass and supermassive black holes. In these sources the emission of the plasma near the black hole is characterized by a power law at X-raymore » energies during times when the jets are produced. We find that the photon index of this power law, which gives information on the underlying particle distribution, correlates with the characteristic break frequency in the jet spectrum, which is dependent on magnetohydrodynamical processes in the outflow. The observed range in break frequencies varies by five orders of magnitude in sources that span nine orders of magnitude in black hole mass, revealing a similarity of jet properties over a large range of black hole masses powering these jets. This correlation demonstrates that the internal properties of the jet rely most critically on the conditions of the plasma close to the black hole, rather than other parameters such as the black hole mass or spin, and will provide a benchmark that should be reproduced by the jet formation models.« less
Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence

USDA-ARS?s Scientific Manuscript database

The binary power law (BPL) has been successfully used to characterize heterogeneity (over dispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial...

Effects of overlapping electric double layer on mass transport of a macro-solute across porous wall of a micro/nanochannel for power law fluid.

PubMed

Bhattacharjee, Saikat; Mondal, Mrinmoy; De, Sirshendu

2017-05-01

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye-Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential -73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Primary Visual Cortex Scales Individual's Perceived Brightness with Power Function: Inner Psychophysics with fMRI

ERIC Educational Resources Information Center

Tsubomi, Hiroyuki; Ikeda, Takashi; Osaka, Naoyuki

2012-01-01

Perceived brightness is well described by Stevens' power function (S. S. Stevens, 1957, On the psychophysical law, "Psychological Review", Vol. 64, pp. 153-181), with a power exponent of 0.33 (the cubic-root function of luminance). The power exponent actually varies across individuals, yet little is known about neural substrates underlying this…
Laboratory constraints on chameleon dark energy and power-law fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steffen, Jason H.; /Fermilab; Upadhye, Amol

2010-10-01

We report results from the GammeV Chameleon Afterglow Search - a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Subaru Weak-lensing Survey of Dark Matter Subhalos in the Coma Cluster: Subhalo Mass Function and Statistical Properties

NASA Astrophysics Data System (ADS)

Okabe, Nobuhiro; Futamase, Toshifumi; Kajisawa, Masaru; Kuroshima, Risa

2014-04-01

We present a 4 deg2 weak gravitational lensing survey of subhalos in the very nearby Coma cluster using the Subaru/Suprime-Cam. The large apparent size of cluster subhalos allows us to measure the mass of 32 subhalos detected in a model-independent manner, down to the order of 10-3 of the virial mass of the cluster. Weak-lensing mass measurements of these shear-selected subhalos enable us to investigate subhalo properties and the correlation between subhalo masses and galaxy luminosities for the first time. The mean distortion profiles stacked over subhalos show a sharply truncated feature which is well-fitted by a Navarro-Frenk-White (NFW) mass model with the truncation radius, as expected due to tidal destruction by the main cluster. We also found that subhalo masses, truncation radii, and mass-to-light ratios decrease toward the cluster center. The subhalo mass function, dn/dln M sub, in the range of 2 orders of magnitude in mass, is well described by a single power law or a Schechter function. Best-fit power indices of 1.09^{+0.42}_{-0.32} for the former model and 0.99_{-0.23}^{+0.34} for the latter, are in remarkable agreement with slopes of ~0.9-1.0 predicted by the cold dark matter paradigm. The tangential distortion signals in the radial range of 0.02-2 h -1 Mpc from the cluster center show a complex structure which is well described by a composition of three mass components of subhalos, the NFW mass distribution as a smooth component of the main cluster, and a lensing model from a large scale structure behind the cluster. Although the lensing signals are 1 order of magnitude lower than those for clusters at z ~ 0.2, the total signal-to-noise ratio, S/N = 13.3, is comparable, or higher, because the enormous number of background source galaxies compensates for the low lensing efficiency of the nearby cluster. Based on data collected from the Subaru Telescope and obtained from SMOKA, operated by the Astronomy Data Center, National Astronomical Observatory of Japan.
CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.

2013-09-01

Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and stellar dynamos. This qualitative agreement fuels the idea that both numerical models and astrophysical objects may operate in the same asymptotic regime of dynamics. This can be tested by exploring the scaling behavior of the models. For convection-driven incompressible spherical shell dynamos with constant material properties, scaling laws had been established previously that relate flow velocity and magnetic field strength to the available power. Here we analyzemore » 273 direct numerical simulations using the anelastic approximation, involving also cases with radius-dependent magnetic, thermal, and viscous diffusivities. These better represent conditions in gas giant planets and low-mass stars compared to Boussinesq models. Our study provides strong support for the hypothesis that both mean velocity and mean magnetic field strength scale as a function of the power generated by buoyancy forces in the same way for a wide range of conditions.« less
Dimensional crossover in fragmentation

NASA Astrophysics Data System (ADS)

Sotolongo-Costa, Oscar; Rodriguez, Arezky H.; Rodgers, G. J.

2000-11-01

Experiments in which thick clay plates and glass rods are fractured have revealed different behavior of fragment mass distribution function in the small and large fragment regions. In this paper we explain this behavior using non-extensive Tsallis statistics and show how the crossover between the two regions is caused by the change in the fragments’ dimensionality during the fracture process. We obtain a physical criterion for the position of this crossover and an expression for the change in the power-law exponent between the small and large fragment regions. These predictions are in good agreement with the experiments on thick clay plates.
An excess of massive stars in the local 30 Doradus starburst

NASA Astrophysics Data System (ADS)

Schneider, F. R. N.; Sana, H.; Evans, C. J.; Bestenlehner, J. M.; Castro, N.; Fossati, L.; Gräfener, G.; Langer, N.; Ramírez-Agudelo, O. H.; Sabín-Sanjulián, C.; Simón-Díaz, S.; Tramper, F.; Crowther, P. A.; de Koter, A.; de Mink, S. E.; Dufton, P. L.; Garcia, M.; Gieles, M.; Hénault-Brunet, V.; Herrero, A.; Izzard, R. G.; Kalari, V.; Lennon, D. J.; Maíz Apellániz, J.; Markova, N.; Najarro, F.; Podsiadlowski, Ph.; Puls, J.; Taylor, W. D.; van Loon, J. Th.; Vink, J. S.; Norman, C.

2018-01-01

The 30 Doradus star-forming region in the Large Magellanic Cloud is a nearby analog of large star-formation events in the distant universe. We determined the recent formation history and the initial mass function (IMF) of massive stars in 30 Doradus on the basis of spectroscopic observations of 247 stars more massive than 15 solar masses (M☉). The main episode of massive star formation began about 8 million years (My) ago, and the star-formation rate seems to have declined in the last 1 My. The IMF is densely sampled up to 200 M☉ and contains 32 ± 12% more stars above 30 M☉ than predicted by a standard Salpeter IMF. In the mass range of 15 to 200 M☉, the IMF power-law exponent is 1.90‑0.26+0.37, shallower than the Salpeter value of 2.35.
An excess of massive stars in the local 30 Doradus starburst.

PubMed

Schneider, F R N; Sana, H; Evans, C J; Bestenlehner, J M; Castro, N; Fossati, L; Gräfener, G; Langer, N; Ramírez-Agudelo, O H; Sabín-Sanjulián, C; Simón-Díaz, S; Tramper, F; Crowther, P A; de Koter, A; de Mink, S E; Dufton, P L; Garcia, M; Gieles, M; Hénault-Brunet, V; Herrero, A; Izzard, R G; Kalari, V; Lennon, D J; Maíz Apellániz, J; Markova, N; Najarro, F; Podsiadlowski, Ph; Puls, J; Taylor, W D; van Loon, J Th; Vink, J S; Norman, C

2018-01-05

The 30 Doradus star-forming region in the Large Magellanic Cloud is a nearby analog of large star-formation events in the distant universe. We determined the recent formation history and the initial mass function (IMF) of massive stars in 30 Doradus on the basis of spectroscopic observations of 247 stars more massive than 15 solar masses ([Formula: see text]). The main episode of massive star formation began about 8 million years (My) ago, and the star-formation rate seems to have declined in the last 1 My. The IMF is densely sampled up to 200 [Formula: see text] and contains 32 ± 12% more stars above 30 [Formula: see text] than predicted by a standard Salpeter IMF. In the mass range of 15 to 200 [Formula: see text], the IMF power-law exponent is [Formula: see text], shallower than the Salpeter value of 2.35. Copyright © 2018, American Association for the Advancement of Science.
Power law relationships for rain attenuation and reflectivity

NASA Technical Reports Server (NTRS)

Devasirvatham, D. M. J.; Hodge, D. B.

1978-01-01

The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.
Evolution of column density distributions within Orion A⋆

NASA Astrophysics Data System (ADS)

Stutz, A. M.; Kainulainen, J.

2015-05-01

We compare the structure of star-forming molecular clouds in different regions of Orion A to determine how the column density probability distribution function (N-PDF) varies with environmental conditions such as the fraction of young protostars. A correlation between the N-PDF slope and Class 0 protostar fraction has been previously observed in a low-mass star-formation region (Perseus); here we test whether a similar correlation is observed in a high-mass star-forming region. We used Herschel PACS and SPIRE cold dust emission observations to derive a column density map of Orion A. We used the Herschel Orion Protostar Survey catalog to accurately identify and classify the Orion A young stellar object content, including the cold and relatively short-lived Class 0 protostars (with a lifetime of ~0.14 Myr). We divided Orion A into eight independent regions of 0.25 square degrees (13.5 pc2); in each region we fit the N-PDF distribution with a power law, and we measured the fraction of Class 0 protostars. We used a maximum-likelihood method to measure the N-PDF power-law index without binning the column density data. We find that the Class 0 fraction is higher in regions with flatter column density distributions. We tested the effects of incompleteness, extinction-driven misclassification of Class 0 sources, resolution, and adopted pixel-scales. We show that these effects cannot account for the observed trend. Our observations demonstrate an association between the slope of the power-law N-PDF and the Class 0 fractions within Orion A. Various interpretations are discussed, including timescales based on the Class 0 protostar fraction assuming a constant star-formation rate. The observed relation suggests that the N-PDF can be related to an evolutionary state of the gas. If universal, such a relation permits evaluating the evolutionary state from the N-PDF power-law index at much greater distances than those accessible with protostar counts. Appendices are available in electronic form at http://www.aanda.orgThe N(H) map as a FITS file is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/577/L6
The Angular Correlation Function of Galaxies from Early Sloan Digital Sky Survey Data

NASA Astrophysics Data System (ADS)

Connolly, Andrew J.; Scranton, Ryan; Johnston, David; Dodelson, Scott; Eisenstein, Daniel J.; Frieman, Joshua A.; Gunn, James E.; Hui, Lam; Jain, Bhuvnesh; Kent, Stephen; Loveday, Jon; Nichol, Robert C.; O'Connell, Liam; Postman, Marc; Scoccimarro, Roman; Sheth, Ravi K.; Stebbins, Albert; Strauss, Michael A.; Szalay, Alexander S.; Szapudi, István; Tegmark, Max; Vogeley, Michael S.; Zehavi, Idit; Annis, James; Bahcall, Neta; Brinkmann, J.; Csabai, István; Doi, Mamoru; Fukugita, Masataka; Hennessy, G. S.; Hindsley, Robert; Ichikawa, Takashi; Ivezić, Željko; Kim, Rita S. J.; Knapp, Gillian R.; Kunszt, Peter; Lamb, D. Q.; Lee, Brian C.; Lupton, Robert H.; McKay, Timothy A.; Munn, Jeff; Peoples, John; Pier, Jeff; Rockosi, Constance; Schlegel, David; Stoughton, Christopher; Tucker, Douglas L.; Yanny, Brian; York, Donald G.

2002-11-01

The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local universe. In this paper we present some of the initial results on the angular two-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18
A NICER Look at the Aql X-1 Hard State

NASA Astrophysics Data System (ADS)

Bult, Peter; Arzoumanian, Zaven; Cackett, Edward M.; Chakrabarty, Deepto; Gendreau, Keith C.; Guillot, Sebastien; Homan, Jeroen; Jaisawal, Gaurava K.; Keek, Laurens; Kenyon, Steve; Lamb, Frederick K.; Ludlam, Renee; Mahmoodifar, Simin; Markwardt, Craig; Miller, Jon M.; Prigozhin, Gregory; Soong, Yang; Strohmayer, Tod E.; Uttley, Phil

2018-05-01

We report on a spectral-timing analysis of the neutron star low-mass X-ray binary (LMXB) Aql X-1 with the Neutron Star Interior Composition Explorer (NICER) on the International Space Station (ISS). Aql X-1 was observed with NICER during a dim outburst in 2017 July, collecting approximately 50 ks of good exposure. The spectral and timing properties of the source correspond to that of a (hard) extreme island state in the atoll classification. We find that the fractional amplitude of the low-frequency (<0.3 Hz) band-limited noise shows a dramatic turnover as a function of energy: it peaks at 0.5 keV with nearly 25% rms, drops to 12% rms at 2 keV, and rises to 15% rms at 10 keV. Through the analysis of covariance spectra, we demonstrate that band-limited noise exists in both the soft thermal emission and the power-law emission. Additionally, we measure hard time lags, indicating the thermal emission at 0.5 keV leads the power-law emission at 10 keV on a timescale of ∼100 ms at 0.3 Hz to ∼10 ms at 3 Hz. Our results demonstrate that the thermal emission in the hard state is intrinsically variable, and is driving the modulation of the higher energy power-law. Interpreting the thermal spectrum as disk emission, we find that our results are consistent with the disk propagation model proposed for accretion onto black holes.
Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise, and multifractality.

PubMed

Kendal, Wayne S; Jørgensen, Bent

2011-12-01

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality.
A Study of THT Cold Cores Population in the Star-Forming Region in Serpens

NASA Astrophysics Data System (ADS)

Fiorellino, Eleonora

2017-11-01

The purpose of this work is to produce the Core Mass Function (CMF) of the Serpens star-forming region and confront it with the Initial Mass Function (IMF), the statistical distribution of initial star mass. As Testi & Sergent (1998) discovered, the power-law index of the slope of the CMF is very close to the one of the Salpeter's IMF (Salpeter, 1955): dN/dM / M2.35. This strongly suggests that the stellar IMF results from the fragmentation process in turbulent cloud cores rather than from stellar accretion mechanisms and gives a huge contribute to undestanding the star formation. For this work, we started from the data delivered by the European satellite Herschel and produced the maps of the Serpens with Unimap code (Piazzo et al, 2015). Hence we obtained a core catalogue with two different softwares getsources (Men'shchikov et al, 2012) and CuTEx (Molinari et al, 2011) and we eliminated from it any source that is not a core. A full discussion of the cores physical propreties as well as the whole region is under preparation.
Density profiles of a self-gravitating lattice gas in one, two, and three dimensions

NASA Astrophysics Data System (ADS)

Bakhti, Benaoumeur; Boukari, Divana; Karbach, Michael; Maass, Philipp; Müller, Gerhard

2018-04-01

We consider a lattice gas in spaces of dimensionality D =1 ,2 ,3 . The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in D =3 , a logarithmic potential in D =2 , and a distance-independent force in D =1 . Under mild additional assumptions regarding symmetry and fluctuations we investigate equilibrium states of self-gravitating material clusters, in particular radial density profiles for closed and open systems. We present exact analytic results in several instances and high-precision numerical data in others. The density profile of a cluster with finite mass is found to exhibit exponential decay in D =1 and power-law decay in D =2 with temperature-dependent exponents in both cases. In D =2 the gas evaporates in a continuous transition at a nonzero critical temperature. We describe clusters of infinite mass in D =3 with a density profile consisting of three layers (core, shell, halo) and an algebraic large-distance asymptotic decay. In D =3 a cluster of finite mass can be stabilized at T >0 via confinement to a sphere of finite radius. In some parameter regime, the gas thus enclosed undergoes a discontinuous transition between distinct density profiles. For the free energy needed to identify the equilibrium state we introduce a construction of gravitational self-energy that works in all D for the lattice gas. The decay rate of the density profile of an open cluster is shown to transform via a stretched exponential for 1
Autocorrelation analysis for the unbiased determination of power-law exponents in single-quantum-dot blinking.

PubMed

Houel, Julien; Doan, Quang T; Cajgfinger, Thomas; Ledoux, Gilles; Amans, David; Aubret, Antoine; Dominjon, Agnès; Ferriol, Sylvain; Barbier, Rémi; Nasilowski, Michel; Lhuillier, Emmanuel; Dubertret, Benoît; Dujardin, Christophe; Kulzer, Florian

2015-01-27

We present an unbiased and robust analysis method for power-law blinking statistics in the photoluminescence of single nanoemitters, allowing us to extract both the bright- and dark-state power-law exponents from the emitters' intensity autocorrelation functions. As opposed to the widely used threshold method, our technique therefore does not require discriminating the emission levels of bright and dark states in the experimental intensity timetraces. We rely on the simultaneous recording of 450 emission timetraces of single CdSe/CdS core/shell quantum dots at a frame rate of 250 Hz with single photon sensitivity. Under these conditions, our approach can determine ON and OFF power-law exponents with a precision of 3% from a comparison to numerical simulations, even for shot-noise-dominated emission signals with an average intensity below 1 photon per frame and per quantum dot. These capabilities pave the way for the unbiased, threshold-free determination of blinking power-law exponents at the microsecond time scale.
Beyond Zipf's Law: The Lavalette Rank Function and Its Properties.

PubMed

Fontanelli, Oscar; Miramontes, Pedro; Yang, Yaning; Cocho, Germinal; Li, Wentian

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.
THE DEPENDENCE OF PRESTELLAR CORE MASS DISTRIBUTIONS ON THE STRUCTURE OF THE PARENTAL CLOUD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parravano, Antonio; Sanchez, Nestor; Alfaro, Emilio J.

2012-08-01

The mass distribution of prestellar cores is obtained for clouds with arbitrary internal mass distributions using a selection criterion based on the thermal and turbulent Jeans mass and applied hierarchically from small to large scales. We have checked this methodology by comparing our results for a log-normal density probability distribution function with the theoretical core mass function (CMF) derived by Hennebelle and Chabrier, namely a power law at large scales and a log-normal cutoff at low scales, but our method can be applied to any mass distributions representing a star-forming cloud. This methodology enables us to connect the parental cloudmore » structure with the mass distribution of the cores and their spatial distribution, providing an efficient tool for investigating the physical properties of the molecular clouds that give rise to the prestellar core distributions observed. Simulated fractional Brownian motion (fBm) clouds with the Hurst exponent close to the value H = 1/3 give the best agreement with the theoretical CMF derived by Hennebelle and Chabrier and Chabrier's system initial mass function. Likewise, the spatial distribution of the cores derived from our methodology shows a surface density of companions compatible with those observed in Trapezium and Ophiucus star-forming regions. This method also allows us to analyze the properties of the mass distribution of cores for different realizations. We found that the variations in the number of cores formed in different realizations of fBm clouds (with the same Hurst exponent) are much larger than the expected root N statistical fluctuations, increasing with H.« less
The Dependence of Prestellar Core Mass Distributions on the Structure of the Parental Cloud

NASA Astrophysics Data System (ADS)

Parravano, Antonio; Sánchez, Néstor; Alfaro, Emilio J.

2012-08-01

The mass distribution of prestellar cores is obtained for clouds with arbitrary internal mass distributions using a selection criterion based on the thermal and turbulent Jeans mass and applied hierarchically from small to large scales. We have checked this methodology by comparing our results for a log-normal density probability distribution function with the theoretical core mass function (CMF) derived by Hennebelle & Chabrier, namely a power law at large scales and a log-normal cutoff at low scales, but our method can be applied to any mass distributions representing a star-forming cloud. This methodology enables us to connect the parental cloud structure with the mass distribution of the cores and their spatial distribution, providing an efficient tool for investigating the physical properties of the molecular clouds that give rise to the prestellar core distributions observed. Simulated fractional Brownian motion (fBm) clouds with the Hurst exponent close to the value H = 1/3 give the best agreement with the theoretical CMF derived by Hennebelle & Chabrier and Chabrier's system initial mass function. Likewise, the spatial distribution of the cores derived from our methodology shows a surface density of companions compatible with those observed in Trapezium and Ophiucus star-forming regions. This method also allows us to analyze the properties of the mass distribution of cores for different realizations. We found that the variations in the number of cores formed in different realizations of fBm clouds (with the same Hurst exponent) are much larger than the expected root {\\cal N} statistical fluctuations, increasing with H.
Thermospheric mass density model error variance as a function of time scale

NASA Astrophysics Data System (ADS)

Emmert, J. T.; Sutton, E. K.

2017-12-01

In the increasingly crowded low-Earth orbit environment, accurate estimation of orbit prediction uncertainties is essential for collision avoidance. Poor characterization of such uncertainty can result in unnecessary and costly avoidance maneuvers (false positives) or disregard of a collision risk (false negatives). Atmospheric drag is a major source of orbit prediction uncertainty, and is particularly challenging to account for because it exerts a cumulative influence on orbital trajectories and is therefore not amenable to representation by a single uncertainty parameter. To address this challenge, we examine the variance of measured accelerometer-derived and orbit-derived mass densities with respect to predictions by thermospheric empirical models, using the data-minus-model variance as a proxy for model uncertainty. Our analysis focuses mainly on the power spectrum of the residuals, and we construct an empirical model of the variance as a function of time scale (from 1 hour to 10 years), altitude, and solar activity. We find that the power spectral density approximately follows a power-law process but with an enhancement near the 27-day solar rotation period. The residual variance increases monotonically with altitude between 250 and 550 km. There are two components to the variance dependence on solar activity: one component is 180 degrees out of phase (largest variance at solar minimum), and the other component lags 2 years behind solar maximum (largest variance in the descending phase of the solar cycle).

Implications of the Observed Ultraluminous X-Ray Source Luminosity Function

NASA Technical Reports Server (NTRS)

Swartz, Douglas A.; Tennant, Allyn; Soria, Roberto; Yukita, Mihoko

2012-01-01

We present the X-ray luminosity function (XLF) of ultraluminous X-ray (ULX) sources with 0.3-10.0 keV luminosities in excess of 10(sup 39) erg/s in a complete sample of nearby galaxies. The XLF shows a break or cut-off at high luminosities that deviates from its pure power law distribution at lower luminosities. The cut-off is at roughly the Eddington luminosity for a 90-140 solar mass accretor. We examine the effects on the observed XLF of sample biases, of small-number statistics (at the high luminosity end) and of measurement uncertainties. We consider the physical implications of the shape and normalization of the XLF. The XLF is also compared and contrasted to results of other recent surveys.
Impact fragmentation of polyurethane and polypropylene cylinder

NASA Astrophysics Data System (ADS)

Kishimura, Hiroaki; Noguchi, Daisuke; Preechasupanya, Worrayut; Matsumoto, Hitoshi

2013-11-01

The impact fragmentation of a bulk polyurethane elastomer (PU) and polypropylene (PP) cylinder have been investigated using a Cu plate projectile launched by a propellant gun at a velocity of 0.53-1.4 km/s. A projectile drills into a PU sample and forms a cavity in the sample. A small number of tiny fragments are formed. When the projectile smashes in at 1.4 km/s, the PU cylinder bursts and PU fragments form. On the other hand, a brittle fracture occurs on the PP cylinder. The mass of fragments from the PU sample generated at a lower impact velocity is distributed in the lognormal form, whereas the mass of fragments from the PU sample generated by a 1.4 km/s impact follows a power-law distribution. The fragment mass distribution of the PP sample generated at a lower impact velocity obeys the power-law form, whereas that generated at a higher impact velocity follows the lognormal form.
Photon Mass, Graviton Mass: Zero or Not?

NASA Astrophysics Data System (ADS)

Scharff Goldhaber, Alfred; Nieto, Michael Martin

2007-04-01

Testing for deviations from simple laws is a time-honored part of physics research. In electricity and magnetism the first approach to such testing, from the eighteenth century well into the twentieth, was to look for departures from -2 of the power of distance between two electric charges or two magnetic poles determining the force between them. Absent a particular length scale, this was a natural choice for parameterizing possible deviations from the simple and esthetic inverse square law. With the advent of relativity and quantum mechanics, and the realization that certain phenomena of light can be described in terms of photon particles, it became appealing to ask if these particles might have a non-zero mass, and Proca found the appropriate modification of the Maxwell equations. Despite the particle-motion origin of this idea, the most powerful way to constrain the size of a possible photon mass is by setting a lower bound on the Compton wavelength, by looking at static electric and especially magnetic fields over increasing length scales. For gravity similar statements apply, but graviton mass is theoretically questionable, and observed phenomena imply either additional sources or departures from Einstein's general relativity.
Layer-dependent Band Alignment and Work Function of Few-Layer Phosphorene

PubMed Central

Cai, Yongqing; Zhang, Gang; Zhang, Yong-Wei

2014-01-01

Using first-principles calculations, we study the electronic properties of few-layer phosphorene focusing on layer-dependent behavior of band gap, work function band alignment and carrier effective mass. It is found that few-layer phosphorene shows a robust direct band gap character, and its band gap decreases with the number of layers following a power law. The work function decreases rapidly from monolayer (5.16 eV) to trilayer (4.56 eV), and then slowly upon further increasing the layer number. Compared to monolayer phosphorene, there is a drastic decrease of hole effective mass along the ridge (zigzag) direction for bilayer phosphorene, indicating a strong interlayer coupling and screening effect. Our study suggests that 1). Few-layer phosphorene with a layer-dependent band gap and a robust direct band gap character is promising for efficient solar energy harvest. 2). Few-layer phosphorene outperforms monolayer counterpart in terms of a lighter carrier effective mass, a higher carrier density and a weaker scattering due to enhanced screening. 3). The layer-dependent band edges and work functions of few-layer phosphorene allow for modification of Schottky barrier with enhanced carrier injection efficiency. It is expected that few-layer phosphorene will present abundant opportunities for a plethora of new electronic applications. PMID:25327586
A catalogue of normalized intensity functions and polarization from a cloud of particles with a size distribution of alpha to the minus 4th power

NASA Technical Reports Server (NTRS)

Craven, P. D.; Gary, G. A.

1972-01-01

The Mie theory of light scattering by spheres was used to calculate the scattered intensity functions resulting from single scattering in a polydispersed collection of spheres. The distribution used behaves according to the inverse fourth power law; graphs and tables for the angular dependence of the intensity and polarization for this law are given. The effects of the particle size range and the integration increment are investigated.
Technology Directions for the 21st Century, volume 1

NASA Technical Reports Server (NTRS)

Crimi, Giles F.; Verheggen, Henry; McIntosh, William; Botta, Robert

1996-01-01

For several decades, semiconductor device density and performance have been doubling about every 18 months (Moore's Law). With present photolithography techniques, this rate can continue for only about another 10 years. Continued improvement will need to rely on newer technologies. Transition from the current micron range for transistor size to the nanometer range will permit Moore's Law to operate well beyond 10 years. The technologies that will enable this extension include: single-electron transistors; quantum well devices; spin transistors; and nanotechnology and molecular engineering. Continuation of Moore's Law will rely on huge capital investments for manufacture as well as on new technologies. Much will depend on the fortunes of Intel, the premier chip manufacturer, which, in turn, depend on the development of mass-market applications and volume sales for chips of higher and higher density. The technology drivers are seen by different forecasters to include video/multimedia applications, digital signal processing, and business automation. Moore's Law will affect NASA in the areas of communications and space technology by reducing size and power requirements for data processing and data fusion functions to be performed onboard spacecraft. In addition, NASA will have the opportunity to be a pioneering contributor to nanotechnology research without incurring huge expenses.
Not even wrong: A philosophical, historical and ultimately a scientific inquiry into the Schmidt Law

NASA Astrophysics Data System (ADS)

Madore, Barry F.; Carlson, Erika K.

2017-03-01

We introduce a novel approach to interpreting the well-known spatial correlation of gas densities with on-going star formation. Treated as a closed-loop process involving two physically distinct phases the data can be subdivided into regions that are active and those that are quiescent. The active regions can be distinguished by the presence of high-mass, short-lived, but recently-formed OB stars; the quiescent regions are marked by an absence of these stars and they are considered to be recovering from the last star-formation event and are re-collapsing. The relative (areal) frequencies of those two phases are directly proportional to the relative timescales. For four Local Group galaxies, NGC 6822, the Large & Small Magellanic Clouds, and M33, the cloud assembly/collapse timescales are all found to be monotonically decreasing power-law functions of density, with as yet to be explained differences.
Long memory behavior of returns after intraday financial jumps

NASA Astrophysics Data System (ADS)

Behfar, Stefan Kambiz

2016-11-01

In this paper, characterization of intraday financial jumps and time dynamics of returns after jumps is investigated, and will be analytically and empirically shown that intraday jumps are power-law distributed with the exponent 1 < μ < 2; in addition, returns after jumps show long-memory behavior. In the theory of finance, it is important to be able to distinguish between jumps and continuous sample path price movements, and this can be achieved by introducing a statistical test via calculating sums of products of returns over small period of time. In the case of having jump, the null hypothesis for normality test is rejected; this is based on the idea that returns are composed of mixture of normally-distributed and power-law distributed data (∼ 1 /r 1 + μ). Probability of rejection of null hypothesis is a function of μ, which is equal to one for 1 < μ < 2 within large intraday sample size M. To test this idea empirically, we downloaded S&P500 index data for both periods of 1997-1998 and 2014-2015, and showed that the Complementary Cumulative Distribution Function of jump return is power-law distributed with the exponent 1 < μ < 2. There are far more jumps in 1997-1998 as compared to 2015-2016; and it represents a power law exponent in 2015-2016 greater than one in 1997-1998. Assuming that i.i.d returns generally follow Poisson distribution, if the jump is a causal factor, high returns after jumps are the effect; we show that returns caused by jump decay as power-law distribution. To test this idea empirically, we average over the time dynamics of all days; therefore the superposed time dynamics after jump represent a power-law, which indicates that there is a long memory with a power-law distribution of return after jump.
Simulating star clusters with the AMUSE software framework. I. Dependence of cluster lifetimes on model assumptions and cluster dissolution modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitehead, Alfred J.; McMillan, Stephen L. W.; Vesperini, Enrico

2013-12-01

We perform a series of simulations of evolving star clusters using the Astrophysical Multipurpose Software Environment (AMUSE), a new community-based multi-physics simulation package, and compare our results to existing work. These simulations model a star cluster beginning with a King model distribution and a selection of power-law initial mass functions and contain a tidal cutoff. They are evolved using collisional stellar dynamics and include mass loss due to stellar evolution. After studying and understanding that the differences between AMUSE results and results from previous studies are understood, we explored the variation in cluster lifetimes due to the random realization noisemore » introduced by transforming a King model to specific initial conditions. This random realization noise can affect the lifetime of a simulated star cluster by up to 30%. Two modes of star cluster dissolution were identified: a mass evolution curve that contains a runaway cluster dissolution with a sudden loss of mass, and a dissolution mode that does not contain this feature. We refer to these dissolution modes as 'dynamical' and 'relaxation' dominated, respectively. For Salpeter-like initial mass functions, we determined the boundary between these two modes in terms of the dynamical and relaxation timescales.« less
Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to extend these ideas to situations where fixed points may not exist — either due to "monotone" flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.
Geomorphological and hydrological implications of a given hydraulic geometry relationship, beyond the power-law

NASA Astrophysics Data System (ADS)

Kim, JongChun; Paik, Kyungrock

2015-04-01

Channel geometry and hydraulic characteristics of a given river network, i.e., spatio-temporal variability of width, depth, and velocity, can be described as power functional relationships of flow discharge, named 'hydraulic geometry' (Leopold and Maddock, 1953). Many studies have focused on the implication of this power-law itself, i.e., self-similarity, and accordingly its exponents. Coefficients of the power functional relationships, on the contrary, have received little attention. They are often regarded as empirical constants, determined by 'best fitting' to the power-law without significant scientific implications. Here, we investigate and claim that power-law coefficients of hydraulic geometry relationships carry vital information of a given river system. We approach the given problem on the basis of 'basin hydraulic geometry' formulation (Stall and Fok, 1968) which decomposes power-law coefficients into more elementary constants. The linkage between classical power-law relationship (Leopold and Maddock, 1953) and the basin hydraulic geometry is provided by Paik and Kumar (2004). On the basis of this earlier study, it can be shown that coefficients and exponents of power-law hydraulic geometry are interrelated. In this sense, we argue that more elementary constants that constitute both exponents and coefficients carry important messages. In this presentation, we will demonstrate how these elementary constants vary over a wide range of catchments provided from Stall and Fok (1968) and Stall and Yang (1970). Findings of this study can provide new insights on fundamental understanding about hydraulic geometry relationships. Further, we expect that this understanding can help interpretation of hydraulic geometry relationship in the context of flood propagation through a river system as well. Keywords: Hydraulic geometry; Power-law; River network References Leopold, L. B., & Maddock, T. J. (1953). The hydraulic geometry of stream channels and some physiographic implications. U. S. Geological Survey Professional Paper, 252. Paik, K., & Kumar, P. (2004). Hydraulic geometry and the nonlinearity of the network instantaneous response, Water Resource Research, 40, W03602. Stall, J. B., & Fok, Y. S. (1968). Hydraulic geometry of Illinois streams. University of Illinois Water Resources Center Research Report, 15. Stall, J. B., & Yang, C. T. (1970). Hydraulic geometry of 12 selected stream systems of the United States. University of Illinois Water Resources Center Research Report, 32.
A family of models for spherical stellar systems

NASA Technical Reports Server (NTRS)

Tremaine, Scott; Richstone, Douglas O.; Byun, Yong-Ik; Dressler, Alan; Faber, S. M.; Grillmair, Carl; Kormendy, John; Lauer, Tod R.

1994-01-01

We describe a one-parameter family of models of stable sperical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts (rho propotional to r(exp -4)) and central power-law density cusps, rho proportional to r(exp 3-eta), 0 less than eta less than or = 3. The family contains the Jaffe (1983) and Hernquist (1990) models as special cases. We evaluate the surface brightness profile, the line-of-sight velocity dispersion profile, and the distribution function, and discuss analogs of King's core-fitting formula for determining mass-to-light ratio. We also generalize the models to a two-parameter family, in which the galaxy contains a central black hole; the second parameter is the mass of the black hole. Our models can be used to estimate the detectability of central black holes and the velocity-dispersion profiles of galaxies that contain central cusps, with or without a central black hole.
Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles

NASA Astrophysics Data System (ADS)

Donkov, Sava; Stefanov, Ivan Z.

2018-03-01

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a non-linear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to an equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.
Galaxies and gas in a cold dark matter universe

NASA Technical Reports Server (NTRS)

Katz, Neal; Hernquist, Lars; Weinberg, David H.

1992-01-01

We use a combined gravity/hydrodynamics code to simulate the formation of structure in a random 22 Mpc cube of a cold dark matter universe. Adiabatic compression and shocks heat much of the gas to temperatures of 10 exp 6 - 10 exp 7 K, but a fraction of the gas cools radiatively to about 10 exp 4 K and condenses into discrete, highly overdense lumps. We identify these lumps with galaxies. The high-mass end of their baryonic mass function fits the form of the observed galaxy luminosity function. They retain independent identities after their dark halos merge, so gravitational clustering produces groups of galaxies embedded in relatively smooth envelopes of hot gas and dark matter. The galaxy correlation function is approximately an r exp -2.1 power law from separations of 35 kpc to 7 Mpc. Galaxy fluctuations are biased relative to dark matter fluctuations by a factor b about 1.5. We find no significant 'velocity bias' between galaxies and dark matter particles. However, virial analysis of the simulation's richest group leads to an estimated Omega of about 0.3, even though the simulation adopts Omega = 1.
Modelling the luminosity function of long gamma-ray bursts using Swift and Fermi

NASA Astrophysics Data System (ADS)

Paul, Debdutta

2018-01-01

I have used a sample of long gamma-ray bursts (GRBs) common to both Swift and Fermi to re-derive the parameters of the Yonetoku correlation. This allowed me to self-consistently estimate pseudo-redshifts of all the bursts with unknown redshifts. This is the first time such a large sample of GRBs from these two instruments is used, both individually and in conjunction, to model the long GRB luminosity function. The GRB formation rate is modelled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass. An exponential cut-off power-law luminosity function fits the data reasonably well, with ν = 0.6 and Lb = 5.4 × 1052 ergs- 1, and does not require a cosmological evolution. In the case of a broken power law, it is required to incorporate a sharp evolution of the break given by Lb ∼ 0.3 × 1052(1 + z)2.90 erg s- 1, and the GRB formation efficiency (degenerate up to a beaming factor of GRBs) decreases with redshift as ∝ (1 + z)-0.80. However, it is not possible to distinguish between the two models. The derived models are then used as templates to predict the distribution of GRBs detectable by CZT Imager onboard AstroSat as a function of redshift and luminosity. This demonstrates that via a quick localization and redshift measurement of even a few CZT Imager GRBs, AstroSat will help in improving the statistics of GRBs both typical and peculiar.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Goudfrooij, Paul, E-mail: goudfroo@stsci.edu

We study mass functions of globular clusters derived from Hubble Space Telescope/Advanced Camera for Surveys images of the early-type merger remnant galaxy NGC 1316, which hosts a significant population of metal-rich globular clusters of intermediate age ({approx}3 Gyr). For the old, metal-poor ({sup b}lue{sup )} clusters, the peak mass of the mass function M{sub p} increases with internal half-mass density {rho}{sub h} as M{sub p}{proportional_to}{rho}{sub h}{sup 0.44}, whereas it stays approximately constant with galactocentric distance R{sub gal}. The mass functions of these clusters are consistent with a simple scenario in which they formed with a Schechter initial mass function andmore » evolved subsequently by internal two-body relaxation. For the intermediate-age population of metal-rich ({sup r}ed{sup )} clusters, the faint end of the previously reported power-law luminosity function of the clusters with R{sub gal} > 9 kpc is due to many of those clusters having radii larger than the theoretical maximum value imposed by the tidal field of NGC 1316 at their R{sub gal}. This renders disruption by two-body relaxation ineffective. Only a few such diffuse clusters are found in the inner regions of NGC 1316. Completeness tests indicate that this is a physical effect. Using comparisons with star clusters in other galaxies and cluster disruption calculations using published models, we hypothesize that most red clusters in the low-{rho}{sub h} tail of the initial distribution have already been destroyed in the inner regions of NGC 1316 by tidal shocking, and that several remaining low-{rho}{sub h} clusters will evolve dynamically to become similar to 'faint fuzzies' that exist in several lenticular galaxies. Finally, we discuss the nature of diffuse red clusters in early-type galaxies.« less
Multiple scattering corrections to the Beer-Lambert law. 2: Detector with a variable field of view.

PubMed

Zardecki, A; Tam, W G

1982-07-01

The multiple scattering corrections to the Beer-Lambert law in the case of a detector with a variable field of view are analyzed. We introduce transmission functions relating the received radiant power to reference power levels relevant to two different experimental situations. In the first case, the transmission function relates the received power to a reference power level appropriate to a nonattenuating medium. In the second case, the reference power level is established by bringing the receiver to the close-up position with respect to the source. To examine the effect of the variation of the detector field of view the behavior of the gain factor is studied. Numerical results modeling the laser beam propagation in fog, cloud, and rain are presented.
Mobility of power-law and Carreau fluids through fibrous media.

PubMed

Shahsavari, Setareh; McKinley, Gareth H

2015-12-01

The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
Organic Lecture Demonstrations of Common-Ion Effect, Ionizing Power of Solvents, and First-Order Reaction Kinetics.

ERIC Educational Resources Information Center

Danen, Wayne C.; Blecha, M. Therese, Sr.

1982-01-01

Background information and experimental procedures are provided for three lecture-demonstrations (involving hydrolysis of tetra-butyl chloride) illustrating: (1) common-ion or mass law effect; (2) effect of changing ionizing power of a solvent on a solvolysis reaction; and (3) collecting/plotting data to illustrate a first-order reaction.…
Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands

NASA Astrophysics Data System (ADS)

Hagin, Paul N.

Laboratory experiments on dry, unconsolidated sands from the Wilmington field, CA, reveal significant viscous creep strain under a variety of loading conditions. In hydrostatic compression tests between 10 and 50 MPa of pressure, the creep strain exceeds the magnitude of the instantaneous strain and follows a power law function of time. Interestingly, the viscous effects only appear when loading a sample beyond its preconsolidation pressure. Cyclic loading tests (at quasi-static frequencies of 10-6 to 10 -2 Hz) show that the bulk modulus increases by a factor of two with increasing frequency while attenuation remains constant. I attempt to fit these observations using three classes of models: linear viscoelastic, viscoplastic, and rate-and-state friction models. For the linear viscoelastic modeling, I investigated two types of models; spring-dashpot (exponential) and power law models. I find that a combined power law-Maxwell solid creep model adequately fits all of the data. Extrapolating the power law-Maxwell creep model out to 30 years (to simulate the lifetime of a reservoir) predicts that the static bulk modulus is 25% of the dynamic modulus, in good agreement with field observations. Laboratory studies also reveal that a large portion of the deformation is permanent, suggesting that an elastic-plastic model is appropriate. However, because the viscous component of deformation is significant, an elastic-viscoplastic model is necessary. An appropriate model for unconsolidated sands is developed by incorporating Perzyna (power law) viscoplasticity theory into the modified Cambridge clay cap model. Hydrostatic compression tests conducted as a function of volumetric strain rate produced values for the required model parameters. As a result, by using an end cap model combined with power law viscoplasticity theory, changes in porosity in both the elastic and viscoplastic regimes can be predicted as a function of both stress path and strain rate. To test whether rate-and-state friction laws can be used to model creep strain, I expand the rate-and-state formulation to include deformation under hydrostatic stress boundary conditions. Results show that the expanded rate-and-state formulation successfully describes the creep strain of unconsolidated sand. Finally, I show that the viscoplastic end cap and rate-and-state models are mathematically similar.

Power laws for gravity and topography of Solar System bodies

NASA Astrophysics Data System (ADS)

Ermakov, A.; Park, R. S.; Bills, B. G.

2017-12-01

When a spacecraft visits a planetary body, it is useful to be able to predict its gravitational and topographic properties. This knowledge is important for determining the level of perturbations in spacecraft's motion as well as for planning the observation campaign. It has been known for the Earth that the power spectrum of gravity follows a power law, also known as the Kaula rule (Kaula, 1963; Rapp, 1989). A similar rule was derived for topography (Vening-Meinesz, 1951). The goal of this paper is to generalize the power law that can characterize the gravity and topography power spectra for bodies across a wide range of size. We have analyzed shape power spectra of the bodies that have either global shape and gravity field measured. These bodies span across five orders of magnitude in their radii and surface gravities and include terrestrial planets, icy moons and minor bodies. We have found that despite having different internal structure, composition and mechanical properties, the topography power spectrum of these bodies' shapes can be modeled with a similar power law rescaled by the surface gravity. Having empirically found a power law for topography, we can map it to a gravity power law. Special care should be taken for low-degree harmonic coefficients due to potential isostatic compensation. For minor bodies, uniform density can be assumed. The gravity coefficients are a linear function of the shape coefficients for close-to-spherical bodoes. In this case, the power law for gravity will be steeper than the power law of topography due to the factor (2n+1) in the gravity expansion (e.g. Eq. 10 in Wieczorek & Phillips, 1998). Higher powers of topography must be retained for irregularly shaped bodies, which breaks the linearity. Therefore, we propose the following procedure to derive an a priori constraint for gravity. First, a surface gravity needs to be determined assuming typical density for the relevant class of bodies. Second, the scaling coefficient of the power law can be found by rescaling the values known for other bodies. Third, an ensemble of synthetic shapes that follow the defined power law can be generated and gravity-from-shape can be found. The averaged power spectrum can be used as an a priori constraint for the gravity field and variance of power can be computed for individual degrees.
On the probability distribution function of the mass surface density of molecular clouds. II.

NASA Astrophysics Data System (ADS)

Fischera, Jörg

2014-11-01

The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF shows two basic components: a broad distribution around the maximum with resemblance to a log-normal function, and a tail at high mass surface densities attributed to turbulence and self-gravity. In a previous paper, the PDF of condensed structures has been analyzed and an analytical formula presented based on a truncated radial density profile, ρ(r) = ρc/ (1 + (r/r0)2)n/ 2 with central density ρc and inner radius r0, widely used in astrophysics as a generalization of physical density profiles. In this paper, the results are applied to analyze the PDF of self-gravitating, isothermal, pressurized, spherical (Bonnor-Ebert spheres) and cylindrical condensed structures with emphasis on the dependence of the PDF on the external pressure pext and on the overpressure q-1 = pc/pext, where pc is the central pressure. Apart from individual clouds, we also consider ensembles of spheres or cylinders, where effects caused by a variation of pressure ratio, a distribution of condensed cores within a turbulent gas, and (in case of cylinders) a distribution of inclination angles on the mean PDF are analyzed. The probability distribution of pressure ratios q-1 is assumed to be given by P(q-1) ∝ q-k1/ (1 + (q0/q)γ)(k1 + k2) /γ, where k1, γ, k2, and q0 are fixed parameters. The PDF of individual spheres with overpressures below ~100 is well represented by the PDF of a sphere with an analytical density profile with n = 3. At higher pressure ratios, the PDF at mass surface densities Σ ≪ Σ(0), where Σ(0) is the central mass surface density, asymptotically approaches the PDF of a sphere with n = 2. Consequently, the power-law asymptote at mass surface densities above the peak steepens from Psph(Σ) ∝ Σ-2 to Psph(Σ) ∝ Σ-3. The corresponding asymptote of the PDF of cylinders for the large q-1 is approximately given by Pcyl(Σ) ∝ Σ-4/3(1 - (Σ/Σ(0))2/3)-1/2. The distribution of overpressures q-1 produces a power-law asymptote at high mass surface densities given by ∝ Σ-2k2 - 1 (spheres) or ∝ Σ-2k2 (cylinders). Appendices are available in electronic form at http://www.aanda.org
Red, Straight, no bends: primordial power spectrum reconstruction from CMB and large-scale structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ravenni, Andrea; Verde, Licia; Cuesta, Antonio J., E-mail: andrea.ravenni@pd.infn.it, E-mail: liciaverde@icc.ub.edu, E-mail: ajcuesta@icc.ub.edu

2016-08-01

We present a minimally parametric, model independent reconstruction of the shape of the primordial power spectrum. Our smoothing spline technique is well-suited to search for smooth features such as deviations from scale invariance, and deviations from a power law such as running of the spectral index or small-scale power suppression. We use a comprehensive set of the state-of the art cosmological data: Planck observations of the temperature and polarisation anisotropies of the cosmic microwave background, WiggleZ and Sloan Digital Sky Survey Data Release 7 galaxy power spectra and the Canada-France-Hawaii Lensing Survey correlation function. This reconstruction strongly supports the evidencemore » for a power law primordial power spectrum with a red tilt and disfavours deviations from a power law power spectrum including small-scale power suppression such as that induced by significantly massive neutrinos. This offers a powerful confirmation of the inflationary paradigm, justifying the adoption of the inflationary prior in cosmological analyses.« less
Red, Straight, no bends: primordial power spectrum reconstruction from CMB and large-scale structure

NASA Astrophysics Data System (ADS)

Ravenni, Andrea; Verde, Licia; Cuesta, Antonio J.

2016-08-01

We present a minimally parametric, model independent reconstruction of the shape of the primordial power spectrum. Our smoothing spline technique is well-suited to search for smooth features such as deviations from scale invariance, and deviations from a power law such as running of the spectral index or small-scale power suppression. We use a comprehensive set of the state-of the art cosmological data: Planck observations of the temperature and polarisation anisotropies of the cosmic microwave background, WiggleZ and Sloan Digital Sky Survey Data Release 7 galaxy power spectra and the Canada-France-Hawaii Lensing Survey correlation function. This reconstruction strongly supports the evidence for a power law primordial power spectrum with a red tilt and disfavours deviations from a power law power spectrum including small-scale power suppression such as that induced by significantly massive neutrinos. This offers a powerful confirmation of the inflationary paradigm, justifying the adoption of the inflationary prior in cosmological analyses.
AGN Space Telescope and Optical Reverberation Mapping Project V. Continuum Time Delays and Disk Inclinations

NASA Astrophysics Data System (ADS)

Starkey, David; Agn Storm Team

2015-01-01

Reverberation mapping is a proven method for obtaining black hole mass estimates and constraining the size of the BLR. We analyze multi-wavelength continuum light curves from the 7 month AGN STORM monitoring of NGC 5548 and use reverberation mapping to model the accretion disk time delays. The model fits the light curves at UV to IR wavelengths assuming reprocessing on a flat, steady-state blackbody accretion disk. We calculate the inclination-dependent transfer function and investigate to what extent our model can determine the disk inclination, black hole MMdot and power law index of the disc temperature-radius relation.
The emergence of different tail exponents in the distributions of firm size variables

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Watanabe, Tsutomu; Mizuno, Takayuki

2013-05-01

We discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed assets K, the number of workers L, and sales Y, we confirm that these variables have power-law tails with different exponents, and that inversion symmetry and Gibrat’s law hold. Based on these findings, we argue that there exists a plane in the three dimensional space (logK,logL,logY), with respect to which the joint probability density function for the three variables is invariant under the exchange of variables. We provide empirical evidence suggesting that this plane fits the data well, and argue that the plane can be interpreted as the Cobb-Douglas production function, which has been extensively used in various areas of economics since it was first introduced almost a century ago.
The language of gene ontology: a Zipf's law analysis.

PubMed

Kalankesh, Leila Ranandeh; Stevens, Robert; Brass, Andy

2012-06-07

Most major genome projects and sequence databases provide a GO annotation of their data, either automatically or through human annotators, creating a large corpus of data written in the language of GO. Texts written in natural language show a statistical power law behaviour, Zipf's law, the exponent of which can provide useful information on the nature of the language being used. We have therefore explored the hypothesis that collections of GO annotations will show similar statistical behaviours to natural language. Annotations from the Gene Ontology Annotation project were found to follow Zipf's law. Surprisingly, the measured power law exponents were consistently different between annotation captured using the three GO sub-ontologies in the corpora (function, process and component). On filtering the corpora using GO evidence codes we found that the value of the measured power law exponent responded in a predictable way as a function of the evidence codes used to support the annotation. Techniques from computational linguistics can provide new insights into the annotation process. GO annotations show similar statistical behaviours to those seen in natural language with measured exponents that provide a signal which correlates with the nature of the evidence codes used to support the annotations, suggesting that the measured exponent might provide a signal regarding the information content of the annotation.
Power Laws in Firm Productivity

NASA Astrophysics Data System (ADS)

Mizuno, T.; Ishikawa, A.; Fujimoto, S.; Watanabe, T.

We estimate firm productivity for about 3.2 million firms from30 countries. We find that the distribution of firm productivity in each country, which is measured by total factor productivity (TFP), has a power law upper tail. However, the power law exponent of a TFP distribution in a country tends to be greater than that of a sales distribution in that country, indicating that the upper tail of a TFP distribution is less heavy compared to that of a sales distribution. We also find that the power law exponent of a TFP distribution tends to be greater than the power law exponents associated with the number of workers or tangible fixed assets. Given the idea that the sales of a firm is determined by the amount of various inputs employed by the firm (i.e., ``production function'' in the terminology of economics), these results suggest that the heavy tail of a sales distribution in a country comes not from the tail of a TFP distribution, but from the tail of the distribution of the number of workers or tangible fixed assets.
Fall Velocities of Hydrometeors in the Atmosphere: Refinements to a Continuous Analytical Power Law.

NASA Astrophysics Data System (ADS)

Khvorostyanov, Vitaly I.; Curry, Judith A.

2005-12-01

This paper extends the previous research of the authors on the unified representation of fall velocities for both liquid and crystalline particles as a power law over the entire size range of hydrometeors observed in the atmosphere. The power-law coefficients are determined as continuous analytical functions of the Best or Reynolds number or of the particle size. Here, analytical expressions are formulated for the turbulent corrections to the Reynolds number and to the power-law coefficients that describe the continuous transition from the laminar to the turbulent flow around a falling particle. A simple analytical expression is found for the correction of fall velocities for temperature and pressure. These expressions and the resulting fall velocities are compared with observations and other calculations for a range of ice crystal habits and sizes. This approach provides a continuous analytical power-law description of the terminal velocities of liquid and crystalline hydrometeors with sufficiently high accuracy and can be directly used in bin-resolving models or incorporated into parameterizations for cloud- and large-scale models and remote sensing techniques.
Super Star Cluster Velocity Dispersions and Virial Masses in the M82 Nuclear Starburst

NASA Astrophysics Data System (ADS)

McCrady, Nate; Graham, James R.

2007-07-01

We use high-resolution near-infrared spectroscopy from Keck Observatory to measure the stellar velocity dispersions of 19 super star clusters (SSCs) in the nuclear starburst of M82. The clusters have ages on the order of 10 Myr, which is many times longer than the crossing times implied by their velocity dispersions and radii. We therefore apply the virial theorem to derive the kinematic mass for 15 of the SSCs. The SSCs have masses of 2×105 to 4×106 Msolar, with a total population mass of 1.4×107 Msolar. Comparison of the loci of the young M82 SSCs and old Milky Way globular clusters in a plot of radius versus velocity dispersion suggests that the SSCs are a population of potential globular clusters. We present the mass function for the SSCs and find a power-law fit with an index of γ=-1.91+/-0.06. This result is nearly identical to the mass function of young SSCs in the Antennae galaxies. Based on observations made at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.
MEASURING THE LUMINOSITY AND VIRIAL BLACK HOLE MASS DEPENDENCE OF QUASAR–GALAXY CLUSTERING AT z ∼ 0.8

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krolewski, Alex G.; Eisenstein, Daniel J., E-mail: akrolewski@college.harvard.edu

2015-04-10

We study the dependence of quasar clustering on quasar luminosity and black hole mass by measuring the angular overdensity of photometrically selected galaxies imaged by the Wide-field Infrared Survey Explorer (WISE) about z ∼ 0.8 quasars from SDSS. By measuring the quasar–galaxy cross-correlation function and using photometrically selected galaxies, we achieve a higher density of tracer objects and a more sensitive detection of clustering than measurements of the quasar autocorrelation function. We test models of quasar formation and evolution by measuring the luminosity dependence of clustering amplitude. We find a significant overdensity of WISE galaxies about z ∼ 0.8 quasarsmore » at 0.2–6.4 h{sup −1} Mpc in projected comoving separation. We find no appreciable increase in clustering amplitude with quasar luminosity across a decade in luminosity, and a power-law fit between luminosity and clustering amplitude gives an exponent of −0.01 ± 0.06 (1 σ error). We also fail to find a significant relationship between clustering amplitude and black hole mass, although our dynamic range in true mass is suppressed due to the large uncertainties in virial black hole mass estimates. Our results indicate that a small range in host dark matter halo mass maps to a large range in quasar luminosity.« less
NEW CONSTRAINTS ON MASS-DEPENDENT DISRUPTION OF STAR CLUSTERS IN M51

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chandar, Rupali; Whitmore, Bradley C.; Regan, Michael

2011-02-01

We use UBVI H{alpha} images of the Whirlpool galaxy, M51, taken with the Advanced Camera for Surveys and WFPC2 cameras on the Hubble Space Telescope (HST) to select star clusters, and to estimate their masses and ages by comparing their observed colors with predictions from population synthesis models. We construct the mass function of intermediate-age (1-4 x 10{sup 8} yr) clusters, and find that it is well described by a power law, {psi}(M) {proportional_to} M{sup {beta}}, with {beta} = -2.1 {+-} 0.2, for clusters more massive than M {approx} 6 x 10{sup 3} M{sub sun}. This extends the mass functionmore » of intermediate-age clusters in M51 to masses lower by nearly a factor of five over previous determinations. The mass function does not show evidence for curvature at either the high or low mass end. This shape indicates that there is no evidence for the earlier disruption of lower mass clusters compared with their higher mass counterparts (i.e., no mass-dependent disruption) over the observed range of masses and ages, or for a physical upper mass limit M{sub C} with which clusters in M51 can form. These conclusions differ from previous suggestions based on poorer-quality HST observations. We discuss their implications for the formation and disruption of the clusters. Ages of clusters in two 'feathers', stellar features extending from the outer portion of a spiral arm, show that the feather with a larger pitch angle formed earlier, and over a longer period, than the other.« less
Size distribution of dust grains: A problem of self-similarity

NASA Technical Reports Server (NTRS)

Henning, TH.; Dorschner, J.; Guertler, J.

1989-01-01

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.
Radiative corrections in the (varying power)-law modified gravity

NASA Astrophysics Data System (ADS)

Hammad, Fayçal

2015-06-01

Although the (varying power)-law modified gravity toy model has the attractive feature of unifying the early- and late-time expansions of the Universe, thanks to the peculiar dependence of the scalar field's potential on the scalar curvature, the model still suffers from the fine-tuning problem when used to explain the actually observed Hubble parameter. Indeed, a more correct estimate of the mass of the scalar field needed to comply with actual observations gives an unnaturally small value. On the other hand, for a massless scalar field the potential would have no minimum and hence the field would always remain massless. What solves these issues are the radiative corrections that modify the field's effective potential. These corrections raise the field's effective mass, rendering the model free from fine-tuning, immune against positive fifth-force tests, and better suited to tackle the dark matter sector.
The gravitational wave contribution to cosmic microwave background anisotropies and the amplitude of mass fluctuations from COBE results

NASA Technical Reports Server (NTRS)

Lucchin, Francesco; Matarrese, Sabino; Mollerach, Silvia

1992-01-01

A stochastic background of primordial gravitational waves may substantially contribute, via the Sachs-Wolfe effect, to the large-scale cosmic microwave background (CMB) anisotropies recently detected by COBE. This implies a bias in any resulting determination of the primordial amplitude of density fluctuations. We consider the constraints imposed on n is less than 1 ('tilted') power-law fluctuation spectra, taking into account the contribution from both scalar and tensor waves, as predicted by power-law inflation. The gravitational wave contribution to CMB anisotropies generally reduces the required rms level of mass fluctuation, thereby increasing the linear bias parameter, even in models where the spectral index is close to the Harrison-Zel'dovich value n = 1. This 'gravitational wave bias' helps to reconcile the predictions of CDM models with observations on pairwise galaxy velocity dispersion on small scales.
The statistical overlap theory of chromatography using power law (fractal) statistics.

PubMed

Schure, Mark R; Davis, Joe M

2011-12-30

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics. Copyright © 2011 Elsevier B.V. All rights reserved.
Variability of the occurrence frequency of solar flares as a function of peak hard X-ray rate

NASA Technical Reports Server (NTRS)

Bai, T.

1993-01-01

We study the occurrence frequency of solar flares as a function of the hard X-ray peak count rate, using observations of the Solar Maximum Mission. The size distributions are well represented by power-law distributions with negative indices. As a better alternative to the conventional method, we devise a maximum likelihood method of determining the power-law index of the size distribution. We find that the power-law index of the size distribution changes with time and with the phase of the 154-day periodicity. The size distribution is steeper during the maximum years of solar cycle 21 (1980 and 1981) than during the declining phase (1982-1984). The size distribution, however, is flatter during the maximum phase of the 154-day periodicity than during the minimum phase. The implications of these findings are discussed.
A new parameterization of an empirical model for wind/ocean scatterometry

NASA Technical Reports Server (NTRS)

Woiceshyn, P. M.; Wurtele, M. G.; Boggs, D. H.; Mcgoldrick, L. F.; Peteherych, S.

1984-01-01

The power law form of the SEASAT A Scatterometer System (SASS) empirical backscatter-to-wind model function does not uniformly meet the instrument performance over the range 4 to 24 /ms. Analysis indicates that the horizontal polarization (H-Pol) and vertical polarization (V-Pol) components of the benchmark SASS1 model function yield self-consistent results only for a small mid-range of speeds at larger incidence angles, and for a somewhat larger range of speeds at smaller incidence angles. Comparison of SASS1 to in situ data over the Gulf of Alaska region further underscores the shortcomings of the power law form. Finally, a physically based empirical SASS model is proposed which corrects some of the deficiencies of power law models like SASS1. The new model allows the mutual determination of sea surface wind stress and wind speed in a consistent manner from SASS backscatter measurements.
PDV-based estimation of ejecta particles' mass-velocity function from shock-loaded tin experiment

NASA Astrophysics Data System (ADS)

Franzkowiak, J.-E.; Prudhomme, G.; Mercier, P.; Lauriot, S.; Dubreuil, E.; Berthe, L.

2018-03-01

A metallic tin plate with a given surface finish of wavelength λ ≃ 60 μm and amplitude h ≃ 8 μm is explosively driven by an electro-detonator with a shock-induced breakout pressure PSB = 28 GPa (unsupported). The resulting dynamic fragmentation process, the so-called "micro-jetting," is the creation of high-speed jets of matter moving faster than the bulk metallic surface. Hydrodynamic instabilities result in the fragmentation of these jets into micron-sized metallic particles constituting a self-expanding cloud of droplets, whose areal mass, velocity, and particle size distributions are unknown. Lithium-niobate-piezoelectric sensor measured areal mass and Photonic Doppler Velocimetry (PDV) was used to get a time-velocity spectrogram of the cloud. In this article, we present both experimental mass and velocity results and we relate the integrated areal mass of the cloud to the PDV power spectral density with the assumption of a power law particle size distribution. Two models of PDV spectrograms are described. The first one accounts for the speckle statistics of the spectrum and the second one describes an average spectrum for which speckle fluctuations are removed. Finally, the second model is used for a maximum likelihood estimation of the cloud's parameters from PDV data. The estimated integrated areal mass from PDV data is found to agree well with piezoelectric results. We highlight the relevance of analyzing PDV data and correlating different diagnostics to retrieve the physical properties of ejecta particles.
HP2 survey. III. The California Molecular Cloud: A sleeping giant revisited

NASA Astrophysics Data System (ADS)

Lada, Charles J.; Lewis, John A.; Lombardi, Marco; Alves, João

2017-10-01

We present new high resolution and dynamic range dust column density and temperature maps of the California Molecular Cloud derived from a combination of Planck and Herschel dust-emission maps, and 2MASS NIR dust-extinction maps. We used these data to determine the ratio of the 2.2 μm extinction coefficient to the 850 μm opacity and found the value to be close to that found in similar studies of the Orion B and Perseus clouds but higher than that characterizing the Orion A cloud, indicating that variations in the fundamental optical properties of dust may exist between local clouds. We show that over a wide range of extinction, the column density probability distribution function (pdf) of the cloud can be well described by a simple power law (I.e., PDFN ∝ AK -n) with an index (n = 4.0 ± 0.1) that represents a steeper decline with AK than found (n ≈ 3) in similar studies of the Orion and Perseus clouds. Using only the protostellar population of the cloud and our extinction maps we investigate the Schmidt relation, that is, the relation between the protostellar surface density, Σ∗, and extinction, AK, within the cloud. We show that Σ∗ is directly proportional to the ratio of the protostellar and cloud pdfs, I.e., PDF∗(AK)/PDFN(AK). We use the cumulative distribution of protostars to infer the functional forms for both Σ∗ and PDF∗. We find that Σ∗ is best described by two power-law functions. At extinctions AK ≲ 2.5 mag, Σ∗ ∝ AK β with β = 3.3 while at higher extinctions β = 2.5, both values steeper than those (≈2) found in other local giant molecular clouds (GMCs). We find that PDF∗ is a declining function of extinction also best described by two power-laws whose behavior mirrors that of Σ∗. Our observations suggest that variations both in the slope of the Schmidt relation and in the sizes of the protostellar populations between GMCs are largely driven by variations in the slope, n, of PDFN(AK). This confirms earlier studies suggesting that cloud structure plays a major role in setting the global star formation rates in GMCs HP2 (Herschel-Planck-2MASS) survey is a continuation of the series originally entitled "Herschel-Planck dust opacity and column density maps" (Lombardi et al. 2014, Zari et al. 2016).The reduced Herschel and Planck map and the column density and temperature maps are available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/606/A100

Mass calibration of galaxy clusters at redshift 0.1–1.0 using weak lensing in the Sloan Digital Sky Survey Stripe 82 co-add

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiesner, Matthew P.; Lin, Huan; Soares-Santos, Marcelle

We present galaxy cluster mass–richness relations found in the Sloan Digital Sky Survey Stripe 82 co-add using clusters found using a Voronoi tessellation cluster finder. These relations were found using stacked weak lensing shear observed in a large sample of galaxy clusters. These mass–richness relations are presented for four redshift bins, 0.1 < z ≤ 0.4, 0.4 < z ≤ 0.7, 0.7 < z ≤ 1.0 and 0.1 < z ≤ 1.0. We describe the sample of galaxy clusters and explain how these clusters were found using a Voronoi tessellation cluster finder. We fit a Navarro-Frenk-White profile to the stackedmore » weak lensing shear signal in redshift and richness bins in order to measure virial mass (M 200). We describe several effects that can bias weak lensing measurements, including photometric redshift bias, the effect of the central BCG, halo miscentering, photometric redshift uncertainty and foreground galaxy contamination. We present mass–richness relations using richness measure N VT with each of these effects considered separately as well as considered altogether. We also examine redshift evolution of the mass–richness relation. As a result, we present measurements of the mass coefficient (M 200|20) and the power-law slope (α) for power-law fits to the mass and richness values in each of the redshift bins. We find values of the mass coefficient of 8.49 ± 0.526, 14.1 ± 1.78, 30.2 ± 8.74 and 9.23 ± 0.525 × 10 13 h –1 M ⊙ for each of the four redshift bins, respectively. As a result, we find values of the power-law slope of 0.905 ± 0.0585, 0.948 ± 0.100, 1.33 ± 0.260 and 0.883 ± 0.0500, respectively.« less
Mass calibration of galaxy clusters at redshift 0.1–1.0 using weak lensing in the Sloan Digital Sky Survey Stripe 82 co-add

DOE PAGES

Wiesner, Matthew P.; Lin, Huan; Soares-Santos, Marcelle

2015-07-08

We present galaxy cluster mass–richness relations found in the Sloan Digital Sky Survey Stripe 82 co-add using clusters found using a Voronoi tessellation cluster finder. These relations were found using stacked weak lensing shear observed in a large sample of galaxy clusters. These mass–richness relations are presented for four redshift bins, 0.1 < z ≤ 0.4, 0.4 < z ≤ 0.7, 0.7 < z ≤ 1.0 and 0.1 < z ≤ 1.0. We describe the sample of galaxy clusters and explain how these clusters were found using a Voronoi tessellation cluster finder. We fit a Navarro-Frenk-White profile to the stackedmore » weak lensing shear signal in redshift and richness bins in order to measure virial mass (M 200). We describe several effects that can bias weak lensing measurements, including photometric redshift bias, the effect of the central BCG, halo miscentering, photometric redshift uncertainty and foreground galaxy contamination. We present mass–richness relations using richness measure N VT with each of these effects considered separately as well as considered altogether. We also examine redshift evolution of the mass–richness relation. As a result, we present measurements of the mass coefficient (M 200|20) and the power-law slope (α) for power-law fits to the mass and richness values in each of the redshift bins. We find values of the mass coefficient of 8.49 ± 0.526, 14.1 ± 1.78, 30.2 ± 8.74 and 9.23 ± 0.525 × 10 13 h –1 M ⊙ for each of the four redshift bins, respectively. As a result, we find values of the power-law slope of 0.905 ± 0.0585, 0.948 ± 0.100, 1.33 ± 0.260 and 0.883 ± 0.0500, respectively.« less
X-Ray Fluctuation Power Spectral Densities of Seyfert 1 Galaxies

NASA Technical Reports Server (NTRS)

Markowitz, A.; Edelson, R.; Vaughan, S.; Uttley, P.; George, I. M.; Griffiths, R. E.; Kaspi, S.; Lawrence, A.; McHandy, I.; Nandra, K.

2003-01-01

By combining complementary monitoring observations spanning long, medium and short time scales, we have constructed power spectral densities (PSDs) of six Seyfert 1 galaxies. These PSDs span approx. greater than 4 orders of magnitude in temporal frequency, sampling variations on time scales ranging from tens of minutes to over a year. In at least four cases, the PSD shows a "break," a significant departure from a power law, typically on time scales of order a few days. This is similar to the behavior of Galactic X-ray binaries (XRBs), lower mass compact systems with breaks on time scales of seconds. NGC 3783 shows tentative evidence for a doubly-broken power law, a feature that until now has only been seen in the (much better-defined) PSDs of low-state XRBs. It is also interesting that (when one previously-observed object is added to make a small sample of seven), an apparently significant correlation is seen between the break time scale T and the putative black hole mass M(sub BH), while none is seen between break time scale and luminosity. The data are consistent with the linear relation T = M(sub BH) /10(exp 6.5) solar mass; extrapolation over 6-7 orders of magnitude is in reasonable agreement with XRBs. All of this strengthens the case for a physical similarity between Seyfert 1s and XRBs.
Impact of compressibility and a guide field on Fermi acceleration during magnetic island coalescence

NASA Astrophysics Data System (ADS)

Montag, P.; Egedal, J.; Lichko, E.; Wetherton, B.

2017-06-01

Previous work has shown that Fermi acceleration can be an effective heating mechanism during magnetic island coalescence, where electrons may undergo repeated reflections as the magnetic field lines contract. This energization has the potential to account for the power-law distributions of particle energy inferred from observations of solar flares. Here, we develop a generalized framework for the analysis of Fermi acceleration that can incorporate the effects of compressibility and non-uniformity along field lines, which have commonly been neglected in previous treatments of the problem. Applying this framework to the simplified case of the uniform flux tube allows us to find both the power-law scaling of the distribution function and the rate at which the power-law behavior develops. We find that a guide magnetic field of order unity effectively suppresses the development of power-law distributions.
Tachyon with an inverse power-law potential in a braneworld cosmology

NASA Astrophysics Data System (ADS)

Bilić, Neven; Domazet, Silvije; Djordjevic, Goran S.

2017-08-01

We study a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall-Sundrum model extended to more general warp functions. A well known prototype of such a generalization is the bulk with a selfinteracting scalar field. As a consequence of a generalized bulk geometry the cosmology on the observer brane is modified by the scale dependent four-dimensional gravitational constant. In particular, we study a power law warp factor which generates an inverse power-law potential V\\propto \\varphi-n of the tachyon field φ. We find a critical power n cr that divides two subclasses with distinct asymptotic behaviors: a dust universe for n>n_cr and a quasi de Sitter universe for 0.
Modelling the ecological niche from functional traits

PubMed Central

Kearney, Michael; Simpson, Stephen J.; Raubenheimer, David; Helmuth, Brian

2010-01-01

The niche concept is central to ecology but is often depicted descriptively through observing associations between organisms and habitats. Here, we argue for the importance of mechanistically modelling niches based on functional traits of organisms and explore the possibilities for achieving this through the integration of three theoretical frameworks: biophysical ecology (BE), the geometric framework for nutrition (GF) and dynamic energy budget (DEB) models. These three frameworks are fundamentally based on the conservation laws of thermodynamics, describing energy and mass balance at the level of the individual and capturing the prodigious predictive power of the concepts of ‘homeostasis’ and ‘evolutionary fitness’. BE and the GF provide mechanistic multi-dimensional depictions of climatic and nutritional niches, respectively, providing a foundation for linking organismal traits (morphology, physiology, behaviour) with habitat characteristics. In turn, they provide driving inputs and cost functions for mass/energy allocation within the individual as determined by DEB models. We show how integration of the three frameworks permits calculation of activity constraints, vital rates (survival, development, growth, reproduction) and ultimately population growth rates and species distributions. When integrated with contemporary niche theory, functional trait niche models hold great promise for tackling major questions in ecology and evolutionary biology. PMID:20921046
The cluster-cluster correlation function. [of galaxies

NASA Technical Reports Server (NTRS)

Postman, M.; Geller, M. J.; Huchra, J. P.

1986-01-01

The clustering properties of the Abell and Zwicky cluster catalogs are studied using the two-point angular and spatial correlation functions. The catalogs are divided into eight subsamples to determine the dependence of the correlation function on distance, richness, and the method of cluster identification. It is found that the Corona Borealis supercluster contributes significant power to the spatial correlation function to the Abell cluster sample with distance class of four or less. The distance-limited catalog of 152 Abell clusters, which is not greatly affected by a single system, has a spatial correlation function consistent with the power law Xi(r) = 300r exp -1.8. In both the distance class four or less and distance-limited samples the signal in the spatial correlation function is a power law detectable out to 60/h Mpc. The amplitude of Xi(r) for clusters of richness class two is about three times that for richness class one clusters. The two-point spatial correlation function is sensitive to the use of estimated redshifts.
The First Billion Years project: constraining the dust attenuation law of star-forming galaxies at z ≃ 5

NASA Astrophysics Data System (ADS)

Cullen, F.; McLure, R. J.; Khochfar, S.; Dunlop, J. S.; Dalla Vecchia, C.

2017-09-01

We present the results of a study investigating the dust attenuation law at z ≃ 5, based on synthetic spectral energy distributions (SEDs) calculated for a sample of N = 498 galaxies drawn from the First Billion Years (FiBY) simulation project. The simulated galaxies at z ≃ 5, which have M1500 ≤ -18.0 and 7.5 ≤ log(M/M}_{⊙}) ≤ 10.2, display a mass-dependent α-enhancement, with a median value of [α /{Fe}]_{z=5} ˜eq 4 × [α /{Fe}]_{Z_{⊙}}. The median Fe/H ratio of the simulated galaxies is 0.14 ± 0.05 which produces steep intrinsic ultraviolet (UV) continuum slopes; 〈βI〉 = -2.4 ± 0.05. Using a set of simple dust attenuation models, in which the wavelength-dependent attenuation is assumed to be of the form A(λ) ∝ λn, we explore the parameter values which best reproduce the observed z = 5 luminosity function (LF) and colour-magnitude relation (CMR). We find that a simple model in which the absolute UV attenuation is a linearly increasing function of log stellar mass (A1500 = 0.5 × log(M/M⊙) - 3.3), and the dust attenuation slope (n) is within the range -0.7 ≤ n ≤ -0.3, can successfully reproduce the LF and CMR over a wide range of stellar population synthesis model assumptions, including the effects of massive binaries. This range of attenuation curves is consistent with a power-law fit to the Calzetti attenuation law in the UV (n = -0.55). In contrast, curves as steep as the Small Magellanic Cloud extinction curve (n = -1.24) are formally ruled out. Finally, we show that our models are consistent with recent 1.3 mm Atacama Large Millimeter Array observations of the Hubble Ultra Deep Field, and predict the form of the z ≃ 5 infrared excess (IRX)-β relation.
A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-03-01

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.
Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---

NASA Astrophysics Data System (ADS)

Kaizoji, T.

In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, P (S > x) ˜ x^{-α}, with an exponent that moves in the range of 1.09 < α < 1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.
The mass distribution of Population III stars

NASA Astrophysics Data System (ADS)

Fraser, M.; Casey, A. R.; Gilmore, G.; Heger, A.; Chan, C.

2017-06-01

Extremely metal-poor (EMP) stars are uniquely informative on the nature of massive Population III stars. Modulo a few elements that vary with stellar evolution, the present-day photospheric abundances observed in EMP stars are representative of their natal gas cloud composition. For this reason, the chemistry of EMP stars closely reflects the nucleosynthetic yields of supernovae from massive Population III stars. Here we collate detailed abundances of 53 EMP stars from the literature and infer the masses of their Population III progenitors. We fit a simple initial mass function (IMF) to a subset of 29 of the inferred Population III star masses, and find that the mass distribution is well represented by a power-law IMF with exponent α = 2.35^{+0.29}_{-0.24}. The inferred maximum progenitor mass for supernovae from massive Population III stars is M_{max} = 87^{+13}_{-33} M⊙, and we find no evidence in our sample for a contribution from stars with masses above ˜120 M⊙. The minimum mass is strongly consistent with the theoretical lower mass limit for Population III supernovae. We conclude that the IMF for massive Population III stars is consistent with the IMF of present-day massive stars and there may well have formed stars much below the supernova mass limit that could have survived to the present day.
Statistical scaling of pore-scale Lagrangian velocities in natural porous media.

PubMed

Siena, M; Guadagnini, A; Riva, M; Bijeljic, B; Pereira Nunes, J P; Blunt, M J

2014-08-01

We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.
New calibration and some predictions of the scaling relations between the mass of supermassive black holes and the properties of the host galaxies

NASA Astrophysics Data System (ADS)

Benedetto, E.; Fallarino, M. T.; Feoli, A.

2013-10-01

We present a new determination of the slope and normalization of three popular scaling laws between the mass of supermassive black holes and stellar velocity dispersion, bulge mass and kinetic energy of the host galaxies. To this aim we have collected 72 objects taken from three different samples and we have used three fitting methods applying the statistical analysis also to the subset of early type galaxies and spirals separately. We find that the relation involving kinetic energy has a slightly better χ2 and linear correlation coefficient than the other two laws. Furthermore, its Hertzsprung-Russell-like behavior is confirmed by the location of young and old galaxies in two different parts of the diagram. A test of its predictive power with the two giant galaxies NGC 3842 and NGC 4889 shows that the mass of the black hole inferred using the kinetic energy law is the closest to the experimental value. The subset of early type galaxies satisfies the theoretical models regarding the black hole mass vs stellar velocity dispersion relation, better than the full sample. Tables 1 and 7 are available in electronic form at http://www.aanda.org
Galaxy And Mass Assembly (GAMA): the galaxy stellar mass function to z = 0.1 from the r-band selected equatorial regions

NASA Astrophysics Data System (ADS)

Wright, A. H.; Robotham, A. S. G.; Driver, S. P.; Alpaslan, M.; Andrews, S. K.; Baldry, I. K.; Bland-Hawthorn, J.; Brough, S.; Brown, M. J. I.; Colless, M.; da Cunha, E.; Davies, L. J. M.; Graham, Alister W.; Holwerda, B. W.; Hopkins, A. M.; Kafle, P. R.; Kelvin, L. S.; Loveday, J.; Maddox, S. J.; Meyer, M. J.; Moffett, A. J.; Norberg, P.; Phillipps, S.; Rowlands, K.; Taylor, E. N.; Wang, L.; Wilkins, S. M.

2017-09-01

We derive the low-redshift galaxy stellar mass function (GSMF), inclusive of dust corrections, for the equatorial Galaxy And Mass Assembly (GAMA) data set covering 180 deg2. We construct the mass function using a density-corrected maximum volume method, using masses corrected for the impact of optically thick and thin dust. We explore the galactic bivariate brightness plane (M⋆-μ), demonstrating that surface brightness effects do not systematically bias our mass function measurement above 107.5 M⊙. The galaxy distribution in the M-μ plane appears well bounded, indicating that no substantial population of massive but diffuse or highly compact galaxies are systematically missed due to the GAMA selection criteria. The GSMF is fitted with a double Schechter function, with M^\\star =10^{10.78± 0.01± 0.20} M_{⊙}, φ ^\\star _1=(2.93± 0.40)× 10^{-3} h_{70}^3 Mpc-3, α1 = -0.62 ± 0.03 ± 0.15, φ ^\\star _2=(0.63± 0.10)× 10^{-3} h_{70}^3 Mpc-3 and α2 = -1.50 ± 0.01 ± 0.15. We find the equivalent faint end slope as previously estimated using the GAMA-I sample, although we find a higher value of M^\\star. Using the full GAMA-II sample, we are able to fit the mass function to masses as low as 107.5 M⊙, and assess limits to 106.5 M⊙. Combining GAMA-II with data from G10-COSMOS, we are able to comment qualitatively on the shape of the GSMF down to masses as low as 106 M⊙. Beyond the well-known upturn seen in the GSMF at 109.5, the distribution appears to maintain a single power-law slope from 109 to 106.5. We calculate the stellar mass density parameter given our best-estimate GSMF, finding Ω _\\star = 1.66^{+0.24}_{-0.23}± 0.97 h^{-1}_{70} × 10^{-3}, inclusive of random and systematic uncertainties.
The dot{M}-M_* relation of pre-main-sequence stars: a consequence of X-ray driven disc evolution

NASA Astrophysics Data System (ADS)

Ercolano, B.; Mayr, D.; Owen, J. E.; Rosotti, G.; Manara, C. F.

2014-03-01

We analyse current measurements of accretion rates on to pre-main-sequence stars as a function of stellar mass, and conclude that the steep dependence of accretion rates on stellar mass is real and not driven by selection/detection threshold, as has been previously feared. These conclusions are reached by means of statistical tests including a survival analysis which can account for upper limits. The power-law slope of the dot{M}-M_* relation is found to be in the range of 1.6-1.9 for young stars with masses lower than 1 M⊙. The measured slopes and distributions can be easily reproduced by means of a simple disc model which includes viscous accretion and X-ray photoevaporation. We conclude that the dot{M}-M_* relation in pre-main-sequence stars bears the signature of disc dispersal by X-ray photoevaporation, suggesting that the relation is a straightforward consequence of disc physics rather than an imprint of initial conditions.
Analytical equation for outflow along the flow in a perforated fluid distribution pipe

PubMed Central

Liu, Huanfang; Lv, Hongxing; Jin, Jin

2017-01-01

Perforated fluid distribution pipes have been widely used in agriculture, water supply and drainage, ventilation, the chemical industry, and other sectors. The momentum equation for variable mass flow with a variable exchange coefficient and variable friction coefficient was developed by using the momentum conservation method under the condition of a certain slope. The change laws of the variable momentum exchange coefficient and the variable resistance coefficient along the flow were analyzed, and the function of the momentum exchange coefficient was given. According to the velocity distribution of the power function, the momentum equation of variable mass flow was solved for different Reynolds numbers. The analytical solution contains components of pressure, gravity, friction and momentum and reflects the influence of various factors on the pressure distribution along the perforated pipe. The calculated results of the analytical solution were compared with the experimental values of the study by Jin et al. 1984 and Wang et al. 2001 with the mean errors 8.2%, 3.8% and 2.7%, and showed that the analytical solution of the variable mass momentum equation was qualitatively and quantitatively consistent with the experimental results. PMID:29065112
Cosmology and astrophysics from relaxed galaxy clusters - V. Consistency with cold dark matter structure formation

NASA Astrophysics Data System (ADS)

Mantz, A. B.; Allen, S. W.; Morris, R. G.

2016-10-01

This is the fifth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically relaxed and hot in Papers I and II of this series. Here we use constraints on cluster mass profiles from X-ray data to test some of the basic predictions of cosmological structure formation in the cold dark matter (CDM) paradigm. We present constraints on the concentration-mass relation for massive clusters, finding a power-law mass dependence with a slope of κm = -0.16 ± 0.07, in agreement with CDM predictions. For this relaxed sample, the relation is consistent with a constant as a function of redshift (power-law slope with 1 + z of κζ = -0.17 ± 0.26), with an intrinsic scatter of σln c = 0.16 ± 0.03. We investigate the shape of cluster mass profiles over the radial range probed by the data (typically ˜50 kpc-1 Mpc), and test for departures from the simple Navarro-Frenk-White (NFW) form, for which the logarithmic slope of the density profile tends to -1 at small radii. Specifically, we consider as alternatives the generalized NFW (GNFW) and Einasto parametrizations. For the GNFW model, we find an average value of (minus) the logarithmic inner slope of β = 1.02 ± 0.08, with an intrinsic scatter of σβ = 0.22 ± 0.07, while in the Einasto case we constrain the average shape parameter to be α = 0.29 ± 0.04 with an intrinsic scatter of σα = 0.12 ± 0.04. Our results are thus consistent with the simple NFW model on average, but we clearly detect the presence of intrinsic, cluster-to-cluster scatter about the average.
Cosmology and astrophysics from relaxed galaxy clusters – V. Consistency with cold dark matter structure formation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mantz, A. B.; Allen, S. W.; Morris, R. G.

This is the fifth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically relaxed and hot in Papers I and II of this series. Here we use constraints on cluster mass profiles from X-ray data to test some of the basic predictions of cosmological structure formation in the cold dark matter (CDM) paradigm. In addition, we present constraints on the concentration–mass relation for massive clusters, finding a power-law mass dependence with a slope of κ m = –0.16 ± 0.07, in agreement with CDMmore » predictions. For this relaxed sample, the relation is consistent with a constant as a function of redshift (power-law slope with 1 + z of κ ζ = –0.17 ± 0.26), with an intrinsic scatter of σln c = 0.16 ± 0.03. We investigate the shape of cluster mass profiles over the radial range probed by the data (typically ~50 kpc–1 Mpc), and test for departures from the simple Navarro–Frenk–White (NFW) form, for which the logarithmic slope of the density profile tends to –1 at small radii. Specifically, we consider as alternatives the generalized NFW (GNFW) and Einasto parametrizations. For the GNFW model, we find an average value of (minus) the logarithmic inner slope of β = 1.02 ± 0.08, with an intrinsic scatter of σ β = 0.22 ± 0.07, while in the Einasto case we constrain the average shape parameter to be α = 0.29 ± 0.04 with an intrinsic scatter of σ α = 0.12 ± 0.04. Our results are thus consistent with the simple NFW model on average, but we clearly detect the presence of intrinsic, cluster-to-cluster scatter about the average.« less
Cosmology and astrophysics from relaxed galaxy clusters – V. Consistency with cold dark matter structure formation

DOE PAGES

Mantz, A. B.; Allen, S. W.; Morris, R. G.

2016-07-15

This is the fifth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically relaxed and hot in Papers I and II of this series. Here we use constraints on cluster mass profiles from X-ray data to test some of the basic predictions of cosmological structure formation in the cold dark matter (CDM) paradigm. In addition, we present constraints on the concentration–mass relation for massive clusters, finding a power-law mass dependence with a slope of κ m = –0.16 ± 0.07, in agreement with CDMmore » predictions. For this relaxed sample, the relation is consistent with a constant as a function of redshift (power-law slope with 1 + z of κ ζ = –0.17 ± 0.26), with an intrinsic scatter of σln c = 0.16 ± 0.03. We investigate the shape of cluster mass profiles over the radial range probed by the data (typically ~50 kpc–1 Mpc), and test for departures from the simple Navarro–Frenk–White (NFW) form, for which the logarithmic slope of the density profile tends to –1 at small radii. Specifically, we consider as alternatives the generalized NFW (GNFW) and Einasto parametrizations. For the GNFW model, we find an average value of (minus) the logarithmic inner slope of β = 1.02 ± 0.08, with an intrinsic scatter of σ β = 0.22 ± 0.07, while in the Einasto case we constrain the average shape parameter to be α = 0.29 ± 0.04 with an intrinsic scatter of σ α = 0.12 ± 0.04. Our results are thus consistent with the simple NFW model on average, but we clearly detect the presence of intrinsic, cluster-to-cluster scatter about the average.« less
Critical quench dynamics in confined systems.

PubMed

Collura, Mario; Karevski, Dragi

2010-05-21

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the nonadiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.

Baryogenesis in nonminimally coupled f (R ) theories

NASA Astrophysics Data System (ADS)

Ramos, M. P. L. P.; Páramos, J.

2017-11-01

We generalize the mechanism for gravitational baryogensis in the context of f (R ) theories of gravity, including a nonminimal coupling between curvature and matter. In these models, the baryon asymmetry is generated through an effective coupling between the Ricci scalar curvature and the net baryon current that dynamically breaks Charge conjugation, parity and time reversal (C P T ) invariance. We study the combinations of characteristic mass scales and exponents for both nontrivial functions present in the modified action functional and establish the allowed region for these parameters: we find that very small deviations from general relativity are consistent with the observed baryon asymmetry and lead to temperatures compatible with the subsequent formation of the primordial abundances of light elements. In particular, we show the viability of a power-law nonminimal coupling function f2(R )˜Rn with 0
A method for the estimation of the significance of cross-correlations in unevenly sampled red-noise time series

NASA Astrophysics Data System (ADS)

Max-Moerbeck, W.; Richards, J. L.; Hovatta, T.; Pavlidou, V.; Pearson, T. J.; Readhead, A. C. S.

2014-11-01

We present a practical implementation of a Monte Carlo method to estimate the significance of cross-correlations in unevenly sampled time series of data, whose statistical properties are modelled with a simple power-law power spectral density. This implementation builds on published methods; we introduce a number of improvements in the normalization of the cross-correlation function estimate and a bootstrap method for estimating the significance of the cross-correlations. A closely related matter is the estimation of a model for the light curves, which is critical for the significance estimates. We present a graphical and quantitative demonstration that uses simulations to show how common it is to get high cross-correlations for unrelated light curves with steep power spectral densities. This demonstration highlights the dangers of interpreting them as signs of a physical connection. We show that by using interpolation and the Hanning sampling window function we are able to reduce the effects of red-noise leakage and to recover steep simple power-law power spectral densities. We also introduce the use of a Neyman construction for the estimation of the errors in the power-law index of the power spectral density. This method provides a consistent way to estimate the significance of cross-correlations in unevenly sampled time series of data.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.
Equivalent refractive-index structure constant of non-Kolmogorov turbulence.

PubMed

Li, Yujie; Zhu, Wenyue; Wu, Xiaoqing; Rao, Ruizhong

2015-09-07

The relationship between the non-Kolmogorov refractive-index structure constant and the Kolmogorov refractive-index structure constant is derived by using the refractive-index structure function and the variance of refractive-index fluctuations. It shows that the non-Kolmogorov structure constant is proportional to the Kolmogorov structure constant and the scaling factor depends on the outer scale and the spectral power law. For a fixed Kolmogorov structure constant, the non-Kolmogorov structure constant increases with a increasing outer scale for the power law less than 11/3, the trend is opposite for the power law greater than 11/3. This equivalent relation provides a way of obtaining the non-Kolmogorov structure constant by using the Kolmogorov structure constant.
Power-law creep behavior of a semiflexible chain.

PubMed

Majumdar, Arnab; Suki, Béla; Rosenblatt, Noah; Alencar, Adriano M; Stamenović, Dimitrije

2008-10-01

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.
Fall with Linear Drag and Wien's Displacement Law: Approximate Solution and Lambert Function

ERIC Educational Resources Information Center

Vial, Alexandre

2012-01-01

We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for…
Improvement of surface flux calculation: A study based on measurements over alpine meadow in the eastern Tibet Plateau in summer

NASA Astrophysics Data System (ADS)

Li, Sen; Zhong, Zhong

2014-02-01

An improved flux-gradient relationship between momentum φm(ζ) and sensible heat φh(ζ) is obtained by the use of the observational data over an alpine meadow in the eastern Tibet Plateau, in Maqu of China during the period June to August, 2010. The empirical coefficients of Businger—Dyer type function for the cases of unstable and stable stratification are modified. Non-dimensional vertical gradients of wind and potential temperature are calculated by three fitting functions; that is, the log—linear, log—square, and log—cubic functions, respectively. It is found that the von Karman constant approaches 0.4025 and the Prandtl number is about 1.10 based on the measurements in near-neutral conditions, which are within reasonable range proposed in previous studies. The revised flux-gradient profile functions of -1/5 power law for momentum and -1/3 power law for sensible heat are best fitted in unstable stratification conditions. Meanwhile, 2/5 power law, instead of linear functions, is more appropriate in stable stratification cases for momentum and sensible heat. Compared with results from previous studies in which traditional functions are used, the momentum and sensible heat fluxes estimated by the revised profile functions in the current study are much closer to the observations for the unstable and stable stratification conditions.
Halo Profiles and the Concentration–Mass Relation for a ΛCDM Universe

NASA Astrophysics Data System (ADS)

Child, Hillary L.; Habib, Salman; Heitmann, Katrin; Frontiere, Nicholas; Finkel, Hal; Pope, Adrian; Morozov, Vitali

2018-05-01

Profiles of dark matter-dominated halos at the group and cluster scales play an important role in modern cosmology. Using results from two very large cosmological N-body simulations, which increase the available volume at their mass resolution by roughly two orders of magnitude, we robustly determine the halo concentration–mass (c‑M) relation over a wide range of masses, employing multiple methods of concentration measurement. We characterize individual halo profiles, as well as stacked profiles, relevant for galaxy–galaxy lensing and next-generation cluster surveys; the redshift range covered is 0 ≤ z ≤ 4, with a minimum halo mass of M 200c ∼ 2 × 1011 M ⊙. Despite the complexity of a proper description of a halo (environmental effects, merger history, nonsphericity, relaxation state), when the mass is scaled by the nonlinear mass scale M ⋆(z), we find that a simple non-power-law form for the c–M/M ⋆ relation provides an excellent description of our simulation results across eight decades in M/M ⋆ and for 0 ≤ z ≤ 4. Over the mass range covered, the c–M relation has two asymptotic forms: an approximate power law below a mass threshold M/M ⋆ ∼ 500–1000, transitioning to a constant value, c 0 ∼ 3 at higher masses. The relaxed halo fraction decreases with mass, transitioning to a constant value of ∼0.5 above the same mass threshold. We compare Navarro–Frenk–White (NFW) and Einasto fits to stacked profiles in narrow mass bins at different redshifts; as expected, the Einasto profile provides a better description of the simulation results. At cluster scales at low redshift, however, both NFW and Einasto profiles are in very good agreement with the simulation results, consistent with recent weak lensing observations.
The Arches cluster out to its tidal radius: dynamical mass segregation and the effect of the extinction law on the stellar mass function

NASA Astrophysics Data System (ADS)

Habibi, M.; Stolte, A.; Brandner, W.; Hußmann, B.; Motohara, K.

2013-08-01

The Galactic center is the most active site of star formation in the Milky Way, where particularly high-mass stars have formed very recently and are still forming today. However, since we are looking at the Galactic center through the Galactic disk, knowledge of extinction is crucial when studying this region. The Arches cluster is a young, massive starburst cluster near the Galactic center. We observed the Arches cluster out to its tidal radius using Ks-band imaging obtained with NAOS/CONICA at the VLT combined with Subaru/CISCO J-band data to gain a full understanding of the cluster mass distribution. We show that the determination of the mass of the most massive star in the Arches cluster, which had been used in previous studies to establish an upper mass limit for the star formation process in the Milky Way, strongly depends on the assumed slope of the extinction law. Assuming the two regimes of widely used infrared extinction laws, we show that the difference can reach up to 30% for individually derived stellar masses and ΔAKs ~ 1 magnitude in acquired Ks-band extinction, while the present-day mass function slope changes by ~ 0.17 dex. The present-day mass function slope derived assuming the more recent extinction law increases from a flat slope of αNishi = -1.50 ± 0.35 in the core (r < 0.2 pc) to αNishi = -2.21 ± 0.27 in the intermediate annulus (0.2 < r < 0.4 pc), where the Salpeter slope is -2.3. The mass function steepens to αNishi = -3.21 ± 0.30 in the outer annulus (0.4 < r < 1.5 pc), indicating that the outer cluster region is depleted of high-mass stars. This picture is consistent with mass segregation owing to the dynamical evolution of the cluster. Based on observations collected at the ESO/VLT under Program ID 081.D-0572(B) (PI: Brandner) and ID 71.C-0344(A) (PI: Eisenhauer, retrieved from the ESO archive). Also based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan.Full Table 5 is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/556/A26
K2 Ultracool Dwarfs Survey. III. White Light Flares Are Ubiquitous in M6-L0 Dwarfs

NASA Astrophysics Data System (ADS)

Paudel, Rishi R.; Gizis, John E.; Mullan, D. J.; Schmidt, Sarah J.; Burgasser, Adam J.; Williams, Peter K. G.; Berger, Edo

2018-05-01

We report the white light flare rates for 10 ultracool dwarfs using Kepler K2 short-cadence data. Among our sample stars, two have spectral type M6, three are M7, three are M8, and two are L0. Most of our targets are old low-mass stars. We identify a total of 283 flares in all of the stars in our sample, with Kepler energies in the range log E Kp ∼ (29–33.5) erg. Using the maximum-likelihood method of line fitting, we find that the flare frequency distribution (FFD) for each star in our sample follows a power law with slope ‑α in the range ‑(1.3–2.0). We find that cooler objects tend to have shallower slopes. For some of our targets, the FFD follows either a broken power law, or a power law with an exponential cutoff. For the L0 dwarf 2MASS J12321827-0951502, we find a very shallow slope (‑α = ‑1.3) in the Kepler energy range (0.82–130) × 1030 erg: this L0 dwarf has flare rates which are comparable to those of high-energy flares in stars of earlier spectral types. In addition, we report photometry of two superflares: one on the L0 dwarf 2MASS J12321827-0951502 and another on the M7 dwarf 2MASS J08352366+1029318. In the case of 2MASS J12321827-0951502, we report a flare brightening by a factor of ∼144 relative to the quiescent photospheric level. Likewise, for 2MASS J08352366+1029318, we report a flare brightening by a factor of ∼60 relative to the quiescent photospheric level. These two superflares have bolometric (ultraviolet/optical/infrared) energies 3.6 × 1033 erg and 8.9 × 1033 erg respectively, while the full width half maximum timescales are very short, ∼2 min. We find that the M8 star TRAPPIST-1 is more active than the M8.5 dwarf 2M03264453+1919309, but less active than another M8 dwarf (2M12215066-0843197).
Generation of intermittent gravitocapillary waves via parametric forcing

NASA Astrophysics Data System (ADS)

Castillo, Gustavo; Falcón, Claudio

2018-04-01

We report on the generation of an intermittent wave field driven by a horizontally moving wave maker interacting with Faraday waves. The spectrum of the local gravitocapillary surface wave fluctuations displays a power law in frequency for a wide range of forcing parameters. We compute the probability density function of the local surface height increments, which show that they change strongly across time scales. The structure functions of these increments are shown to display power laws as a function of the time lag, with exponents that are nonlinear functions of the order of the structure function. We argue that the origin of this scale-invariant intermittent spectrum is the Faraday wave pattern breakup due to its advection by the propagating gravity waves. Finally, some interpretations are proposed to explain the appearance of this intermittent spectrum.
Omori Law After Exogenous Shocks on Supplier-Customer Network

NASA Astrophysics Data System (ADS)

Fujiwara, Yoshi

We study the relaxation process of a supplier-customer network after mass destruction due to two giant earthquakes, Kobe 1995 and East Japan 2011, by investigating the number of chained failures. Firstly, a mass destruction and intervention of business activities in the damaged areas can be considered as a main shock. The exogenous shock was propagated on the supplier-customer network deteriorating financial states of other firms, even if they are not located in geographical neighbors. To quantify such aftershocks, we use chained failures on the network assuming that they indicate the trace of propagation of shocks. We show that the number of chained failures in its temporal change obeys an Omori-law, a power-law relaxation. This finding implies that the relaxation is much more sluggish than one would naively expect, and that it might be possible to estimate the extent and duration of aftershocks by using the empirical law. Several issues are discussed including the origin of the long-time relaxation.
An Empirical Examination of Counterdrug Interdiction Program Effectiveness.

DTIC Science & Technology

1997-01-01

inversely correlated with the street price index. Chapter IV examines the time dependence of the street price index and argues that interdiction activities...essentially asymptotic behavior in which the cumulative distribution function, for large values of the independent variable, converges to an inverse power-law...log(S) /log(M). Such an inverse power-law relation between unit purchase price and purchase volume is indeed observed within the STRIDE data
On the effects of surrogacy of energy dissipation in determining the intermittency exponent in fully developed turbulence

NASA Astrophysics Data System (ADS)

Cleve, J.; Greiner, M.; Sreenivasan, K. R.

2003-03-01

The two-point correlation function of the energy dissipation, obtained from a one-point time record of an atmospheric boundary layer, reveals a rigorous power law scaling with intermittency exponent μ approx 0.20 over almost the entire inertial range of scales. However, for the related integral moment, the power law scaling is restricted to the upper part of the inertial range only. This observation is explained in terms of the operational surrogacy of the construction of energy dissipation, which influences the behaviour of the correlation function for small separation distances.
Evidence of Self-Organized Criticality in Dry Sliding Friction

NASA Technical Reports Server (NTRS)

Zypman, Fredy R.; Ferrante, John; Jansen, Mark; Scanlon, Kathleen; Abel, Phillip

2003-01-01

This letter presents experimental results on unlubricated friction, which suggests that stick-slip is described by self-organized criticality (SOC). The data, obtained with a pin-on-disc tribometer examines the variation of the friction force as a function of time-or sliding distance. This is the first time that standard tribological equipment has been used to examine the possibility of SOC. The materials were matching pins and discs of aluminium loaded with 250, 500 and 1000 g masses, and matching M50 steel couples loaded with a 1000 g mass. An analysis of the data shows that the probability distribution of slip sizes follows a power law. We perform a careful analysis of all the properties, beyond the two just mentioned, which are required to imply the presence of SOC. Our data strongly support the existence of SOC for stick-slip in dry sliding friction.
Mechanism-based model of a mass rapid transit system: A perspective

NASA Astrophysics Data System (ADS)

Legara, Erika Fille; Khoon, Lee Kee; Guang, Hung Gih; Monterola, Christopher

2015-01-01

In this paper, we discuss our findings on the spatiotemporal dynamics within the mass rapid transit (MRT) system of Singapore. We show that the trip distribution of Origin-Destination (OD) station pairs follows a power-law, implying the existence of critical OD pairs. We then present and discuss the empirically validated agent-based model (ABM) we have developed. The model allows recreation of the observed statistics and the setting up of various scenarios and their effects on the system, such as increasing the commuter population and the propagation of travel delays within the transportation network. The proposed model further enables identification of bottlenecks that can cause the MRT to break down, and consequently provide foresight on how such disruptions can possibly be managed. This can potentially provide a versatile approach for transport planners and government regulators to make quantifiable policies that optimally balance cost and convenience as a function of the number of the commuting public.
From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2014-12-01

The entropy-maximization paradigm of statistical physics is well known to generate the omnipresent Gauss law. In this paper we establish an analogous socioeconomic model which maximizes social equality, rather than physical disorder, in the context of the distributions of income and wealth in human societies. We show that-on a logarithmic scale-the Laplace law is the socioeconomic equality-maximizing counterpart of the physical entropy-maximizing Gauss law, and that this law manifests an optimized balance between two opposing forces: (i) the rich and powerful, striving to amass ever more wealth, and thus to increase social inequality; and (ii) the masses, struggling to form more egalitarian societies, and thus to increase social equality. Our results lead from log-Gauss statistics to log-Laplace statistics, yield Paretian power-law tails of income and wealth distributions, and show how the emergence of a middle-class depends on the underlying levels of socioeconomic inequality and variability. Also, in the context of asset-prices with Laplace-distributed returns, our results imply that financial markets generate an optimized balance between risk and predictability.
Analytical Derivation of Power Laws in Firm Size Variables from Gibrat's Law and Quasi-inversion Symmetry: A Geomorphological Approach

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu

2014-03-01

We start from Gibrat's law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.
Mapping Power Law Distributions in Digital Health Social Networks: Methods, Interpretations, and Practical Implications.

PubMed

van Mierlo, Trevor; Hyatt, Douglas; Ching, Andrew T

2015-06-25

Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.
NON-Shock-Plasticity/Fracture Burst Acoustic-Emission(BAE) ``1''/f -``Noise'' Power-Spectrum Power-Law UNIVERSALITY is Merely F=ma Time-Series Integral-Transform, aka ``Bak'' -``SOC'' REdiscovery'' PRE(1687)-``Bak''(1988)

NASA Astrophysics Data System (ADS)

Siegel, Edward; Nabarro, Frank; Brailsford, Alan; Tatro, Clement

2011-06-01

NON-shock-plasticity/fracture BAE[E.S.:MSE 8,310(71);PSS:(a)5,601/607(71);Xl.-Latt. Defects 5,277(74);Scripta Met.:6,785(72); 8,587/617(74);3rd Tokyo AE Symp.(76);Acta Met. 25,383(77);JMMM 7,312(78)] ``1''/ ω-``noise'' power-spectrum ``pink''-Zipf-(NOT ``red''-Pareto) power-law UNIVERSALITY is manifestly-demonstrated in two distinct ways to be nothing but Newton Law of Motion F = ma REdiscovery!!!(aka ``Bak''(1988)-``SOC'':1687 < < < 1988: 1988-1687=301-years!!! PHYSICS:(1687) cross-multiplied F=ma rewritten as 1/m=a/F=OUTPUT/IN-PUT=EFFECT/CAUSE=inverse-mass mechanical-susceptibility=X(`` ω'') X(`` ω '') ~(F.-D. thm.) ~P(`` ω'') ``noise'' power-spectrum; (``Max & Al show''): E ~ ω , & E ~(or any/all media with upper-limiting-speeds) ~m. Thus: ω ~ E ~m inverting: 1/ ω ~ 1/E ~1/m ~a/F= X(`` ω'') ~ P(`` ω'') thus: F=ma integral-transform(I-T) is ```SOC'''s'' P(ω) ~ 1/ ω !!!; ``PURE''-MATHS: F=ma DOUBLE-integral time-series(T-S) s(t)=[v0t+(1/2)at2] I-T formally defines power-spectrum:

Large trilinear At soft supersymmetry breaking coupling from 5D MSSM

NASA Astrophysics Data System (ADS)

Abdalgabar, Ammar; Cornell, A. S.

2015-10-01

The possibility of generating a large trilinear At soft supersymmetry breaking coupling at low energies through renormalisation group evolution in the 5D MSSM is investigated. Using the power law running in five dimensions and a compactification scale in the 10-103 TeV range, we show that gluino mass may drive a large enough At to reproduce the measured Higgs mass and have a light stop superpartner below ∼ 1 TeV, as preferred by the fine tuning argument for the Higgs mass.
Thermodynamics of the relativistic Fermi gas in D dimensions

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.; Piña, Omar

2017-09-01

The influence of spatial dimensionality and particle-antiparticle pair production on the thermodynamic properties of the relativistic Fermi gas, at finite chemical potential, is studied. Resembling a "phase transition", qualitatively different behaviors of the thermodynamic susceptibilities, namely the isothermal compressibility and the specific heat, are markedly observed at different temperature regimes as function of the system dimensionality and of the rest mass of the particles. A minimum in the temperature dependence of the isothermal compressibility marks a characteristic temperature, in the range of tenths of the Fermi temperature, at which the system transit from a "normal" phase, to a phase where the gas compressibility grows as a power law of the temperature.
Power law analysis of the human microbiome.

PubMed

Ma, Zhanshan Sam

2015-11-01

Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs. © 2015 John Wiley & Sons Ltd.
An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle

NASA Astrophysics Data System (ADS)

Yong, Nuo; Ni, Shunjiang; Shen, Shifei; Ji, Xuewei

2016-08-01

We studied the distribution of entry time interval in Beijing subway traffic by analyzing the smart card transaction data, and then deduced the probability distribution function of entry time interval based on the Maximum Entropy Principle. Both theoretical derivation and data statistics indicated that the entry time interval obeys power-law distribution with an exponential cutoff. In addition, we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function. It is speculated that for bursts and heavy tails in human dynamics, when the fitted power exponent is less than 1.0, it cannot be a pure power-law distribution, but with an exponential cutoff, which may be ignored in the previous studies.
Deviation from Power Law Behavior in Landslide Phenomenon

NASA Astrophysics Data System (ADS)

Li, L.; Lan, H.; Wu, Y.

2013-12-01

Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law behavior in landslide phenomenon. Figure shows that a rollover of landslide size distribution in the small size end is produced as the probability for V/S (the failure volume to failure surface ratio of landslide) exceeding the mechanical threshold applied to the power law distribution of landslide volume.
Photometric and Structural Properties of NGC 6544: A Combined VVV-Hubble Space Telescope Study

NASA Astrophysics Data System (ADS)

Cohen, Roger E.; Mauro, Francesco; Geisler, Doug; Moni Bidin, Christian; Dotter, Aaron; Bonatto, Charles

2014-07-01

We combine archival Hubble Space Telescope imaging with wide-field near-infrared photometry to study the neglected metal-poor Galactic globular cluster NGC 6544. A high spatial resolution map of differential reddening over the inner portion of the cluster is constructed, revealing variations of up to half of the total reddening, and the resulting corrected color-magnitude diagrams reveal a sparse blue horizontal branch and centrally concentrated blue straggler population, verified via relative proper motions. Using the corrected photometry to investigate the cluster distance, reddening, and age via direct comparison to well-calibrated photometry of clusters with similar metallicities, we estimate (m - M)0 = 11.96, E(B - V) = 0.79, and an age coeval with M13 to within the relevant uncertainties. Although our data are insufficient to place tight constraints on the reddening law toward NGC 6544, we find no strong evidence that it is non-standard at optical or near-infrared wavelengths. We also provide near-infrared fiducial sequences extending nearly 2 mag below the cluster main sequence turnoff, generated from a statistically decontaminated sample of cluster stars. Lastly, we redetermine the cluster center and construct a radial number density profile which is well fit by an atypically flat power law with a slope of about 1.7. We discuss this result, together with a flattened main sequence luminosity function and inverted mass function, in the context of mass segregation and tidal stripping via interactions with Milky Way potential.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.

PubMed

Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L

2011-10-01

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.
Bounds of memory strength for power-law series.

PubMed

Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao

2017-05-01

Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α. By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α, which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1<α≤3, as α grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when α>3, the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
Bounds of memory strength for power-law series

NASA Astrophysics Data System (ADS)

Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao

2017-05-01

Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α . By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α , which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1 <α ≤3 , as α grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when α >3 , the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
Early-Time Observations of the GRB 050319 Optical Transient

NASA Astrophysics Data System (ADS)

Quimby, R. M.; Rykoff, E. S.; Yost, S. A.; Aharonian, F.; Akerlof, C. W.; Alatalo, K.; Ashley, M. C. B.; Göǧüş, E.; Güver, T.; Horns, D.; Kehoe, R. L.; Kιzιloǧlu, Ü.; Mckay, T. A.; Özel, M.; Phillips, A.; Schaefer, B. E.; Smith, D. A.; Swan, H. F.; Vestrand, W. T.; Wheeler, J. C.; Wren, J.

2006-03-01

We present the unfiltered ROTSE-III light curve of the optical transient associated with GRB 050319 beginning 4 s after the cessation of γ-ray activity. We fit a power-law function to the data using the revised trigger time given by Chincarini and coworkers, and a smoothly broken power-law to the data using the original trigger disseminated through the GCN notices. Including the RAPTOR data from Woźniak and coworkers, the best-fit power-law indices are α=-0.854+/-0.014 for the single power-law and α1=-0.364+0.020-0.019, α2=-0.881+0.030-0.031, with a break at tb=418+31-30 s for the smoothly broken fit. We discuss the fit results, with emphasis placed on the importance of knowing the true start time of the optical transient for this multipeaked burst. As Swift continues to provide prompt GRB locations, it becomes more important to answer the question, ``when does the afterglow begin?'' in order to correctly interpret the light curves.
Impact of compressibility and a guide field on Fermi acceleration during magnetic island coalescence

NASA Astrophysics Data System (ADS)

Montag, Peter; Egedal, Jan; Lichko, Emily; Wetherton, Blake

2017-10-01

Previous work has shown that Fermi acceleration can be an effective heating mechanism during magnetic island coalescence, where electrons may undergo repeated reflections as the magnetic field lines contract. This energization has the potential to account for the power-law distributions of particle energy inferred from observations of solar flares. Here, we develop a generalized framework for the analysis of Fermi acceleration that can incorporate the effects of compressibility and non-uniformity along field lines, which have commonly been neglected in previous treatments of the problem. Applying this framework to the simplified case of the uniform flux tube allows us to find both the power-law scaling of the distribution function and the rate at which the power-law behavior develops. We find that a guide magnetic field of order unity effectively suppresses the development of power-law distributions. The work was supported by NASA Grant No. NNX14AC68G, NSF GEM Grant No. 1405166, NSF Award 1404166, and NASA Award NNX15AJ73G.
Definition of (so MIScalled) ''Complexity'' as UTTER-SIMPLICITY!!! Versus Deviations From it as Complicatedness-Measure

NASA Astrophysics Data System (ADS)

Young, F.; Siegel, Edward Carl-Ludwig

2011-03-01

(so MIScalled) "complexity" with INHERENT BOTH SCALE-Invariance Symmetry-RESTORING, AND 1 / w (1.000..) "pink" Zipf-law Archimedes-HYPERBOLICITY INEVITABILITY power-spectrum power-law decay algebraicity. Their CONNECTION is via simple-calculus SCALE-Invariance Symmetry-RESTORING logarithm-function derivative: (d/ d ω) ln(ω) = 1 / ω , i.e. (d/ d ω) [SCALE-Invariance Symmetry-RESTORING](ω) = 1/ ω . Via Noether-theorem continuous-symmetries relation to conservation-laws: (d/ d ω) [inter-scale 4-current 4-div-ergence} = 0](ω) = 1 / ω . Hence (so MIScalled) "complexity" is information inter-scale conservation, in agreement with Anderson-Mandell [Fractals of Brain/Mind, G. Stamov ed.(1994)] experimental-psychology!!!], i.e. (so MIScalled) "complexity" is UTTER-SIMPLICITY!!! Versus COMPLICATEDNESS either PLUS (Additive) VS. TIMES (Multiplicative) COMPLICATIONS of various system-specifics. COMPLICATEDNESS-MEASURE DEVIATIONS FROM complexity's UTTER-SIMPLICITY!!!: EITHER [SCALE-Invariance Symmetry-BREAKING] MINUS [SCALE-Invariance Symmetry-RESTORING] via power-spectrum power-law algebraicity decays DIFFERENCES: ["red"-Pareto] MINUS ["pink"-Zipf Archimedes-HYPERBOLICITY INEVITABILITY]!!!
Development of an Atmospheric Dispersion Model for Heavier-Than-Air Gas Mixtures. Volume 3. DEGADIS User’s Manual.

DTIC Science & Technology

1985-05-01

interpolates between a pair of points based on a list of supplied values (C-2). () ALP estimates the ambient wind profile power a by minimizing the integral...Typical Values of Surface Roughness 7 1.2. Representative Konin-Obukhov Lengths arnd Power Law Exponents for Different Atmospheric Stabilities 8 IV.1...a constant in power law wind profile 0 constant in a correlation r gama function 𔄁 ratio of (p - pa)/Cc 6 constant in a correlation y AMonin-Obukhov
A tale of four surveys:What have we learned about the variable sky?

NASA Astrophysics Data System (ADS)

Howell, S. B.

2008-03-01

Four tales concerning a set of photometric imaging surveys are spun. The reader is lead through a brief description of each survey and major results are presented. The four surveys are summarized in a few simple "rules": 1) The fraction of point sources that are variable with respect to those that are found to be constant, increases as a power law as the photometric precision of the survey improves, and 2) This fact can be simply formulated as a power law function granting the user a predictive power.
Long-time correlation for the chaotic orbit in the two-wave Hamiltonian

NASA Astrophysics Data System (ADS)

Hatori, Tadatsugu; Irie, Haruyuki

1987-03-01

The time correlation function of velocity is found to decay with the power law for the orbit governed by a Hamiltonian, H=v sup 2/2 - Mcosx - Pcos (k(x-t)). The renormalization group technique can predict the power of decay for the correlation function defined by the ensemble average. The power spectrum becomes the 1/f-type for a special case.
Ionospheric scintillation by a random phase screen Spectral approach

NASA Technical Reports Server (NTRS)

Rufenach, C. L.

1975-01-01

The theory developed by Briggs and Parkin, given in terms of an anisotropic gaussian correlation function, is extended to a spectral description specified as a continuous function of spatial wavenumber with an intrinsic outer scale as would be expected from a turbulent medium. Two spectral forms were selected for comparison: (1) a power-law variation in wavenumber with a constant three-dimensional index equal to 4, and (2) Gaussian spectral variation. The results are applied to the F-region ionosphere with an outer-scale wavenumber of 2 per km (approximately equal to the Fresnel wavenumber) for the power-law variation, and 0.2 per km for the Gaussian spectral variation. The power-law form with a small outer-scale wavenumber is consistent with recent F-region in-situ measurements, whereas the gaussian form is mathematically convenient and, hence, mostly used in the previous developments before the recent in-situ measurements. Some comparison with microwave scintillation in equatorial areas is made.
Nonrelativistic Yang-Mills theory for a naturally light Higgs boson

NASA Astrophysics Data System (ADS)

Berthier, Laure; Grosvenor, Kevin T.; Yan, Ziqi

2017-11-01

We continue the study of the nonrelativistic short-distance completions of a naturally light Higgs, focusing on the interplay between the gauge symmetries and the polynomial shift symmetries. We investigate the naturalness of nonrelativistic scalar quantum electrodynamics with a dynamical critical exponent z =3 by computing leading power law divergences to the scalar propagator in this theory. We find that power law divergences exhibit a more refined structure in theories that lack boost symmetries. Finally, in this toy model, we show that it is possible to preserve a fairly large hierarchy between the scalar mass and the high-energy naturalness scale across 7 orders of magnitude, while accommodating a gauge coupling of order 0.1.
MODELING THE TIME VARIABILITY OF SDSS STRIPE 82 QUASARS AS A DAMPED RANDOM WALK

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacLeod, C. L.; Ivezic, Z.; Bullock, E.

2010-10-01

We model the time variability of {approx}9000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk (DRW). Using 2.7 million photometric measurements collected over 10 yr, we confirm the results of Kelly et al. and Kozlowski et al. that this model can explain quasar light curves at an impressive fidelity level (0.01-0.02 mag). The DRW model provides a simple, fast (O(N) for N data points), and powerful statistical description of quasar light curves by a characteristic timescale ({tau}) and an asymptotic rms variability on long timescales (SF{sub {infinity}}). We searched for correlations between these two variability parametersmore » and physical parameters such as luminosity and black hole mass, and rest-frame wavelength. Our analysis shows SF{sub {infinity}} to increase with decreasing luminosity and rest-frame wavelength as observed previously, and without a correlation with redshift. We find a correlation between SF{sub {infinity}} and black hole mass with a power-law index of 0.18 {+-} 0.03, independent of the anti-correlation with luminosity. We find that {tau} increases with increasing wavelength with a power-law index of 0.17, remains nearly constant with redshift and luminosity, and increases with increasing black hole mass with a power-law index of 0.21 {+-} 0.07. The amplitude of variability is anti-correlated with the Eddington ratio, which suggests a scenario where optical fluctuations are tied to variations in the accretion rate. However, we find an additional dependence on luminosity and/or black hole mass that cannot be explained by the trend with Eddington ratio. The radio-loudest quasars have systematically larger variability amplitudes by about 30%, when corrected for the other observed trends, while the distribution of their characteristic timescale is indistinguishable from that of the full sample. We do not detect any statistically robust differences in the characteristic timescale and variability amplitude between the full sample and the small subsample of quasars detected by ROSAT. Our results provide a simple quantitative framework for generating mock quasar light curves, such as currently used in LSST image simulations.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Mittal, Tushar; Chen, Christine H.; Jang-Condell, Hannah

During the Spitzer Space Telescope cryogenic mission, astronomers obtained Infrared Spectrograph (IRS) observations of hundreds of debris disk candidates that have been compiled in the Spitzer IRS Debris Disk Catalog. We have discovered 10 and/or 20 μm silicate emission features toward 120 targets in the catalog and modeled the IRS spectra of these sources, consistent with MIPS 70 μm observations, assuming that the grains are composed of silicates (olivine, pyroxene, forsterite, and enstatite) and are located either in a continuous disk with power-law size and surface density distributions or thin rings that are well-characterized using two separate dust grain temperatures.more » For systems better fit by the continuous disk model, we find that (1) the dust size distribution power-law index is consistent with that expected from a collisional cascade, q = 3.5-4.0, with a large number of values outside this range, and (2) the minimum grain size, a {sub min}, increases with stellar luminosity, L {sub *}, but the dependence of a {sub min} on L {sub *} is weaker than expected from radiation pressure alone. In addition, we also find that (3) the crystalline fraction of dust in debris disks evolves as a function of time with a large dispersion in crystalline fractions for stars of any particular stellar age or mass, (4) the disk inner edge is correlated with host star mass, and (5) there exists substantial variation in the properties of coeval disks in Sco-Cen, indicating that the observed variation is probably due to stochasticity and diversity in planet formation.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Gair, Jonathan R.; Tang, Christopher; Volonteri, Marta

One of the sources of gravitational waves for the proposed space-based gravitational wave detector, the Laser Interferometer Space Antenna (LISA), are the inspirals of compact objects into supermassive black holes in the centers of galaxies--extreme-mass-ratio inspirals (EMRIs). Using LISA observations, we will be able to measure the parameters of each EMRI system detected to very high precision. However, the statistics of the set of EMRI events observed by LISA will be more important in constraining astrophysical models than extremely precise measurements for individual systems. The black holes to which LISA is most sensitive are in a mass range that ismore » difficult to probe using other techniques, so LISA provides an almost unique window onto these objects. In this paper we explore, using Bayesian techniques, the constraints that LISA EMRI observations can place on the mass function of black holes at low redshift. We describe a general framework for approaching inference of this type--using multiple observations in combination to constrain a parametrized source population. Assuming that the scaling of the EMRI rate with the black-hole mass is known and taking a black-hole distribution given by a simple power law, dn/dlnM=A{sub 0}(M/M{sub *}){sup {alpha}}{sub 0}, we find that LISA could measure the parameters to a precision of {Delta}(lnA{sub 0}){approx}0.08, and {Delta}({alpha}{sub 0}){approx}0.03 for a reference model that predicts {approx}1000 events. Even with as few as 10 events, LISA should constrain the slope to a precision {approx}0.3, which is the current level of observational uncertainty in the low-mass slope of the black-hole mass function. We also consider a model in which A{sub 0} and {alpha}{sub 0} evolve with redshift, but find that EMRI observations alone do not have much power to probe such an evolution.« less

The use of broken power-laws to describe the distributions of daily flow above the mean annual flow across the conterminous U.S.

Treesearch

Catalina Segura; Davide Lazzati; Arumugam Sankarasubramanian

2013-01-01

A recent study employed a broken power-law (BPL) distribution for understanding the scaling frequency of bankfull discharge in snowmelt-dominated basins. This study, grounded from those findings, investigated the ability of a BPL function to describe the distribution of daily flows above the mean annual flow in 1217 sites across the conterminous U.S. (CONUS). The...
Dynamic intersectoral models with power-law memory

NASA Astrophysics Data System (ADS)

Tarasova, Valentina V.; Tarasov, Vasily E.

2018-01-01

Intersectoral dynamic models with power-law memory are proposed. The equations of open and closed intersectoral models, in which the memory effects are described by the Caputo derivatives of non-integer orders, are derived. We suggest solutions of these equations, which have the form of linear combinations of the Mittag-Leffler functions and which are characterized by different effective growth rates. Examples of intersectoral dynamics with power-law memory are suggested for two sectoral cases. We formulate two principles of intersectoral dynamics with memory: the principle of changing of technological growth rates and the principle of domination change. It has been shown that in the input-output economic dynamics the effects of fading memory can change the economic growth rate and dominant behavior of economic sectors.
Mass Distribution in Galaxy Cluster Cores

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogan, M. T.; McNamara, B. R.; Pulido, F.

Many processes within galaxy clusters, such as those believed to govern the onset of thermally unstable cooling and active galactic nucleus feedback, are dependent upon local dynamical timescales. However, accurate mapping of the mass distribution within individual clusters is challenging, particularly toward cluster centers where the total mass budget has substantial radially dependent contributions from the stellar ( M {sub *}), gas ( M {sub gas}), and dark matter ( M {sub DM}) components. In this paper we use a small sample of galaxy clusters with deep Chandra observations and good ancillary tracers of their gravitating mass at both largemore » and small radii to develop a method for determining mass profiles that span a wide radial range and extend down into the central galaxy. We also consider potential observational pitfalls in understanding cooling in hot cluster atmospheres, and find tentative evidence for a relationship between the radial extent of cooling X-ray gas and nebular H α emission in cool-core clusters. At large radii the entropy profiles of our clusters agree with the baseline power law of K ∝ r {sup 1.1} expected from gravity alone. At smaller radii our entropy profiles become shallower but continue with a power law of the form K ∝ r {sup 0.67} down to our resolution limit. Among this small sample of cool-core clusters we therefore find no support for the existence of a central flat “entropy floor.”.« less
Membership and Dynamical Parameters of the Open Cluster NGC 1039

NASA Astrophysics Data System (ADS)

Wang, Jiaxin; Ma, Jun; Wu, Zhenyu; Zhou, Xu

2017-11-01

In this paper, we analyze the open cluster NGC 1039. This young open cluster is observed as a part of Beijing-Arizona-Taiwan-Connecticut Multicolor Sky Survey. Combining our observations with the Sloan Digital Sky Survey photometric data, we employ the Padova stellar model and the zero-age main-sequence curve to the data to derive a reddening, E(B-V)=0.10+/- 0.02, and a distance modulus, {(m-M)}0=8.4+/- 0.2, for NGC 1039. The photometric membership probabilities of stars in the region of NGC 1039 are derived using the spectral energy distribution-fitting method. According to the membership probabilities ({P}{SED}) obtained here, 582 stars are cluster members with {P}{SED} larger than 60%. In addition, we determine the structural parameters of NGC 1039 by fitting its radial density profile with the King model. These parameters are a core radius, {R}{{c}}=4.44+/- 1.31 {pc}; a tidal radius, {R}{{t}}=13.57+/- 4.85 {pc}; and a concentration parameter of {C}0={log}({R}{{t}}/{R}{{c}})=0.49+/- 0.20. We also fit the observed mass function of NGC 1039 with masses from 0.3 {M}⊙ to 1.65 {M}⊙ with a power-law function {{Φ }}(m)\\propto {m}α to derive its slopes of mass functions of different spatial regions. The results obtained here show that the slope of the mass function of NGC 1039 is flatter in the central regions (α = 0.117), becomes steeper at larger radii (α = -2.878), and breaks at {m}{break}≈ 0.80 {M}⊙ . In particular, for the first time, our results show that the mass segregation appears in NGC 1039.
Relativity, nonextensivity, and extended power law distributions.

PubMed

Silva, R; Lima, J A S

2005-11-01

A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.
The global star formation law of galaxies revisited in the radio continuum

NASA Astrophysics Data System (ADS)

Liu, LiJie; Gao, Yu

2012-02-01

We study the global star formation law, the relation between the gas and star formation rate (SFR) in a sample of 130 local galaxies with infrared (IR) luminosities spanning over three orders of magnitude (109-1012 L⊙), which includes 91 normal spiral galaxies and 39 (ultra)luminous IR galaxies [(U)LIRGs]. We derive their total (atomic and molecular) gas and dense molecular gas masses using newly available HI, CO and HCN data from the literature. The SFR of galaxies is determined from total IR (8-1000 μm) and 1.4 GHz radio continuum (RC) luminosities. The galaxy disk sizes are defined by the de-convolved elliptical Gaussian FWHM of the RC maps. We derive the galaxy disk-averaged SFRs and various gas surface densities, and investigate their relationships. We find that the galaxy disk-averaged surface density of dense molecular gas mass has the tightest correlation with that of SFR (scatter ˜0.26 dex), and is linear in log-log space (power-law slope of N=1.03±0.02) across the full galaxy sample. The correlation between the total gas and SFR surface densities for the full sample has a somewhat larger scatter (˜0.48 dex), and is best fit by a power-law with slope 1.45±0.02. However, the slope changes from ˜1 when only normal spirals are considered, to ˜1.5 when more and more (U)LIRGs are included in the fitting. When different CO-to-H2 conversion factors are used to infer molecular gas masses for normal galaxies and (U)LIRGs, the bi-modal relations claimed recently in CO observations of high-redshift galaxies appear to also exist in local populations of star-forming galaxies.
Development of Jet Noise Power Spectral Laws Using SHJAR Data

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James

2009-01-01

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.
A grid of MHD models for stellar mass loss and spin-down rates of solar analogs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cohen, O.; Drake, J. J.

2014-03-01

Stellar winds are believed to be the dominant factor in the spin-down of stars over time. However, stellar winds of solar analogs are poorly constrained due to observational challenges. In this paper, we present a grid of magnetohydrodynamic models to study and quantify the values of stellar mass loss and angular momentum loss rates as a function of the stellar rotation period, magnetic dipole component, and coronal base density. We derive simple scaling laws for the loss rates as a function of these parameters, and constrain the possible mass loss rate of stars with thermally driven winds. Despite the successmore » of our scaling law in matching the results of the model, we find a deviation between the 'solar dipole' case and a real case based on solar observations that overestimates the actual solar mass loss rate by a factor of three. This implies that the model for stellar fields might require a further investigation with additional complexity. Mass loss rates in general are largely controlled by the magnetic field strength, with the wind density varying in proportion to the confining magnetic pressure B {sup 2}. We also find that the mass loss rates obtained using our grid models drop much faster with the increase in rotation period than scaling laws derived using observed stellar activity. For main-sequence solar-like stars, our scaling law for angular momentum loss versus poloidal magnetic field strength retrieves the well-known Skumanich decline of angular velocity with time, Ω{sub *}∝t {sup –1/2}, if the large-scale poloidal magnetic field scales with rotation rate as B{sub p}∝Ω{sub ⋆}{sup 2}.« less
Universal Expression of Efficiency at Maximum Power: A Quantum-Mechanical Brayton Engine Working with a Single Particle Confined in a Power-Law Trap

NASA Astrophysics Data System (ADS)

Ye, Zhuo-Lin; Li, Wei-Sheng; Lai, Yi-Ming; He, Ji-Zhou; Wang, Jian-Hui

2015-12-01

We propose a quantum-mechanical Brayton engine model that works between two superposed states, employing a single particle confined in an arbitrary power-law trap as the working substance. Applying the superposition principle, we obtain the explicit expressions of the power and efficiency, and find that the efficiency at maximum power is bounded from above by the function: η+ = θ/(θ + 1), with θ being a potential-dependent exponent. Supported by the National Natural Science Foundation of China under Grant Nos. 11505091, 11265010, and 11365015, and the Jiangxi Provincial Natural Science Foundation under Grant No. 20132BAB212009
Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.
Tsallis entropy and complexity theory in the understanding of physics of precursory accelerating seismicity.

NASA Astrophysics Data System (ADS)

Vallianatos, Filippos; Chatzopoulos, George

2014-05-01

Strong observational indications support the hypothesis that many large earthquakes are preceded by accelerating seismic release rates which described by a power law time to failure relation. In the present work, a unified theoretical framework is discussed based on the ideas of non-extensive statistical physics along with fundamental principles of physics such as the energy conservation in a faulted crustal volume undergoing stress loading. We derive the time-to-failure power-law of: a) cumulative number of earthquakes, b) cumulative Benioff strain and c) cumulative energy released in a fault system that obeys a hierarchical distribution law extracted from Tsallis entropy. Considering the analytic conditions near the time of failure, we derive from first principles the time-to-failure power-law and show that a common critical exponent m(q) exists, which is a function of the non-extensive entropic parameter q. We conclude that the cumulative precursory parameters are function of the energy supplied to the system and the size of the precursory volume. In addition the q-exponential distribution which describes the fault system is a crucial factor on the appearance of power-law acceleration in the seismicity. Our results based on Tsallis entropy and the energy conservation gives a new view on the empirical laws derived by other researchers. Examples and applications of this technique to observations of accelerating seismicity will also be presented and discussed. This work was implemented through the project IMPACT-ARC in the framework of action "ARCHIMEDES III-Support of Research Teams at TEI of Crete" (MIS380353) of the Operational Program "Education and Lifelong Learning" and is co-financed by the European Union (European Social Fund) and Greek national funds
Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox

PubMed Central

Marshall, Najja; Timme, Nicholas M.; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M.

2016-01-01

Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of “neural avalanches” (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods—power-law fitting, avalanche shape collapse, and neural complexity—have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox. PMID:27445842
Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox.

PubMed

Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M

2016-01-01

Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W., Jr.

2003-01-01

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
Constraining the physical structure of the inner few 100 AU scales of deeply embedded low-mass protostars

NASA Astrophysics Data System (ADS)

Persson, M. V.; Harsono, D.; Tobin, J. J.; van Dishoeck, E. F.; Jørgensen, J. K.; Murillo, N.; Lai, S.-P.

2016-05-01

Context. The physical structure of deeply embedded low-mass protostars (Class 0) on scales of less than 300 AU is still poorly constrained. While molecular line observations demonstrate the presence of disks with Keplerian rotation toward a handful of sources, others show no hint of rotation. Determining the structure on small scales (a few 100 AU) is crucial for understanding the physical and chemical evolution from cores to disks. Aims: We determine the presence and characteristics of compact, disk-like structures in deeply embedded low-mass protostars. A related goal is investigating how the derived structure affects the determination of gas-phase molecular abundances on hot-core scales. Methods: Two models of the emission, a Gaussian disk intensity distribution and a parametrized power-law disk model, are fitted to subarcsecond resolution interferometric continuum observations of five Class 0 sources, including one source with a confirmed Keplerian disk. Prior to fitting the models to the de-projected real visibilities, the estimated envelope from an independent model and any companion sources are subtracted. For reference, a spherically symmetric single power-law envelope is fitted to the larger scale emission (~1000 AU) and investigated further for one of the sources on smaller scales. Results: The radii of the fitted disk-like structures range from ~90-170 AU, and the derived masses depend on the method. Using the Gaussian disk model results in masses of 54-556 × 10-3 M⊙, and using the power-law disk model gives 9-140 × 10-3 M⊙. While the disk radii agree with previous estimates the masses are different for some of the sources studied. Assuming a typical temperature distribution (r-0.5), the fractional amount of mass in the disk above 100 K varies from 7% to 30%. Conclusions: A thin disk model can approximate the emission and physical structure in the inner few 100 AU scales of the studied deeply embedded low-mass protostars and paves the way for analysis of a larger sample with ALMA. Kinematic data are needed to determine the presence of any Keplerian disk. Using previous observations of p-H218O, we estimate the relative gas phase water abundances relative to total warm H2 to be 6.2 × 10-5 (IRAS 2A), 0.33 × 10-5 (IRAS 4A-NW), 1.8 × 10-7 (IRAS 4B), and < 2 × 10-7 (IRAS 4A-SE), roughly an order of magnitude higher than previously inferred when both warm and cold H2 were used as reference. A spherically symmetric single power-law envelope model fails to simultaneously reproduce both the small- and large-scale emission. Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).Continuum data for the sources are available through http://dx.doi.org/10.5281/zenodo.47642 and at CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/590/A33
The solar gravitational figure: J2 and J4

NASA Technical Reports Server (NTRS)

Ulrich, R. K.; Hawkins, G. W.

1980-01-01

The theory of the solar gravitational figure is derived including the effects of differential rotation. It is shown that J sub 4 is smaller than J sub 2 by a factor of about 10 rather than being of order J sub 2 squared as would be expected for rigid rotation. The dependence of both J sub 2 and J sub 4 on envelope mass is given. High order p-mode oscillation frequencies provide a constraint on solar structure which limits the range in envelope mass to the range 0.01 M sub E/solar mass 0.04. For an assumed rotation law in which the surface pattern of differential rotation extends uniformly throughout the convective envelope, this structural constraint limits the ranges of J sub 2 and J sub 4 in units of 10 to the -8th power to 10 J sub 2 15 and 0.6 -J sub 4 1.5. Deviations from these ranges would imply that the rotation law is not constant with depth and would provide a measure of this rotation law.
Self-organized criticality in a cold plasma

NASA Astrophysics Data System (ADS)

Alex, Prince; Carreras, Benjamin Andres; Arumugam, Saravanan; Sinha, Suraj Kumar

2017-12-01

We present direct evidence for the existence of self-organized critical behavior in cold plasma. A multiple anodic double layer structure generated in a double discharge plasma setup shows critical behavior for the anode bias above a threshold value. Analysis of the floating potential fluctuations reveals the existence of long-range time correlations and power law behavior in the tail of the probability distribution function of the fluctuations. The measured Hurst exponent and the power law tail in the rank function are strong indication of the self-organized critical behavior of the system and hence provide a condition under which complexities arise in cold plasma.
2MASS wide-field extinction maps. V. Corona Australis

NASA Astrophysics Data System (ADS)

Alves, João; Lombardi, Marco; Lada, Charles J.

2014-05-01

We present a near-infrared extinction map of a large region (~870 deg2) covering the isolated Corona Australis complex of molecular clouds. We reach a 1-σ error of 0.02 mag in the K-band extinction with a resolution of 3 arcmin over the entire map. We find that the Corona Australis cloud is about three times as large as revealed by previous CO and dust emission surveys. The cloud consists of a 45 pc long complex of filamentary structure from the well known star forming Western-end (the head, N ≥ 1023 cm-2) to the diffuse Eastern-end (the tail, N ≤ 1021 cm-2). Remarkably, about two thirds of the complex both in size and mass lie beneath AV ~ 1 mag. We find that the probability density function (PDF) of the cloud cannot be described by a single log-normal function. Similar to prior studies, we found a significant excess at high column densities, but a log-normal + power-law tail fit does not work well at low column densities. We show that at low column densities near the peak of the observed PDF, both the amplitude and shape of the PDF are dominated by noise in the extinction measurements making it impractical to derive the intrinsic cloud PDF below AK < 0.15 mag. Above AK ~ 0.15 mag, essentially the molecular component of the cloud, the PDF appears to be best described by a power-law with index -3, but could also described as the tail of a broad and relatively low amplitude, log-normal PDF that peaks at very low column densities. FITS files of the extinction maps are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/565/A18
Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties.

PubMed

Ryabov, Artem; Berestneva, Ekaterina; Holubec, Viktor

2015-09-21

The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, U(x, t) = g(t)log(x), subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of diffusion-controlled reactions of charged molecules or escape of Brownian particles over a time-dependent entropic barrier at the end of a biological pore. We present a simple asymptotic theory which yields the long-time behavior of both the survival probability (first-passage properties) and the moments of the particle position (dynamics). The asymptotic survival probability, i.e., the probability that the particle will not hit the origin before a given time, is a functional of the potential strength. As such, it exhibits a rather varied behavior for different functions g(t). The latter can be grouped into three classes according to the regime of the asymptotic decay of the survival probability. We distinguish 1. the regular (power-law decay), 2. the marginal (power law times a slow function of time), and 3. the regime of enhanced absorption (decay faster than the power law, e.g., exponential). Results of the asymptotic theory show good agreement with numerical simulations.
Weak lensing measurement of the mass–richness relation of SDSS redMaPPer clusters

DOE PAGES

Simet, Melanie; McClintock, Tom; Mandelbaum, Rachel; ...

2016-12-15

Here, we perform a measurement of the mass–richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey. We carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-zz biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centering, halo triaxiality, and projection effects. We then compare measurements of the lensing signal from two independently-produced shear and photometric redshift catalogues to characterize systematic errors in the lensing signal itself. Using a sample of 5,570 clusters from 0.1 ≤ zz ≤ 0.33, the normalization of our power-law mass vs. λ relation is log 10[M 200m/h -1 M ⊙] = 14.344 ± 0.021 (statistical) ±0.023 (systematic) at a richness λ = 40, a 7 per cent calibration uncertainty, with a power-law index of 1.33+0.09-0.101.33more » $$+0.09\\atop{-0.10}$$ (1σ). Finally, the detailed systematics characterization in this work renders it the definitive weak lensing mass calibration for SDSS redMaPPer clusters at this time.« less

A new experimental correlation for non-Newtonian behavior of COOH-DWCNTs/antifreeze nanofluid

NASA Astrophysics Data System (ADS)

Izadi, Farhad; Ranjbarzadeh, Ramin; Kalbasi, Rasool; Afrand, Masoud

2018-04-01

In this paper, the rheological behavior of nano-antifreeze consisting of 50%vol. water, 50%vol. ethylene glycol and different quantities of functionalized double walled carbon nanotubes has been investigated experimentally. Initially, nano-antifreeze samples were prepared with solid volume fractions of 0.05, 0.1, 0.2, 0.4, 0.6, 0.8 and 1% using two-step method. Then, the dynamic viscosity of the nano-antifreeze samples was measured at different shear rates and temperatures. At this stage, the results showed that base fluid had the Newtonian behavior, while the behavior of all nano-antifreeze samples was non-Newtonian. Since the behavior of the samples was similar to power law model, it was attempted to find the constants of this model including consistency index and power law index. Therefore, using the measured viscosity and shear rates, consistency index and power law index were obtained by curve-fitting method. The obtained values showed that consistency index amplified with increasing volume fraction, while reduced with enhancing temperature. Besides, the obtained values for power law index were less than 1 for all samples which means shear thinning behavior. Lastly, new correlations were suggested to estimate the consistency index and power law index using curve-fitting.
Correlation analysis of radio properties and accretion-disk luminosity for low luminosity AGNs

NASA Astrophysics Data System (ADS)

Su, Renzhi; Liu, Xiang; Zhang, Zhen

2017-01-01

The correlation between the jet power and accretion disk luminosity is investigated and analyzed with our model for 7 samples of low luminosity active galactic nuclei (LLAGNs). The main results are: (1) the power-law correlation index (P_{jet} ∝ L_{disk} ^{μ}) typically ranges μ=0.4-0.7 for the LLAGN samples, and there is a hint of steep index for the LLAGN sample which hosted by a high fraction of elliptical galaxies, and there are no significant correlation between the μ and the LLAGN types (Seyfert, LINER); (2) for μ≈1, as noted in Liu et al., the accretion disk dominates the jet power and the black hole (BH) spin is not important, for the LLAGN samples studied in this paper we find that the μ is significantly less than unity, implying that BH spin may play a significant role in the jet power of LLAGNs; (3) the BH spin-jet power is negatively correlated with the BH mass in our model, which means a high spin-jet efficiency in the `low' BH-mass LLAGNs; (4) an anti-correlation between radio loudness and disk luminosity is found, which is apparently due to the flatter power-law index in the jet-disk correlation of the LLAGNs, and the radio loudness can be higher in the LLAGNs than in luminous AGNs/quasars when the BH spin-jet power is comparable to or dominate over the accretion-jet power in the LLAGNs. The high radio-core dominance of the LLAGNs is also discussed.
The low-mass star and sub-stellar populations of the 25 Orionis group

NASA Astrophysics Data System (ADS)

Downes, Juan José; Briceño, César; Mateu, Cecilia; Hernández, Jesús; Vivas, Anna Katherina; Calvet, Nuria; Hartmann, Lee; Petr-Gotzens, Monika G.; Allen, Lori

2014-10-01

We present the results of a survey of the low-mass star and brown dwarf population of the 25 Orionis group. Using optical photometry from the CIDA (Centro de Investigaciones de Astronomía `Francisco J. Duarte', Mérida, Venezuela) Deep Survey of Orion, near-IR photometry from the Visible and Infrared Survey Telescope for Astronomy and low-resolution spectroscopy obtained with Hectospec at the MMT telescope, we selected 1246 photometric candidates to low-mass stars and brown dwarfs with estimated masses within 0.02 ≲ M/M⊙ ≲ 0.8 and spectroscopically confirmed a sample of 77 low-mass stars as new members of the cluster with a mean age of ˜7 Myr. We have obtained a system initial mass function of the group that can be well described by either a Kroupa power-law function with indices α3 = -1.73 ± 0.31 and α2 = 0.68 ± 0.41 in the mass ranges 0.03 ≤ M/M⊙ ≤ 0.08 and 0.08 ≤ M/M⊙ ≤ 0.5, respectively, or a Scalo lognormal function with coefficients m_c=0.21^{+0.02}_{-0.02} and σ = 0.36 ± 0.03 in the mass range 0.03 ≤ M/M⊙ ≤ 0.8. From the analysis of the spatial distribution of this numerous candidate sample, we have confirmed the east-west elongation of the 25 Orionis group observed in previous works, and rule out a possible southern extension of the group. We find that the spatial distributions of low-mass stars and brown dwarfs in 25 Orionis are statistically indistinguishable. Finally, we found that the fraction of brown dwarfs showing IR excesses is higher than for low-mass stars, supporting the scenario in which the evolution of circumstellar discs around the least massive objects could be more prolonged.
Hard X-ray luminosity function of tidal disruption events: First results from the MAXI extragalactic survey

NASA Astrophysics Data System (ADS)

Kawamuro, Taiki; Ueda, Yoshihiro; Shidatsu, Megumi; Hori, Takafumi; Kawai, Nobuyuki; Negoro, Hitoshi; Mihara, Tatehiro

2016-08-01

We derive the first hard X-ray luminosity function (XLF) of stellar tidal disruption events (TDEs) by supermassive black holes (SMBHs), which gives an occurrence rate of TDEs per unit volume as a function of peak luminosity and redshift, utilizing an unbiased sample observed by the Monitor of All-sky X-ray Image (MAXI). On the basis of the light curves characterized by a power-law decay with an index of -5/3, a systematic search using the MAXI data detected four TDEs in the first 37 months of observations, all of which have been found in the literature. To formulate the TDE XLF, we consider the mass function of SMBHs, that of disrupted stars, the specific TDE rate as a function of SMBH mass, and the fraction of TDEs with relativistic jets. We perform an unbinned maximum likelihood fit to the MAXI TDE list and check the consistency with the observed TDE rate in the ROSAT all-sky survey. The results suggest that the intrinsic fraction of the jet-accompanying events is 0.0007%-34%. We confirm that at z ≲ 1.5 the contamination of the hard X-ray luminosity functions of active galactic nuclei by TDEs is not significant and hence that their contribution to the growth of SMBHs is negligible at the redshifts.
Constraints on the Evolution of the Galaxy Stellar Mass Function I: Role of Star Formation, Mergers, and Stellar Stripping

NASA Astrophysics Data System (ADS)

Contini, E.; Kang, Xi; Romeo, A. D.; Xia, Q.

2017-03-01

We study the connection between the observed star formation rate-stellar mass (SFR-M *) relation and the evolution of the stellar mass function (SMF) by means of a subhalo abundance matching technique coupled to merger trees extracted from an N-body simulation. Our approach, which considers both galaxy mergers and stellar stripping, is to force the model to match the observed SMF at redshift z> 2, and let it evolve down to the present time according to the observed SFR-M * relation. In this study, we use two different sets of SMFs and two SFR-M * relations: a simple power law and a relation with a mass-dependent slope. Our analysis shows that the evolution of the SMF is more consistent with an SFR-M * relation with a mass-dependent slope, in agreement with predictions from other models of galaxy evolution and recent observations. In order to fully and realistically describe the evolution of the SMF, both mergers and stellar stripping must be considered, and we find that both have almost equal effects on the evolution of SMF at the massive end. Taking into account the systematic uncertainties in the observed data, the high-mass end of the SMF obtained by considering stellar stripping results in good agreement with recent observational data from the Sloan Digital Sky Survey. At {log} {M}* < 11.2, our prediction at z = 0.1 is close to Li & White data, but the high-mass end ({log} {M}* > 11.2) is in better agreement with D’Souza et al. data which account for more massive galaxies.
Segmental front line dynamics of randomly pinned ferroelastic domain walls

NASA Astrophysics Data System (ADS)

Puchberger, S.; Soprunyuk, V.; Schranz, W.; Carpenter, M. A.

2018-01-01

Dynamic mechanical analysis (DMA) measurements as a function of temperature, frequency, and dynamic force amplitude are used to perform a detailed study of the domain wall motion in LaAlO3. In previous DMA measurements Harrison et al. [Phys. Rev. B 69, 144101 (2004), 10.1103/PhysRevB.69.144101] found evidence for dynamic phase transitions of ferroelastic domain walls in LaAlO3. In the present work we focus on the creep-to-relaxation region of domain wall motion using two complementary methods. We determine, in addition to dynamic susceptibility data, waiting time distributions of strain jerks during slowly increasing stress. These strain jerks, which result from self-similar avalanches close to the depinning threshold, follow a power-law behavior with an energy exponent ɛ =1.7 ±0.1 . Also, the distribution of waiting times between events follows a power law N (tw) ∝tw-(n +1 ) with an exponent n =0.9 , which transforms to a power law of susceptibility S (ω ) ∝ω-n . The present dynamic susceptibility data can be well fitted with a power law, with the same exponent (n =0.9 ) up to a characteristic frequency ω ≈ω* , where a crossover from stochastic DW motion to the pinned regime is well described using the scaling function of Fedorenko et al. [Phys. Rev. B 70, 224104 (2004), 10.1103/PhysRevB.70.224104].
Nature of convection-stabilized dc arcs in dual-flow nozzle geometry. I - The cold flow field and dc arc characteristics. II - Optical diagnostics and theory

NASA Astrophysics Data System (ADS)

Serbetci, Ilter; Nagamatsu, H. T.

1990-02-01

Steady-state low-current air arcs in a dual-flow nozzle system are studied experimentally. The cold flow field with no arc is investigated using a 12.7-mm diameter dual-flow nozzle in a steady-flow facility. Mach number and mass flux distributions are determined for various nozzle-pressure ratios and nozzle-gap spacing. It is found that the shock waves in the converging-diverging nozzles result in a decrease in overal resistance by about 15 percent. Also, Schlieren and differential interferometry techniques are used to visualize the density gradients within the arc plasma and thermal mantle. Both optical techniques reveal a laminar arc structure for a reservoir pressure of 1 atm at various current levels. Experimentally determined axial static pressure and cold-flow mass flux rate distributions and a channel-flow model with constant arc temperatre are used to solve the energy integral for the arc radius as a function of axial distance. The arc electric field strength, voltage, resistance, and power are determined with Ohm's law and the total heat transfer is related to arc power.
Convergence on the Prediction of Ice Particle Mass and Projected Area in Ice Clouds

NASA Astrophysics Data System (ADS)

Mitchell, D. L.

2013-12-01

Ice particle mass- and area-dimensional power law (henceforth m-D and A-D) relationships are building-blocks for formulating microphysical processes and optical properties in cloud and climate models, and they are critical for ice cloud remote sensing algorithms, affecting the retrieval accuracy. They can be estimated by (1) directly measuring the sizes, masses and areas of individual ice particles at ground-level and (2) using aircraft probes to simultaneously measure the ice water content (IWC) and ice particle size distribution. A third indirect method is to use observations from method 1 to develop an m-A relationship representing mean conditions in ice clouds. Owing to a tighter correlation (relative to m-D data), this m-A relationship can be used to estimate m from aircraft probe measurements of A. This has the advantage of estimating m at small sizes, down to 10 μm using the 2D-Sterio probe. In this way, 2D-S measurements of maximum dimension D can be related to corresponding estimates of m to develop ice cloud type and temperature dependent m-D expressions. However, these expressions are no longer linear in log-log space, but are slowly varying curves covering most of the size range of natural ice particles. This work compares all three of the above methods and demonstrates close agreement between them. Regarding (1), 4869 ice particles and corresponding melted hemispheres were measured during a field campaign to obtain D and m. Selecting only those unrimed habits that formed between -20°C and -40°C, the mean mass values for selected size intervals are within 35% of the corresponding masses predicted by the Method 3 curve based on a similar temperature range. Moreover, the most recent m-D expression based on Method 2 differs by no more than 50% with the m-D curve from Method 3. Method 3 appears to be the most accurate over the observed ice particle size range (10-4000 μm). An m-D/A-D scheme was developed by which self-consistent m-D and A-D power laws are extracted from Method 3 for a given ice particle number concentration N and IWC, appropriate for the relevant size range inferred from N and IWC. The resulting m-D/A-D power laws are based on the same data set comprised of 24 flights in ice clouds during a 6-month field campaign. Standard deviations for these power law constants are determined, which are much needed for cloud property remote sensing algorithms. Comparison of Method 3 (curve fit) with Method 1 (red std. deviations from measurements of ice particles found in cirrus clouds) and Method 2 (Cotton et al. and Heymsfield et al.).
Grupos de galaxias en el catálogo 2dF: La estructura en gran escala con grupos

NASA Astrophysics Data System (ADS)

Zandivarez, A.; Merchán, M. E.; Padilla, N. D.

We use the 2dF Galaxy Group Catalogue constructed by Merchán & Zandivarez to study the large scale structure of the Universe traced by galaxy groups. The resulting group power spectrum shows a similar shape to the galaxy power spectrum of the 2dF Galaxy Redshift Survey, but with a higher amplitude quantified by a relative bias in redshift space of bs(k) ˜ 1.5. The group two point correlation function ξ(s) for the total sample is well described by a power law with correlation length s0=8.9 ± 0.3 h-1 Mpc and slope γ=-1.6 ± 0.1. In order to study the dependence of the clustering properties on group mass we split the catalogue in four subsamples defined by different ranges of group virial masses finding that our results are consistent with a 40% increase of the correlation length s0. These computations allow a fair estimate of the relation described by s0 and the mean intergroup separation dc. An empirical scaling law s0=4.7 dc0.32 provides a very good fit to the results from this work, as well as to previous results obtained for groups and clusters of galaxies and for dark matter haloes in N-body simulations of ΛCDM models. We also study the redshift space distortions of galaxy groups, finding that the anisotropies in the clustering pattern of groups are consistent with gravitational instability, with a flattening of the ξ(s) contours in the direction of the line of sight and group pairwise velocities found for almost the whole sample of groups are consistent with < w2 >1/2 = (280+50-110)km/s, in agreement with ΛCDM cosmological simulations. The bias factor for the 2dF groups of moderate masses is consistent with the values predicted by the combination of a CDM model and the ellipsoidal collapse model for the formation of structures.
Evolution of the Mass and Luminosity Functions of Globular Star Clusters

NASA Astrophysics Data System (ADS)

Goudfrooij, Paul; Fall, S. Michael

2016-12-01

We reexamine the dynamical evolution of the mass and luminosity functions of globular star clusters (GCMF and GCLF). Fall & Zhang (2001, FZ01) showed that a power-law MF, as commonly seen among young cluster systems, would evolve by dynamical processes over a Hubble time into a peaked MF with a shape very similar to the observed GCMF in the Milky Way and other galaxies. To simplify the calculations, the semi-analytical FZ01 model adopted the “classical” theory of stellar escape from clusters, and neglected variations in the M/L ratios of clusters. Kruijssen & Portegies Zwart (2009, KPZ09) modified the FZ01 model to include “retarded” and mass-dependent stellar escape, the latter causing significant M/L variations. KPZ09 asserted that their model was compatible with observations, whereas the FZ01 model was not. We show here that this claim is not correct; the FZ01 and KPZ09 models fit the observed Galactic GCLF equally well. We also show that there is no detectable correlation between M/L and L for GCs in the Milky Way and Andromeda galaxies, in contradiction with the KPZ09 model. Our comparisons of the FZ01 and KPZ09 models with observations can be explained most simply if stars escape at rates approaching the classical limit for high-mass clusters, as expected on theoretical grounds.
Comparison of muscle/lean mass measurement methods: correlation with functional and biochemical testing.

PubMed

Buehring, B; Siglinsky, E; Krueger, D; Evans, W; Hellerstein, M; Yamada, Y; Binkley, N

2018-03-01

DXA-measured lean mass is often used to assess muscle mass but has limitations. Thus, we compared DXA lean mass with two novel methods-bioelectric impedance spectroscopy and creatine (methyl-d3) dilution. The examined methodologies did not measure lean mass similarly and the correlation with muscle biomarkers/function varied. Muscle function tests predict adverse health outcomes better than lean mass measurement. This may reflect limitations of current mass measurement methods. Newer approaches, e.g., bioelectric impedance spectroscopy (BIS) and creatine (methyl-d3) dilution (D3-C), may more accurately assess muscle mass. We hypothesized that BIS and D3-C measured muscle mass would better correlate with function and bone/muscle biomarkers than DXA measured lean mass. Evaluations of muscle/lean mass, function, and serum biomarkers were obtained in older community-dwelling adults. Mass was assessed by DXA, BIS, and orally administered D3-C. Grip strength, timed up and go, and jump power were examined. Potential muscle/bone serum biomarkers were measured. Mass measurements were compared with functional and serum data using regression analyses; differences between techniques were determined by paired t tests. Mean (SD) age of the 112 (89F/23M) participants was 80.6 (6.0) years. The lean/muscle mass assessments were correlated (.57-.88) but differed (p < 0.0001) from one another with DXA total body less head being highest at 37.8 (7.3) kg, D3-C muscle mass at 21.1 (4.6) kg, and BIS total body intracellular water at 17.4 (3.5) kg. All mass assessment methods correlated with grip strength and jump power (R = 0.35-0.63, p < 0.0002), but not with gait speed or repeat chair rise. Lean mass measures were unrelated to the serum biomarkers measured. These three methodologies do not similarly measure muscle/lean mass and should not be viewed as being equivalent. Functional tests assessing maximal muscle strength/power (grip strength and jump power) correlated with all mass measures whereas gait speed was not. None of the selected serum measures correlated with mass. Efforts to optimize muscle mass assessment and identify their relationships with health outcomes are needed.
Galaxy And Mass Assembly (GAMA): galaxy close pairs, mergers and the future fate of stellar mass

NASA Astrophysics Data System (ADS)

Robotham, A. S. G.; Driver, S. P.; Davies, L. J. M.; Hopkins, A. M.; Baldry, I. K.; Agius, N. K.; Bauer, A. E.; Bland-Hawthorn, J.; Brough, S.; Brown, M. J. I.; Cluver, M.; De Propris, R.; Drinkwater, M. J.; Holwerda, B. W.; Kelvin, L. S.; Lara-Lopez, M. A.; Liske, J.; López-Sánchez, Á. R.; Loveday, J.; Mahajan, S.; McNaught-Roberts, T.; Moffett, A.; Norberg, P.; Obreschkow, D.; Owers, M. S.; Penny, S. J.; Pimbblet, K.; Prescott, M.; Taylor, E. N.; van Kampen, E.; Wilkins, S. M.

2014-11-01

We use a highly complete subset of the Galaxy And Mass Assembly II (GAMA-II) redshift sample to fully describe the stellar mass dependence of close pairs and mergers between 108 and 1012 M⊙. Using the analytic form of this fit we investigate the total stellar mass accreting on to more massive galaxies across all mass ratios. Depending on how conservatively we select our robust merging systems, the fraction of mass merging on to more massive companions is 2.0-5.6 per cent. Using the GAMA-II data we see no significant evidence for a change in the close pair fraction between redshift z = 0.05 and 0.2. However, we find a systematically higher fraction of galaxies in similar mass close pairs compared to published results over a similar redshift baseline. Using a compendium of data and the function γM = A(1 + z)m to predict the major close pair fraction, we find fitting parameters of A = 0.021 ± 0.001 and m = 1.53 ± 0.08, which represents a higher low-redshift normalization and shallower power-law slope than recent literature values. We find that the relative importance of in situ star formation versus galaxy merging is inversely correlated, with star formation dominating the addition of stellar material below M^* and merger accretion events dominating beyond M^*. We find mergers have a measurable impact on the whole extent of the galaxy stellar mass function (GSMF), manifest as a deepening of the `dip' in the GSMF over the next ˜Gyr and an increase in M^* by as much as 0.01-0.05 dex.
Temperature-dependent and optimized thermal emission by spheres

NASA Astrophysics Data System (ADS)

Nguyen, K. L.; Merchiers, O.; Chapuis, P.-O.

2018-03-01

We investigate the temperature and size dependencies of thermal emission by homogeneous spheres as a function of their dielectric properties. Different power laws obtained in this work show that the emitted power can depart strongly from the usual fourth power of temperature given by Planck's law and from the square or the cube of the radius. We also show how to optimize the thermal emission by selecting permittivities leading to resonances, which allow for the so-called super-Planckian regime. These results will be useful as spheres, i.e. the simplest finite objects, are often considered as building blocks of more complex objects.
Statistical properties of business firms structure and growth

NASA Astrophysics Data System (ADS)

Matia, K.; Fu, Dongfeng; Buldyrev, S. V.; Pammolli, F.; Riccaboni, M.; Stanley, H. E.

2004-08-01

We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992 2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent β = 0.20 ± 0.01. We also find that the average sales of products scales with the firm sales as a power law with exponent α = 0.57 ± 0.02. And that the average number products of a firm scales with the firm sales as a power law with exponent γ = 0.42 ± 0.02. We compare these findings with the predictions of models proposed till date on growth of business firms.
The virialization density of peaks with general density profiles under spherical collapse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rubin, Douglas; Loeb, Abraham, E-mail: dsrubin@physics.harvard.edu, E-mail: aloeb@cfa.harvard.edu

2013-12-01

We calculate the non-linear virialization density, Δ{sub c}, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of Δ{sub c} which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for Δ{sub c} for halos in an Einstein de-Sitter and a ΛCDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles calculated from the statisticsmore » of a Gaussian random field. We find that, depending on the profiles used, Δ{sub c} is smaller by a factor of a few to as much as a factor of 10 as compared to the density given by the standard calculation ( ≈ 200). Using our results, we show that, for halo finding algorithms that identify halos through an over-density threshold, the halo mass function measured from cosmological simulations can be enhanced at all halo masses by a factor of a few. This difference could be important when using numerical simulations to assess the validity of analytic models of the halo mass function.« less
46 CFR 502.147 - Functions and powers.

Code of Federal Regulations, 2010 CFR

2010-10-01

..., disorderly, or contumacious language or conduct. (b) All of the functions delegated in subparts A to Q and subpart T of this part, inclusive, to the Chief Judge, presiding officer, or administrative law judge...
Dynamical analysis for a scalar-tensor model with kinetic and nonminimal couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Jimenez, D. F.

We study the autonomous system for a scalar-tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.
Non-parametric model selection for subject-specific topological organization of resting-state functional connectivity.

PubMed

Ferrarini, Luca; Veer, Ilya M; van Lew, Baldur; Oei, Nicole Y L; van Buchem, Mark A; Reiber, Johan H C; Rombouts, Serge A R B; Milles, J

2011-06-01

In recent years, graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain. Most of these networks have shown small-world topological characteristics: high efficiency in long distance communication between nodes, combined with highly interconnected local clusters of nodes. Moreover, functional studies performed at high resolutions have presented convincing evidence that resting-state functional connectivity networks exhibits (exponentially truncated) scale-free behavior. Such evidence, however, was mostly presented qualitatively, in terms of linear regressions of the degree distributions on log-log plots. Even when quantitative measures were given, these were usually limited to the r(2) correlation coefficient. However, the r(2) statistic is not an optimal estimator of explained variance, when dealing with (truncated) power-law models. Recent developments in statistics have introduced new non-parametric approaches, based on the Kolmogorov-Smirnov test, for the problem of model selection. In this work, we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest. The analysis, performed at voxel level and in a subject-specific fashion, confirmed the superiority of a truncated power-law model, showing high consistency across subjects. Moreover, the most highly connected voxels were found to be consistently part of the default mode network. Our results provide statistically sound support to the evidence previously presented in literature for a truncated power-law model of resting-state functional connectivity. Copyright © 2010 Elsevier Inc. All rights reserved.
Why the bigger live longer and travel farther: animals, vehicles, rivers and the winds.

PubMed

Bejan, Adrian

2012-01-01

Here we show that constructal-law physics unifies the design of animate and inanimate movement by requiring that larger bodies move farther, and their movement on the landscape last longer. The life span of mammals must scale as the body mass (M) raised to the power 1/4, and the distance traveled during the lifetime must increase with body size. The same size effect on life span and distance traveled holds for the other flows that move mass on earth: atmospheric and oceanic jets and plumes, river basins, animals and human operated vehicles. The physics is the same for all flow systems on the landscape: the scaling rules of "design" are expressions of the natural tendency of all flow systems to generate designs that facilitate flow access. This natural tendency is the constructal law of design and evolution in nature. Larger bodies are more efficient movers of mass on the landscape.
Analysis of mass incident diffusion in Weibo based on self-organization theory

NASA Astrophysics Data System (ADS)

Pan, Jun; Shen, Huizhang

2018-02-01

This study introduces some theories and methods of self-organization system to the research of the diffusion mechanism of mass incidents in Weibo (Chinese Twitter). Based on the analysis on massive Weibo data from Songjiang battery factory incident happened in 2013 and Jiiangsu Qidong OJI PAPER incident happened in 2012, we find out that diffusion system of mass incident in Weibo satisfies Power Law, Zipf's Law, 1/f noise and Self-similarity. It means this system is the self-organization criticality system and dissemination bursts can be understood as one kind of Self-organization behavior. As the consequence, self-organized criticality (SOC) theory can be used to explain the evolution of mass incident diffusion and people may come up with the right strategy to control such kind of diffusion if they can handle the key ingredients of Self-organization well. Such a study is of practical importance which can offer opportunities for policy makers to have good management on these events.

A simple scaling law for the equation of state and the radial distribution functions calculated by density-functional theory molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.

2018-06-01

It is shown that the equation of state (EOS) and the radial distribution functions obtained by density-functional theory molecular dynamics (DFT-MD) obey a simple scaling law. At given temperature, the thermodynamic properties and the radial distribution functions given by a DFT-MD simulation remain unchanged if the mole fractions of nuclei of given charge and the average volume per atom remain unchanged. A practical interest of this scaling law is to obtain an EOS table for a fluid from that already obtained for another fluid if it has the right characteristics. Another practical interest of this result is that an asymmetric mixture made up of light and heavy atoms requiring very different time steps can be replaced by a mixture of atoms of equal mass, which facilitates the exploration of the configuration space in a DFT-MD simulation. The scaling law is illustrated by numerical results.
Dynamical evolution of dense star clusters in galactic nuclei

NASA Astrophysics Data System (ADS)

Haas, Jaroslav; Šubr, Ladislav

2014-05-01

By means of direct numerical N-body modeling, we investigate the orbital evolution of an initially thin, central mass dominated stellar disk. We include the perturbative gravitational influence of an extended spherically symmetric star cluster and the mutual gravitational interaction of the stars within the disk. Our results show that the two-body relaxation of the disk leads to significant changes of its radial density profile. In particular, the disk naturally evolves, for a variety of initial configurations, a similar broken power-law surface density profile. Hence, it appears that the single power-law surface density profile ∝R -2 suggested by various authors to describe the young stellar disk observed in the Sgr A* region does not match theoretical expectations.
Twelve and a Half Years of Observations of Centaurus A with RXTE

NASA Technical Reports Server (NTRS)

Rothschild, R. E.; Markowitz, A.; Rivers, L.; Suchy, S.; Pottschmidt, K.; Kadler, M.; Mueller, C.; Wilms, J.

2011-01-01

The Rossi X-ray Timing Explorer has observed the nearest radio galaxy, Centaurus A, in 13 intervals from 1996 August to 2009 February over the 3 - 200 keV band. Spectra accumulated over the 13 intervals were well described with an absorbed power law and an iron line. Cut-off power laws and Compton reflection from cold matter did not provide a better description. For the 2009 January observation we set a lower limit on the cutoff energy at over 2 MeV. The power spectral density function was generated from RXTE/ASM and PCA data as well as an XMM-Newton long look, and clear evidence for a break at 18(+18/-7) days (68% conf.) was seen. Given Cen A's high black hole mass and very low value of L(sub x)/L(sub Edd), the break was a factor of 17+/-9 times higher than the break frequency predicted by the McHardy and coworkers relation, which was empirically derived for a sample of objects, which are radio-quiet and accreting at relatively high values of L(sub bol)/L(sub Edd). We have interpreted our observations in the context of a clumpy molecular torus. The variability characteristics and the broadband spectral energy distribution, when compared to Seyferts, imply that the bright hard X-ray continuum emission may originate at the base of the jet, yet from behind the absorbing line of sight material, in contrast to what is commonly observed from blazars.
Lower Jump Power Rather Than Muscle Mass Itself is Associated with Vertebral Fracture in Community-Dwelling Elderly Korean Women.

PubMed

Lee, Eun Young; Lee, Su Jin; Kim, Kyoung Min; Seo, Da Hea; Lee, Seung Won; Choi, Han Sol; Kim, Hyeon Chang; Youm, Yoosik; Kim, Chang Oh; Rhee, Yumie

2017-06-01

Sarcopenia is considered to be a risk factor for osteoporotic fracture, which is a major health problem in elderly women. In this study, we aimed to investigate the association of sarcopenia, with regard to muscle mass and function, with prevalent vertebral fracture in community-dwelling elderly women. We recruited 1281 women aged 64 to 87 years from the Korean Urban Rural Elderly cohort study. Muscle mass and function were measured using bioimpedance analysis and jumping mechanography. Skeletal muscle index (SMI) and jump power were used as an indicator of muscle mass and function, respectively. Among the participants, we observed 282 (18.9%) vertebral fractures and 564 (44.0%) osteoporosis. Although age, body mass index, and prevalence of osteoporosis increased as both SMI and jump power decreased, prevalence of vertebral fracture increased only when jump power decreased. In univariate analysis, compared with the highest quartile of jump power, the lowest quartile had a significant odds ratio of 2.80 (95% CI 1.79-4.36) for vertebral fracture. This association between jump power and vertebral fracture remained significant, with an odds ratio of 3.04 (95% CI 1.77-5.23), even after adjusting for other risk factors including age, bone mineral density, previous fracture, and cognitive function. In contrast, there was no association between SMI and vertebral fracture. Based on our results, low jump power, but not SMI, is associated with vertebral fracture in community-dwelling elderly Korean women. This finding suggests that jump power may have a more important role than muscle mass itself for osteoporotic fracture.
The angular momentum-mass relation: a fundamental law from dwarf irregulars to massive spirals

NASA Astrophysics Data System (ADS)

Posti, Lorenzo; Fraternali, Filippo; Di Teodoro, Enrico M.; Pezzulli, Gabriele

2018-05-01

In a Λ CDM Universe, the specific stellar angular momentum (j*) and stellar mass (M*) of a galaxy are correlated as a consequence of the scaling existing for dark matter haloes (jh ∝2/3). The shape of this law is crucial to test galaxy formation models, which are currently discrepant especially at the lowest masses, allowing to constrain fundamental parameters, such as, for example, the retained fraction of angular momentum. In this study, we accurately determine the empirical j*-M* relation (Fall relation) for 92 nearby spiral galaxies (from S0 to Irr) selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample in the unprecedented mass range 7 ≲ log M*/M⊙≲ 11.5. We significantly improve all previous estimates of the Fall relation by determining j* profiles homogeneously for all galaxies, using extended HI rotation curves, and selecting only galaxies for which a robust j* could be measured (converged j*(
Testing modified gravity at large distances with the HI Nearby Galaxy Survey's rotation curves

NASA Astrophysics Data System (ADS)

Mastache, Jorge; Cervantes-Cota, Jorge L.; de la Macorra, Axel

2013-03-01

Recently a new—quantum motivated—theory of gravity has been proposed that modifies the standard Newtonian potential at large distances when spherical symmetry is considered. Accordingly, Newtonian gravity is altered by adding an extra Rindler acceleration term that has to be phenomenologically determined. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential. The new terms in the gravitational potential are hypothesized to play the role of dark matter in galaxies. Our galactic model includes the mass of the integrated gas, and stars for which we consider three stellar mass functions (Kroupa, diet-Salpeter, and free mass model). We test this idea by fitting rotation curves of seventeen low surface brightness galaxies from the HI Nearby Galaxy Survey (THINGS). We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to standard dark matter profiles (Navarro-Frenk-White and Burkert) and, in addition, the computed parameters of the Rindler gravity show a high spread, posing the model as a nonacceptable alternative to dark matter.
Characteristic Structure of Star-forming Clouds

NASA Astrophysics Data System (ADS)

Myers, Philip C.

2015-06-01

This paper presents a new method to diagnose the star-forming potential of a molecular cloud region from the probability density function of its column density (N-pdf). This method provides expressions for the column density and mass profiles of a symmetric filament having the same N-pdf as a filamentary region. The central concentration of this characteristic filament can distinguish regions and can quantify their fertility for star formation. Profiles are calculated for N-pdfs which are pure lognormal, pure power law, or a combination. In relation to models of singular polytropic cylinders, characteristic filaments can be unbound, bound, or collapsing depending on their central concentration. Such filamentary models of the dynamical state of N-pdf gas are more relevant to star-forming regions than are spherical collapse models. The star formation fertility of a bound or collapsing filament is quantified by its mean mass accretion rate when in radial free fall. For a given mass per length, the fertility increases with the filament mean column density and with its initial concentration. In selected regions the fertility of their characteristic filaments increases with the level of star formation.
A Snapshot of the Continuous Emission of the Active Galactic Nucleus in NGC 3783 from Gamma-Ray to Radio Wavelengths

NASA Technical Reports Server (NTRS)

Alloin, D.; Santos-Lleo, M.; Peterson, B. M.; Wamsteker, W.; Altieri, B.; Brinkmann, W.; Clavel, J.; Crenshaw, D. M.; George, I. M.; Glass, I. S.;

1995-01-01

To better understand the physical processes that produce the continuous emission in active galactic nuclei (AGN), a snapshot of the overall continuous energy distribution of NGC 3783, from gamma ray to radio wavelengths, has been obtained within the framework of the World Astronomy Days. The data collected in this campaign are from GRO, ROSAT, Voyager 2, IUE, HST, CTIO, SAAO, and the VLA. Great care has been taken in disentangling the genuine AGN continusous emission from other contributions; depending on the waveband, the latter might be (1) unrelated contaminating sources in cases where the instrument field of view is large (2) components within which the AGN is embedded, such as the stellar bulge population which accounts for a significant fraction of the optical continuum, and free-bound and FE2 blends wich contribute to the ultraviolet flux. After correction for these other contributins, the continuous emission of the isolated AGN appears to be rather flat (i.e., approximately equal energy per unit logarithmic frequency) from soft gamma ray to infrared wavelengths. At high energies (0.1 MeV to 0.1 keV), the AGN continuum can be fitted by a power law F nu approaches Nu(exp -a) with a spectral index of alpha approximately 1. At longer wavelengths, two excesses above this power law ('bumps') appear: in the ultraviolet, the classical big blue bump, which can be interpreted as thermal emission from the accretion disc surrounding a massive black hole, and in the infrared, a second bump which can be ascribed to thermal emission from dust in the vicinity of the AGN, heated by ultraviolet radiation from the central source. By fitting accretion-disk models to the observed AGN spectral energy distribution, we find values for the accretion disk innermost temperature, accretion rate, and black hole mass, with some differences that depend on whether or not we extrapolate the high energy power law up to infrared wavelengths. A fit to the IR bump above the extended alpha equals 1 power law suggests the presence of a dust component covering the region from a distance rho approximately equals 80 light days (hot grains at a temperature of approximately equals 1500 K) to rho approximately equals 60 light years (cool grains at T approximately equals 200 K). The total mass of dust is around 60 solar masses.

Energy Cascade in Quantum Gases

NASA Astrophysics Data System (ADS)

Yin, X. Y.; Ho, Tin-Lun

Energy cascade is ubiquitous in systems far from equilibrium. Facilitated by particle interactions and external forces, it can lead to highly complex phenomena like fully developed turbulence, characterized by power law velocity correlation functions. Yet despite decades of research, how these power laws emerge from first principle remains unclear. Recently, experiments show that when a Bose condensate is subjected to periodic shaking, its momentum distribution exhibits a power law behavior. The flexibility of cold atom experiments has provided new opportunities to explore the emergence of these power laws, and to disentangle different sources of energy cascade. Here, we point out that recent experiments in cold atoms imply that classical turbulence is part of a larger family of scale invariant phenomena that include ideal gases. Moreover, the property of the entire family is contained in the structure of its Floquet states. For ideal gases, we show analytically that its momentum distribution acquires a 1 /q2 tail in each dimension when it is shaken periodically. We acknowledge NSF Grant DMR1309615, MURI Grant FP054294-D, and NASA Fundamental Physics Grant 1518233.
Convective hydromagnetic instabilities of a power-law liquid saturating a porous medium: Flux conditions

NASA Astrophysics Data System (ADS)

Chahtour, C.; Ben Hamed, H.; Beji, H.; Guizani, A.; Alimi, W.

2018-01-01

We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

USGS Publications Warehouse

Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.

2011-01-01

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.
Derivation of the Effective Nonlinear Schrodinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing

DTIC Science & Technology

2011-03-01

An e?ective Nonlinear Schr?dinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a... soliton amplitude profiles are displayed as a hyperbolic secant function and hold there profile at short distances on the order of centimeters. Dark ...spatial solitons are similar but have hyperbolic tangent type profiles. Dark spatial solitons were first observed by Jerominek in 1985 and Belanger and
Damped and sub-damped Lyman-α absorbers in z > 4 QSOs

NASA Astrophysics Data System (ADS)

Guimarães, R.; Petitjean, P.; de Carvalho, R. R.; Djorgovski, S. G.; Noterdaeme, P.; Castro, S.; Poppe, P. C. Da R.; Aghaee, A.

2009-12-01

We present the results of a survey of damped (DLA, log~N(H i)>20.3) and sub-damped Lyman-α systems (19.5 2.55 along the lines-of-sight to 77 quasars with emission redshifts in the range 419.5 were detected of which 40 systems are damped Lyman-α systems for an absorption length of Δ X = 378. About half of the lines of sight of this homogeneous survey have never been investigated for DLAs. We study the evolution with redshift of the cosmological density of the neutral gas and find, consistent with previous studies at similar resolution, that ΩDLA, H_I decreases at z>3.5. The overall cosmological evolution of Ω_HI shows a peak around this redshift. The H i column density distribution for log N(H i)≥20.3 is fitted, consistent with previous surveys, with a single power-law of index α ˜ -1.8 ±0.25. This power-law overpredicts data at the high-end and a second, much steeper, power-law (or a gamma function) is needed. There is a flattening of the function at lower H i column densities with an index of α ˜ -1.4 for the column density range log N(H i)=19.5-21. The fraction of H i mass in sub-DLAs is of the order of 30%. The H i column density distribution does not evolve strongly from z˜ 2.5 to z˜ 4.5. The observations reported here were obtained with the W. M. Keck Observatory, which is operated by the California Association for Research in Astronomy, a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. Tables 1, 2 and Appendices are only available in electronic form at http://www.aanda.org
Far-infrared emission and star formation in spiral galaxies

NASA Technical Reports Server (NTRS)

Trinchieri, G.; Fabbiano, G.; Bandiera, R.

1989-01-01

The correlations between the emission in the far-IR, H-alpha, and blue in a sample of normal spiral galaxies are investigated. It is found that the luminosities in these three bands are all tightly correlated, although both the strength of the correlations and their functional dependencies are a function of the galaxies' morphological types. The best-fit power laws to these correlations are different for the comparison of different quantities and deviate significantly from linearity in some cases, implying the presence of additional emission mechanisms not related to the general increase of luminosity with galactic mass. Clear evidence is found of two independent effects in the incidence of warm far-IR emission in late-type spirals. One is a luminosity effect shown by the presence of excess far-IR relative to H-alpha or optical emission in the more luminous galaxies. The other is a dependence on widespread star-formation activity.
A simple and general method for solving detailed chemical evolution with delayed production of iron and other chemical elements

NASA Astrophysics Data System (ADS)

Vincenzo, F.; Matteucci, F.; Spitoni, E.

2017-04-01

We present a theoretical method for solving the chemical evolution of galaxies by assuming an instantaneous recycling approximation for chemical elements restored by massive stars and the delay time distribution formalism for delayed chemical enrichment by Type Ia Supernovae. The galaxy gas mass assembly history, together with the assumed stellar yields and initial mass function, represents the starting point of this method. We derive a simple and general equation, which closely relates the Laplace transforms of the galaxy gas accretion history and star formation history, which can be used to simplify the problem of retrieving these quantities in the galaxy evolution models assuming a linear Schmidt-Kennicutt law. We find that - once the galaxy star formation history has been reconstructed from our assumptions - the differential equation for the evolution of the chemical element X can be suitably solved with classical methods. We apply our model to reproduce the [O/Fe] and [Si/Fe] versus [Fe/H] chemical abundance patterns as observed at the solar neighbourhood by assuming a decaying exponential infall rate of gas and different delay time distributions for Type Ia Supernovae; we also explore the effect of assuming a non-linear Schmidt-Kennicutt law, with the index of the power law being k = 1.4. Although approximate, we conclude that our model with the single-degenerate scenario for Type Ia Supernovae provides the best agreement with the observed set of data. Our method can be used by other complementary galaxy stellar population synthesis models to predict also the chemical evolution of galaxies.
Wide range scaling laws for radiation driven shock speed, wall albedo and ablation parameters for high-Z materials

NASA Astrophysics Data System (ADS)

Mishra, Gaurav; Ghosh, Karabi; Ray, Aditi; Gupta, N. K.

2018-06-01

Radiation hydrodynamic (RHD) simulations for four different potential high-Z hohlraum materials, namely Tungsten (W), Gold (Au), Lead (Pb), and Uranium (U) are performed in order to investigate their performance with respect to x-ray absorption, re-emission and ablation properties, when irradiated by constant temperature drives. A universal functional form is derived for estimating time dependent wall albedo for high-Z materials. Among the high-Z materials studied, it is observed that for a fixed simulation time the albedo is maximum for Au below 250 eV, whereas it is maximum for U above 250 eV. New scaling laws for shock speed vs drive temperature, applicable over a wide temperature range of 100 eV to 500 eV, are proposed based on the physics of x-ray driven stationary ablation. The resulting scaling relation for a reference material Aluminium (Al), shows good agreement with that of Kauffman's power law for temperatures ranging from 100 eV to 275 eV. New scaling relations are also obtained for temperature dependent mass ablation rate and ablation pressure, through RHD simulation. Finally, our study reveals that for temperatures above 250 eV, U serves as a better hohlraum material since it offers maximum re-emission for x-rays along with comparable mass ablation rate. Nevertheless, traditional choice, Au works well for temperatures below 250 eV. Besides inertial confinement fusion (ICF), the new scaling relations may find its application in view-factor codes, which generally ignore atomic physics calculations of opacities and emissivities, details of laser-plasma interaction and hydrodynamic motions.
The Low End of the Initial Mass Function in Young Clusters. II. Evidence for Primordial Mass Segregation in NGC 330 in the Small Magellanic Cloud

NASA Astrophysics Data System (ADS)

Sirianni, Marco; Nota, Antonella; De Marchi, Guido; Leitherer, Claus; Clampin, Mark

2002-11-01

As part of a larger program aimed at investigating the universality of the initial mass function (IMF) at low masses in a number of young clusters in the LMC and SMC, we present a new study of the low end of the stellar IMF of NGC 330, the richest young star cluster in the SMC, from deep broadband V and I images obtained with HST/WFPC2. We detect stars down to a limiting magnitude of m555=24.9, which corresponds to stellar masses of ~0.8Msolar at the distance of the SMC. A comparison of the cluster color-magnitude diagram with theoretical evolutionary tracks indicates an age of ~30 Myr for NGC 330, in agreement with previous published results. We derive the cluster luminosity function, which we correct for background contamination using an adjacent SMC field, and construct the mass function in the 1-7Msolar mass range. Given the young cluster age, the MF can well approximate the IMF. We find that the IMF in the central cluster regions (within 30") is well reproduced by a power law with a slope consistent with Salpeter's. In addition, the richness of the cluster allows us to investigate the IMF as a function of radial distance from the center. We find that the IMF becomes steeper at increasing distances from the cluster center (between 30" and 90"), with the number of massive stars (>5Msolar) decreasing from the core to the outskirts of the cluster 5 times more rapidly than the less-massive objects (~=1Msolar). We believe the observed mass segregation to be of a primordial nature rather than dynamical since the age of NGC 330 is 10 times shorter than the expected relaxation time of the cluster. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS5-26555.
Slope mass movements on rocky sea-cliffs: A power-law distributed natural hazard on the Barlavento Coast, Algarve, Portugal

NASA Astrophysics Data System (ADS)

Teixeira, Sebastião Braz

2006-06-01

The coast of the Central Algarve, Portugal, is dominated by sea-cliffs, cut on Miocene calcarenites; here, the main coastal geologic hazards result from the conflict between human occupation and sea-cliff recession. The evolution of this rocky coast occurs through an intermittent and discontinuous series of slope mass movements, along a 46 km cliff front. For the last 30 years, the increase of tourism occupation has amplified the risks to both people and buildings. In the last decade we have seen several accidents caused by cliff failure, which killed or wounded people and destroyed several buildings. The definition of buffer zones limited by hazard lines parallel to the cliff edge, where land use is restricted, is a widely used and effective preventive measure for mitigating risk. Rocky coasts typically show a slow cliff evolution. The process of gathering statistically significant field inventories of mass movements is, thus, very long. Although mass movement catalogues provide fundamental information on sea cliff evolution patterns and are an outstanding tool in hazard assessment, published data sets are still rare. In this work, we use two inventories of mass movement width, recorded on sea cliffs cut on Miocene calcarenites: a nine year long continuous field inventory (1995-2004) with 140 recorded events, and a 44 year long catalogue based on comparative analysis of aerial photographs (1947-1991), that includes 177 events. The cumulative frequency-width distributions of both data sets fit, above a critical width value corresponding to the threshold of full completeness of the inventories, to power-law distributions. The knowledge of the limits of the catalogues enabled the construction of a 53 year long record inventory over the range of mean width ⩾3 m ( n=167 events) and maximum width ⩾4 m ( n=155 events). The data assembled corresponds to a partial series and was converted to a return period-size distribution. Both return period-width distributions (mean width and maximum width) are also power-law distributions. Equations of return period-width distributions give the width of hazard lines corresponding to the width of mass movement, in which return period equals the period that hazard line is referred to.
Multiple scattering corrections to the Beer-Lambert law. 1: Open detector.

PubMed

Tam, W G; Zardecki, A

1982-07-01

Multiple scattering corrections to the Beer-Lambert law are analyzed by means of a rigorous small-angle solution to the radiative transfer equation. Transmission functions for predicting the received radiant power-a directly measured quantity in contrast to the spectral radiance in the Beer-Lambert law-are derived. Numerical algorithms and results relating to the multiple scattering effects for laser propagation in fog, cloud, and rain are presented.
Breast cancer risk assessment and diagnosis model using fuzzy support vector machine based expert system

NASA Astrophysics Data System (ADS)

Dheeba, J.; Jaya, T.; Singh, N. Albert

2017-09-01

Classification of cancerous masses is a challenging task in many computerised detection systems. Cancerous masses are difficult to detect because these masses are obscured and subtle in mammograms. This paper investigates an intelligent classifier - fuzzy support vector machine (FSVM) applied to classify the tissues containing masses on mammograms for breast cancer diagnosis. The algorithm utilises texture features extracted using Laws texture energy measures and a FSVM to classify the suspicious masses. The new FSVM treats every feature as both normal and abnormal samples, but with different membership. By this way, the new FSVM have more generalisation ability to classify the masses in mammograms. The classifier analysed 219 clinical mammograms collected from breast cancer screening laboratory. The tests made on the real clinical mammograms shows that the proposed detection system has better discriminating power than the conventional support vector machine. With the best combination of FSVM and Laws texture features, the area under the Receiver operating characteristic curve reached .95, which corresponds to a sensitivity of 93.27% with a specificity of 87.17%. The results suggest that detecting masses using FSVM contribute to computer-aided detection of breast cancer and as a decision support system for radiologists.

Polarization asymmetry in two-electron photodetachment - A cogent test of the ionization threshold law

NASA Technical Reports Server (NTRS)

Temkin, A.; Bhatia, A. K.

1988-01-01

A very sensitive test of the electron-atom ionization threshold law is suggested: for spin-aligned heavy negative ions it consists of measuring the polarization asymmetry A(PA) coming from double detachment by left- versus right-circularly polarized light. The respective yields are worked out for the Te(-) (5p)5 2P(3/2) ion. The Coulomb-dipole theory predicts A(PA) to be the ratio of two oscillating functions in sharp contrast to any power law (specifically that of Wannier, 1953) for which the ratio is expected to be a smooth function of energy.
Optimization of motion control laws for tether crawler or elevator systems

NASA Technical Reports Server (NTRS)

Swenson, Frank R.; Von Tiesenhausen, Georg

1988-01-01

Based on the proposal of a motion control law by Lorenzini (1987), a method is developed for optimizing motion control laws for tether crawler or elevator systems in terms of the performance measures of travel time, the smoothness of acceleration and deceleration, and the maximum values of velocity and acceleration. The Lorenzini motion control law, based on powers of the hyperbolic tangent function, is modified by the addition of a constant-velocity section, and this modified function is then optimized by parameter selections to minimize the peak acceleration value for a selected travel time or to minimize travel time for the selected peak values of velocity and acceleration. It is shown that the addition of a constant-velocity segment permits further optimization of the motion control law performance.
Diverse stellar haloes in nearby Milky Way mass disc galaxies

NASA Astrophysics Data System (ADS)

Harmsen, Benjamin; Monachesi, Antonela; Bell, Eric F.; de Jong, Roelof S.; Bailin, Jeremy; Radburn-Smith, David J.; Holwerda, Benne W.

2017-04-01

We have examined the resolved stellar populations at large galactocentric distances along the minor axis (from 10 kpc up to between 40 and 75 kpc), with limited major axis coverage, of six nearby highly inclined Milky Way (MW) mass disc galaxies using Hubble Space Telescope data from the Galaxy haloes, Outer discs, Substructure, Thick discs, and Star clusters (GHOSTS) survey. We select red giant branch stars to derive stellar halo density profiles. The projected minor axis density profiles can be approximated by power laws with projected slopes of -2 to -3.7 and a diversity of stellar halo masses of 1-6 × 109 M⊙, or 2-14 per cent of the total galaxy stellar masses. The typical intrinsic scatter around a smooth power-law fit is 0.05-0.1 dex owing to substructure. By comparing the minor and major axis profiles, we infer projected axis ratios c/a at ˜25 kpc between 0.4and0.75. The GHOSTS stellar haloes are diverse, lying between the extremes charted out by the (rather atypical) haloes of the MW and M31. We find a strong correlation between the stellar halo metallicities and the stellar halo masses. We compare our results with cosmological models, finding good agreement between our observations and accretion-only models where the stellar haloes are formed by the disruption of dwarf satellites. In particular, the strong observed correlation between stellar halo metallicity and mass is naturally reproduced. Low-resolution hydrodynamical models have unrealistically high stellar halo masses. Current high-resolution hydrodynamical models appear to predict stellar halo masses somewhat higher than observed but with reasonable metallicities, metallicity gradients, and density profiles.
Population patterns in World’s administrative units

PubMed Central

Miramontes, Pedro; Cocho, Germinal

2017-01-01

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution. PMID:28791153
So You Think the Crab is Described by a Power-Law Spectrum

NASA Technical Reports Server (NTRS)

Weisskopf, Martin C.

2008-01-01

X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.
Quantitative relations between risk, return and firm size

NASA Astrophysics Data System (ADS)

Podobnik, B.; Horvatic, D.; Petersen, A. M.; Stanley, H. E.

2009-03-01

We analyze —for a large set of stocks comprising four financial indices— the annual logarithmic growth rate R and the firm size, quantified by the market capitalization MC. For the Nasdaq Composite and the New York Stock Exchange Composite we find that the probability density functions of growth rates are Laplace ones in the broad central region, where the standard deviation σ(R), as a measure of risk, decreases with the MC as a power law σ(R)~(MC)- β. For both the Nasdaq Composite and the S&P 500, we find that the average growth rate langRrang decreases faster than σ(R) with MC, implying that the return-to-risk ratio langRrang/σ(R) also decreases with MC. For the S&P 500, langRrang and langRrang/σ(R) also follow power laws. For a 20-year time horizon, for the Nasdaq Composite we find that σ(R) vs. MC exhibits a functional form called a volatility smile, while for the NYSE Composite, we find power law stability between σ(r) and MC.
Starburst clusters in the Galactic center

NASA Astrophysics Data System (ADS)

Habibi, Maryam

2014-09-01

The central region of the Galaxy is the most active site of star formation in the Milky Way, where massive stars have formed very recently and are still forming today. The rich population of massive stars in the Galactic center provide a unique opportunity to study massive stars in their birth environment and probe their initial mass function, which is the spectrum of stellar masses at their birth. The Arches cluster is the youngest among the three massive clusters in the Galactic center, providing a collection of high-mass stars and a very dense core which makes this cluster an excellent site to address questions about massive star formation, the stellar mass function and the dynamical evolution of massive clusters in the Galactic center. In this thesis, I perform an observational study of the Arches cluster using K_{s}-band imaging obtained with NAOS/CONICA at the VLT combined with Subaru/Cisco J-band data to gain a full understanding of the cluster mass distribution out to its tidal radius for the first time. Since the light from the Galactic center reaches us through the Galactic disc, the extinction correction is crucial when studying this region. I use a Bayesian method to construct a realistic extinction map of the cluster. It is shown in this study that the determination of the mass of the most massive star in the Arches cluster, which had been used in previous studies to establish an upper mass limit for the star formation process in the Milky Way, strongly depends on the assumed slope of the extinction law. Assuming the two regimes of widely used infrared extinction laws, I show that the difference can reach up to 30% for individually derived stellar masses and Δ A_{Ks}˜ 1 magnitude in acquired K_{s}-band extinction, while the present-day mass function slope changes by ˜ 0.17 dex. The present-day mass function slope derived assuming the more recent extinction law, which suggests a steeper wavelength dependence for the infrared extinction law, reveals an overpopulation of massive stars in the core (r<0.2 pc) with a flat slope of α_{Nishi}=-1.50 ±0.35 in comparison to the Salpeter slope of α=-2.3. The slope of the mass function increases to α_{Nishi}=-2.21 ±0.27 in the intermediate annulus (0.2
CFHTLenS: co-evolution of galaxies and their dark matter haloes

NASA Astrophysics Data System (ADS)

Hudson, Michael J.; Gillis, Bryan R.; Coupon, Jean; Hildebrandt, Hendrik; Erben, Thomas; Heymans, Catherine; Hoekstra, Henk; Kitching, Thomas D.; Mellier, Yannick; Miller, Lance; Van Waerbeke, Ludovic; Bonnett, Christopher; Fu, Liping; Kuijken, Konrad; Rowe, Barnaby; Schrabback, Tim; Semboloni, Elisabetta; van Uitert, Edo; Velander, Malin

2015-02-01

Galaxy-galaxy weak lensing is a direct probe of the mean matter distribution around galaxies. The depth and sky coverage of the Canada-France-Hawaii Telescope Legacy Survey yield statistically significant galaxy halo mass measurements over a much wider range of stellar masses (108.75 to 1011.3 M⊙) and redshifts (0.2 < z < 0.8) than previous weak lensing studies. At redshift z ˜ 0.5, the stellar-to-halo mass ratio (SHMR) reaches a maximum of 4.0 ± 0.2 per cent as a function of halo mass at ˜1012.25 M⊙. We find, for the first time from weak lensing alone, evidence for significant evolution in the SHMR: the peak ratio falls as a function of cosmic time from 4.5 ± 0.3 per cent at z ˜ 0.7 to 3.4 ± 0.2 per cent at z ˜ 0.3, and shifts to lower stellar mass haloes. These evolutionary trends are dominated by red galaxies, and are consistent with a model in which the stellar mass above which star formation is quenched `downsizes' with cosmic time. In contrast, the SHMR of blue, star-forming galaxies is well fitted by a power law that does not evolve with time. This suggests that blue galaxies form stars at a rate that is balanced with their dark matter accretion in such a way that they evolve along the SHMR locus. The redshift dependence of the SHMR can be used to constrain the evolution of the galaxy population over cosmic time.
Modification of the gravity model and application to the metropolitan Seoul subway system.

PubMed

Goh, Segun; Lee, Keumsook; Park, Jong Soo; Choi, M Y

2012-08-01

The Metropolitan Seoul Subway system is examined through the use of the gravity model. Exponents describing the power-law dependence on the time distance between stations are obtained, which reveals a universality for subway lines of the same topology. In the short (time) distance regime the number of passengers between stations does not grow with the decrease in the distance, thus deviating from the power-law behavior. It is found that such reduction in passengers is well described by the Hill function. Further, temporal fluctuations in the passenger flow data, fitted to the gravity model modified by the Hill function, are analyzed to reveal the Yule-type nature inherent in the structure of Seoul.
Photometric and structural properties of NGC 6544: A combined VVV-Hubble space telescope study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cohen, Roger E.; Mauro, Francesco; Geisler, Doug

We combine archival Hubble Space Telescope imaging with wide-field near-infrared photometry to study the neglected metal-poor Galactic globular cluster NGC 6544. A high spatial resolution map of differential reddening over the inner portion of the cluster is constructed, revealing variations of up to half of the total reddening, and the resulting corrected color-magnitude diagrams reveal a sparse blue horizontal branch and centrally concentrated blue straggler population, verified via relative proper motions. Using the corrected photometry to investigate the cluster distance, reddening, and age via direct comparison to well-calibrated photometry of clusters with similar metallicities, we estimate (m – M){sub 0}more » = 11.96, E(B – V) = 0.79, and an age coeval with M13 to within the relevant uncertainties. Although our data are insufficient to place tight constraints on the reddening law toward NGC 6544, we find no strong evidence that it is non-standard at optical or near-infrared wavelengths. We also provide near-infrared fiducial sequences extending nearly 2 mag below the cluster main sequence turnoff, generated from a statistically decontaminated sample of cluster stars. Lastly, we redetermine the cluster center and construct a radial number density profile which is well fit by an atypically flat power law with a slope of about 1.7. We discuss this result, together with a flattened main sequence luminosity function and inverted mass function, in the context of mass segregation and tidal stripping via interactions with Milky Way potential.« less
Orphan and gene related CpG Islands follow power-law-like distributions in several genomes: evidence of function-related and taxonomy-related modes of distribution.

PubMed

Tsiagkas, Giannis; Nikolaou, Christoforos; Almirantis, Yannis

2014-12-01

CpG Islands (CGIs) are compositionally defined short genomic stretches, which have been studied in the human, mouse, chicken and later in several other genomes. Initially, they were assigned the role of transcriptional regulation of protein-coding genes, especially the house-keeping ones, while more recently there is found evidence that they are involved in several other functions as well, which might include regulation of the expression of RNA genes, DNA replication etc. Here, an investigation of their distributional characteristics in a variety of genomes is undertaken for both whole CGI populations as well as for CGI subsets that lie away from known genes (gene-unrelated or "orphan" CGIs). In both cases power-law-like linearity in double logarithmic scale is found. An evolutionary model, initially put forward for the explanation of a similar pattern found in gene populations is implemented. It includes segmental duplication events and eliminations of most of the duplicated CGIs, while a moderate rate of non-duplicated CGI eliminations is also applied in some cases. Simulations reproduce all the main features of the observed inter-CGI chromosomal size distributions. Our results on power-law-like linearity found in orphan CGI populations suggest that the observed distributional pattern is independent of the analogous pattern that protein coding segments were reported to follow. The power-law-like patterns in the genomic distributions of CGIs described herein are found to be compatible with several other features of the composition, abundance or functional role of CGIs reported in the current literature across several genomes, on the basis of the proposed evolutionary model. Copyright © 2014 Elsevier Ltd. All rights reserved.
Understanding the determinants of volatility clustering in terms of stationary Markovian processes

NASA Astrophysics Data System (ADS)

Miccichè, S.

2016-11-01

Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ-β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock's volatility is a linear function of the average correlation of such stock's volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts. As a result, the diagonalized volatilities result to share with the original volatilities either the power-law decay of the probability density function and the power-law decay of the autocorrelation function. This would indicate that volatility clustering is already present in the diagonalized un-correlated volatilities. We therefore present a parsimonious univariate model based on a non-linear Langevin equation that well reproduces these two stylized facts of volatility. The model helps us in understanding that the main source of volatility clustering, once volatilities have been diagonalized, is that the economic forces driving volatility can be modeled in terms of a Smoluchowski potential with logarithmic tails.
Fractal dynamics of earthquakes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bak, P.; Chen, K.

1995-05-01

Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function ofmore » time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).« less
Simulating flaring events in complex active regions driven by observed magnetograms

NASA Astrophysics Data System (ADS)

Dimitropoulou, M.; Isliker, H.; Vlahos, L.; Georgoulis, M. K.

2011-05-01

Context. We interpret solar flares as events originating in active regions that have reached the self organized critical state, by using a refined cellular automaton model with initial conditions derived from observations. Aims: We investigate whether the system, with its imposed physical elements, reaches a self organized critical state and whether well-known statistical properties of flares, such as scaling laws observed in the distribution functions of characteristic parameters, are reproduced after this state has been reached. Methods: To investigate whether the distribution functions of total energy, peak energy and event duration follow the expected scaling laws, we first applied a nonlinear force-free extrapolation that reconstructs the three-dimensional magnetic fields from two-dimensional vector magnetograms. We then locate magnetic discontinuities exceeding a threshold in the Laplacian of the magnetic field. These discontinuities are relaxed in local diffusion events, implemented in the form of cellular automaton evolution rules. Subsequent loading and relaxation steps lead the system to self organized criticality, after which the statistical properties of the simulated events are examined. Physical requirements, such as the divergence-free condition for the magnetic field vector, are approximately imposed on all elements of the model. Results: Our results show that self organized criticality is indeed reached when applying specific loading and relaxation rules. Power-law indices obtained from the distribution functions of the modeled flaring events are in good agreement with observations. Single power laws (peak and total flare energy) are obtained, as are power laws with exponential cutoff and double power laws (flare duration). The results are also compared with observational X-ray data from the GOES satellite for our active-region sample. Conclusions: We conclude that well-known statistical properties of flares are reproduced after the system has reached self organized criticality. A significant enhancement of our refined cellular automaton model is that it commences the simulation from observed vector magnetograms, thus facilitating energy calculation in physical units. The model described in this study remains consistent with fundamental physical requirements, and imposes physically meaningful driving and redistribution rules.
Zipf's law from scale-free geometry.

PubMed

Lin, Henry W; Loeb, Abraham

2016-03-01

The spatial distribution of people exhibits clustering across a wide range of scales, from household (∼10(-2) km) to continental (∼10(4) km) scales. Empirical data indicate simple power-law scalings for the size distribution of cities (known as Zipf's law) and the population density fluctuations as a function of scale. Using techniques from random field theory and statistical physics, we show that these power laws are fundamentally a consequence of the scale-free spatial clustering of human populations and the fact that humans inhabit a two-dimensional surface. In this sense, the symmetries of scale invariance in two spatial dimensions are intimately connected to urban sociology. We test our theory by empirically measuring the power spectrum of population density fluctuations and show that the logarithmic slope α=2.04 ± 0.09, in excellent agreement with our theoretical prediction α=2. The model enables the analytic computation of many new predictions by importing the mathematical formalism of random fields.
Toward Complete Statistics of Massive Binary Stars: Penultimate Results from the Cygnus OB2 Radial Velocity Survey

NASA Astrophysics Data System (ADS)

Kobulnicky, Henry A.; Kiminki, Daniel C.; Lundquist, Michael J.; Burke, Jamison; Chapman, James; Keller, Erica; Lester, Kathryn; Rolen, Emily K.; Topel, Eric; Bhattacharjee, Anirban; Smullen, Rachel A.; Vargas Álvarez, Carlos A.; Runnoe, Jessie C.; Dale, Daniel A.; Brotherton, Michael M.

2014-08-01

We analyze orbital solutions for 48 massive multiple-star systems in the Cygnus OB2 association, 23 of which are newly presented here, to find that the observed distribution of orbital periods is approximately uniform in log P for P < 45 days, but it is not scale-free. Inflections in the cumulative distribution near 6 days, 14 days, and 45 days suggest key physical scales of sime0.2, sime0.4, and sime1 A.U. where yet-to-be-identified phenomena create distinct features. No single power law provides a statistically compelling prescription, but if features are ignored, a power law with exponent β ~= -0.22 provides a crude approximation over P = 1.4-2000 days, as does a piece-wise linear function with a break near 45 days. The cumulative period distribution flattens at P > 45 days, even after correction for completeness, indicating either a lower binary fraction or a shift toward low-mass companions. A high degree of similarity (91% likelihood) between the Cyg OB2 period distribution and that of other surveys suggests that the binary properties at P <~ 25 days are determined by local physics of disk/clump fragmentation and are relatively insensitive to environmental and evolutionary factors. Fully 30% of the unbiased parent sample is a binary with period P < 45 days. Completeness corrections imply a binary fraction near 55% for P < 5000 days. The observed distribution of mass ratios 0.2 < q < 1 is consistent with uniform, while the observed distribution of eccentricities 0.1 < e < 0.6 is consistent with uniform plus an excess of e ~= 0 systems. We identify six stars, all supergiants, that exhibit aperiodic velocity variations of ~30 km s-1 attributed to atmospheric fluctuations.
Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

NASA Astrophysics Data System (ADS)

Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

2018-03-01

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.
Critical Concavity of a Drainage Basin for Steady-State

NASA Astrophysics Data System (ADS)

Byun, Jongmin; Paik, Kyungrock

2015-04-01

Longitudinal profiles of natural streams are known to show concave forms. Saying A as drainage area, channel gradient S can be expressed as the power-law, S≈A-θ (Flint, 1974), which is one of the scale-invariant features of drainage basin. According to literature, θ of most natural streams falls into a narrow range (0.4 < θ < 0.7) (Tucker and Whipple, 2002). It leads to fundamental questions: 'Why does θ falls into such narrow range?' and 'How is this related with other power-law scaling relationships reported in natural drainage basins?' To answer above questions, we analytically derive θ for a steady-state drainage basin following Lane's equilibrium (Lane, 1955) throughout the corridor and named this specific case as the 'critical concavity'. In the derivation, sediment transport capacity is estimated by unit stream power model (Yang, 1976), yielding a power function of upstream area. Stability of channel at a local point occurs when incoming flux equals outgoing flux at the point. Therefore, given the drainage at steady-state where all channel beds are stable, the exponent of the power function should be zero. From this, we can determine the critical concavity. Considering ranges of variables associated in this derivation, critical concavity cannot be resolved as a single definite value, rather a range of critical concavity is suggested. This range well agrees with the widely reported range of θ (0.4 < θ < 0.7) in natural streams. In this theoretical study, inter-relationships between power-laws such as hydraulic geometry (Leopold and Maddock, 1953), dominant discharge-drainage area (Knighton et al., 1999), and concavity, are coupled into the power-law framework of stream power sediment transport model. This allows us to explore close relationships between their power-law exponents: their relative roles and sensitivity. Detailed analysis and implications will be presented. References Flint, J. J., 1974, Stream gradient as a function of order, magnitude, and discharge, Water Resources Research, 10, 969-973. Knighton, A. D., 1999, Downstream variation in stream power, Geomorphology, 29, 293-306. Lane, E. W., 1955, The importance of fluvial morphology in hydraulic engineering, American Society of Civil Engineers, Proceedings, 81, 1-17 Leopold, L. B., Maddock, T., 1953, The hydraulic geometry of stream channels and some physiographic implications, United States Government Printing Office, 1953. Tucker, G. E., Whipple, K. X., 2002, Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison, Journal of Geophysical Research, 107(B9), 2179, doi:10.1029/2001JB000162, 2002. Yang, C. T., 1976, Minimum unit stream power and fluvial hydraulics, Journal of Hydraulics Division, ASCE 102, 919-934.
There is More than a Power Law in Zipf

PubMed Central

Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano

2012-01-01

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law. PMID:23139862
Galaxy And Mass Assembly (GAMA): the signatures of galaxy interactions as viewed from small scale galaxy clustering

NASA Astrophysics Data System (ADS)

Gunawardhana, M. L. P.; Norberg, P.; Zehavi, I.; Farrow, D. J.; Loveday, J.; Hopkins, A. M.; Davies, L. J. M.; Wang, L.; Alpaslan, M.; Bland-Hawthorn, J.; Brough, S.; Holwerda, B. W.; Owers, M. S.; Wright, A. H.

2018-06-01

Statistical studies of galaxy-galaxy interactions often utilise net change in physical properties of progenitors as a function of the separation between their nuclei to trace both the strength and the observable timescale of their interaction. In this study, we use two-point auto, cross and mark correlation functions to investigate the extent to which small-scale clustering properties of star forming galaxies can be used to gain physical insight into galaxy-galaxy interactions between galaxies of similar optical brightness and stellar mass. The Hα star formers, drawn from the highly spatially complete Galaxy And Mass Assembly (GAMA) survey, show an increase in clustering on small separations. Moreover, the clustering strength shows a strong dependence on optical brightness and stellar mass, where (1) the clustering amplitude of optically brighter galaxies at a given separation is larger than that of optically fainter systems, (2) the small scale clustering properties (e.g. the strength, the scale at which the signal relative to the fiducial power law plateaus) of star forming galaxies appear to differ as a function of increasing optical brightness of galaxies. According to cross and mark correlation analyses, the former result is largely driven by the increased dust content in optically bright star forming galaxies. The latter could be interpreted as evidence of a correlation between interaction-scale and optical brightness of galaxies, where physical evidence of interactions between optically bright star formers, likely hosted within relatively massive halos, persist over larger separations than those between optically faint star formers.

Impact of Interstellar Vehicle Acceleration and Cruise Velocity on Total Mission Mass and Trip Time

NASA Technical Reports Server (NTRS)

Frisbee, Robert H.

2006-01-01

Far-term interstellar missions, like their near-term solar system exploration counterparts, seek to minimize overall mission trip time and transportation system mass. Trip time is especially important in interstellar missions because of the enormous distances between stars and the finite limit of the speed of light (c). In this paper, we investigate the impact of vehicle acceleration and maximum or cruise velocity (Vcruise) on the total mission trip time. We also consider the impact that acceleration has on the transportation system mass (M) and power (P) (e.g., acceleration approx. power/mass and mass approx. power), as well as the impact that the cruise velocity has on the vehicle mass (e.g., the total mission change in velocity ((Delta)V) approx. Vcruise). For example, a Matter-Antimatter Annihilation Rocket's wet mass (Mwet) with propellant (Mp) will be a function of the dry mass of the vehicle (Mdry) and (Delta)V through the Rocket Equation. Similarly, a laser-driven LightSail's sail mass and laser power and mass will be a function of acceleration, Vcruise, and power-beaming distance (because of the need to focus the laser beam over interstellar distances).
Soliton sustainable socio-economic distribution

NASA Astrophysics Data System (ADS)

Dresvyannikov, M. A.; Petrova, M. V.; Tshovrebov, A. M.

2017-11-01

In the work presented, from close positions, we consider: 1) the question of the stability of socio-economic distributions; 2) the question of the possible mechanism for the formation of fractional power-law dependences in the Cobb/Douglas production function; 3) the introduction of a fractional order derivative for a general analysis of a fractional power function; 4) bringing in a state of mutual matching of the interest rate and the production function of Cobb/Douglas.
Immobile defects in ferroelastic walls: Wall nucleation at defect sites

NASA Astrophysics Data System (ADS)

He, X.; Salje, E. K. H.; Ding, X.; Sun, J.

2018-02-01

Randomly distributed, static defects are enriched in ferroelastic domain walls. The relative concentration of defects in walls, Nd, follows a power law distribution as a function of the total defect concentration C: N d ˜ C α with α = 0.4 . The enrichment Nd/C ranges from ˜50 times when C = 10 ppm to ˜3 times when C = 1000 ppm. The resulting enrichment is due to nucleation at defect sites as observed in large scale MD simulations. The dynamics of domain nucleation and switching is dependent on the defect concentration. Their energy distribution follows the power law with exponents during yield between ɛ ˜ 1.82 and 2.0 when the defect concentration increases. The power law exponent is ɛ ≈ 2.7 in the plastic regime, independent of the defect concentration.
Numerical simulation of nanofluids based on power-law fluids with flow and heat transfer

NASA Astrophysics Data System (ADS)

Li, Lin; Jiang, Yongyue; Chen, Aixin

2017-04-01

In this paper, we investigate the heat transfer of nanofluids based on power-law fluids and movement of nanoparticles with the effect of thermophoresis in a rotating circular groove. The velocity of circular groove rotating is a constant and the temperature on the wall is kept to be zero all the time which is different from the temperature of nanofluids in the initial time. The effects of thermophoresis and Brownian diffusion are considered in temperature and concentration equations, and it is assumed that the thermal conductivity of nanofluids is a function of concentration of nanoparticles. Based on numerical results, it can be found that nanofluids improve the process of heat transfer than base fluids in a rotating circular groove. The enhancement of heat transfer increases as the power law index of base fluids decreases.
Power law-based local search in spider monkey optimisation for lower order system modelling

NASA Astrophysics Data System (ADS)

Sharma, Ajay; Sharma, Harish; Bhargava, Annapurna; Sharma, Nirmala

2017-01-01

The nature-inspired algorithms (NIAs) have shown efficiency to solve many complex real-world optimisation problems. The efficiency of NIAs is measured by their ability to find adequate results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. This paper presents a solution for lower order system modelling using spider monkey optimisation (SMO) algorithm to obtain a better approximation for lower order systems and reflects almost original higher order system's characteristics. Further, a local search strategy, namely, power law-based local search is incorporated with SMO. The proposed strategy is named as power law-based local search in SMO (PLSMO). The efficiency, accuracy and reliability of the proposed algorithm is tested over 20 well-known benchmark functions. Then, the PLSMO algorithm is applied to solve the lower order system modelling problem.
Evaluation and linking of effective parameters in particle-based models and continuum models for mixing-limited bimolecular reactions

NASA Astrophysics Data System (ADS)

Zhang, Yong; Papelis, Charalambos; Sun, Pengtao; Yu, Zhongbo

2013-08-01

Particle-based models and continuum models have been developed to quantify mixing-limited bimolecular reactions for decades. Effective model parameters control reaction kinetics, but the relationship between the particle-based model parameter (such as the interaction radius R) and the continuum model parameter (i.e., the effective rate coefficient Kf) remains obscure. This study attempts to evaluate and link R and Kf for the second-order bimolecular reaction in both the bulk and the sharp-concentration-gradient (SCG) systems. First, in the bulk system, the agent-based method reveals that R remains constant for irreversible reactions and decreases nonlinearly in time for a reversible reaction, while mathematical analysis shows that Kf transitions from an exponential to a power-law function. Qualitative link between R and Kf can then be built for the irreversible reaction with equal initial reactant concentrations. Second, in the SCG system with a reaction interface, numerical experiments show that when R and Kf decline as t-1/2 (for example, to account for the reactant front expansion), the two models capture the transient power-law growth of product mass, and their effective parameters have the same functional form. Finally, revisiting of laboratory experiments further shows that the best fit factor in R and Kf is on the same order, and both models can efficiently describe chemical kinetics observed in the SCG system. Effective model parameters used to describe reaction kinetics therefore may be linked directly, where the exact linkage may depend on the chemical and physical properties of the system.
Dynamical Mass Measurements of Contaminated Galaxy Clusters Using Support Distribution Machines

NASA Astrophysics Data System (ADS)

Ntampaka, Michelle; Trac, Hy; Sutherland, Dougal; Fromenteau, Sebastien; Poczos, Barnabas; Schneider, Jeff

2018-01-01

We study dynamical mass measurements of galaxy clusters contaminated by interlopers and show that a modern machine learning (ML) algorithm can predict masses by better than a factor of two compared to a standard scaling relation approach. We create two mock catalogs from Multidark’s publicly available N-body MDPL1 simulation, one with perfect galaxy cluster membership infor- mation and the other where a simple cylindrical cut around the cluster center allows interlopers to contaminate the clusters. In the standard approach, we use a power-law scaling relation to infer cluster mass from galaxy line-of-sight (LOS) velocity dispersion. Assuming perfect membership knowledge, this unrealistic case produces a wide fractional mass error distribution, with a width E=0.87. Interlopers introduce additional scatter, significantly widening the error distribution further (E=2.13). We employ the support distribution machine (SDM) class of algorithms to learn from distributions of data to predict single values. Applied to distributions of galaxy observables such as LOS velocity and projected distance from the cluster center, SDM yields better than a factor-of-two improvement (E=0.67) for the contaminated case. Remarkably, SDM applied to contaminated clusters is better able to recover masses than even the scaling relation approach applied to uncon- taminated clusters. We show that the SDM method more accurately reproduces the cluster mass function, making it a valuable tool for employing cluster observations to evaluate cosmological models.
28 CFR 0.130 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.130 Section 0.130..., Tobacco, Firearms, and Explosives § 0.130 General functions. Subject to the direction of the Attorney... functions and powers of the Attorney General under the following provisions of law: (1) 18 U.S.C. chapters...
Quantitative Characterization of Shear-Induced Platelet Receptor Shedding: Glycoprotein Ibα, Glycoprotein VI, and Glycoprotein IIb/IIIa.

PubMed

Chen, Zengsheng; Koenig, Steven C; Slaughter, Mark S; Griffith, Bartley P; Wu, Zhongjun J

2017-11-07

The structural integrity of platelet receptors is essential for platelets to play the normal hemostatic function. The high non-physiologic shear stress (NPSS) commonly exists in blood-contacting medical devices and has been shown to cause platelet receptor shedding. The loss of platelet receptors may impair the normal hemostatic function of platelets. The aim of this study was to quantify NPSS-induced shedding of three key receptors on the platelet surface. Human blood was subjected to the matrix of well-defined shear stresses and exposure times, generated by using a custom-designed blood-shearing device. The expression of three key platelet receptors, glycoprotein (GP) Ibα, GPVI, and GPIIb/IIIa, in sheared blood was quantified using flow cytometry. The quantitative relationship between the loss of each of the three receptors on the platelet surface and shear condition (shear stress level and exposure time) was explored. It was found that these relationships followed well the power law functional form. The coefficients of the power law models for the shear-induced shedding of these platelet receptors were derived with coefficients of determination (R) of 0.77, 0.73, and 0.78, respectively. The power law models with these coefficients may be potentially used to predict the shear-induced platelet receptor shedding of human blood.
Modeling Fractal Structure of City-Size Distributions Using Correlation Functions

PubMed Central

Chen, Yanguang

2011-01-01

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences. PMID:21949753
M Dwarfs from Hubble Space Telescope Star Counts. IV.

NASA Astrophysics Data System (ADS)

Zheng, Zheng; Flynn, Chris; Gould, Andrew; Bahcall, John N.; Salim, Samir

2001-07-01

We study a sample of about 1400 disk M dwarfs that are found in 148 fields observed with the Wide Field Camera 2 (WFC2) on the Hubble Space Telescope and 162 fields observed with pre-repair Planetary Camera 1 (PC1), of which 95 of the WFC2 fields are newly analyzed. The method of maximum likelihood is applied to derive the luminosity function and the Galactic disk parameters. At first, we use a local color-magnitude relation and a locally determined mass-luminosity relation in our analysis. The results are consistent with those of previous work but with considerably reduced statistical errors. These small statistical errors motivate us to investigate the systematic uncertainties. Considering the metallicity gradient above the Galactic plane, we introduce a modified color-magnitude relation that is a function of Galactic height. The resultant M dwarf luminosity function has a shape similar to that derived using the local color-magnitude relation but with a higher peak value. The peak occurs at MV~12, and the luminosity function drops sharply toward MV~14. We then apply a height-dependent mass-luminosity function interpolated from theoretical models with different metallicities to calculate the mass function. Unlike the mass function obtained using local relations, which has a power-law index α=0.47, the one derived from the height-dependent relations tends to be flat (α=-0.10). The resultant local surface density of disk M dwarfs (12.2+/-1.6 Msolar pc-2) is somewhat smaller than the one obtained using local relations (14.3+/-1.3 Msolar pc-2). Our measurement favors a short disk scale length, H=2.75+/-0.16 (statistical)+/-0.25 (systematic) kpc. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
THE LONGEST TIMESCALE X-RAY VARIABILITY REVEALS EVIDENCE FOR ACTIVE GALACTIC NUCLEI IN THE HIGH ACCRETION STATE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Youhong, E-mail: youhong.zhang@mail.tsinghua.edu.cn

2011-01-01

The All Sky Monitor (ASM) on board the Rossi X-ray Timing Explorer has continuously monitored a number of active galactic nuclei (AGNs) with similar sampling rates for 14 years, from 1996 January to 2009 December. Utilizing the archival ASM data of 27 AGNs, we calculate the normalized excess variances of the 300-day binned X-ray light curves on the longest timescale (between 300 days and 14 years) explored so far. The observed variance appears to be independent of AGN black-hole mass and bolometric luminosity. According to the scaling relation of black-hole mass (and bolometric luminosity) from galactic black hole X-ray binariesmore » (GBHs) to AGNs, the break timescales that correspond to the break frequencies detected in the power spectral density (PSD) of our AGNs are larger than the binsize (300 days) of the ASM light curves. As a result, the singly broken power-law (soft-state) PSD predicts the variance to be independent of mass and luminosity. Nevertheless, the doubly broken power-law (hard-state) PSD predicts, with the widely accepted ratio of the two break frequencies, that the variance increases with increasing mass and decreases with increasing luminosity. Therefore, the independence of the observed variance on mass and luminosity suggests that AGNs should have soft-state PSDs. Taking into account the scaling of the break timescale with mass and luminosity synchronously, the observed variances are also more consistent with the soft-state than the hard-state PSD predictions. With the averaged variance of AGNs and the soft-state PSD assumption, we obtain a universal PSD amplitude of 0.030 {+-} 0.022. By analogy with the GBH PSDs in the high/soft state, the longest timescale variability supports the standpoint that AGNs are scaled-up GBHs in the high accretion state, as already implied by the direct PSD analysis.« less
Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

NASA Technical Reports Server (NTRS)

Geisler, J. E.; Fowlis, W. W.

1980-01-01

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.
Stochastic methods for analysis of power flow in electric networks

NASA Astrophysics Data System (ADS)

1982-09-01

The modeling and effects of probabilistic behavior on steady state power system operation were analyzed. A solution to the steady state network flow equations which adhere both to Kirchoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques was obtained. The development of sound techniques for producing meaningful data to serve as input is examined. Electric demand modeling, equipment failure analysis, and algorithm development are investigated. Two major development areas are described: a decomposition of stochastic processes which gives stationarity, ergodicity, and even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
Viscosity of meson matter

NASA Astrophysics Data System (ADS)

Dobado, Antonio; Llanes-Estrada, Felipe J.

2004-06-01

We report a calculation of the shear viscosity in a relativistic multicomponent meson gas as a function of temperature and chemical potentials. We approximately solve the Uehling-Uhlenbeck transport equation of kinetic theory, appropriate for a boson gas, with relativistic kinematics. Since at low temperatures the gas can be taken as mostly composed of pions, with a fraction of kaons and etas, we explore the region where binary elastic collisions with at least one pion are the dominant scattering processes. Our input meson scattering phase shifts are fits to the experimental data obtained from chiral perturbation theory and the inverse amplitude method. Our results take the correct nonrelativistic limit (viscosity proportional to the square root of the temperature), show a viscosity of the order of the cube of the pion mass up to temperatures somewhat below that mass, and then a large increase due to kaons and etas. Our approximation may break down at even higher temperatures, where the viscosity follows a temperature power law with an exponent near 3.
Mechanistic Analysis of Cocrystal Dissolution as a Function of pH and Micellar Solubilization

PubMed Central

2016-01-01

The purpose of this work is to provide a mechanistic understanding of the dissolution behavior of cocrystals under the influence of ionization and micellar solubilization. Mass transport models were developed by applying Fick’s law of diffusion to dissolution with simultaneous chemical reactions in the hydrodynamic boundary layer adjacent to the dissolving cocrystal surface to predict the pH at the dissolving solid–liquid interface (i.e., interfacial pH) and the flux of cocrystals. To evaluate the predictive power of these models, dissolution studies of carbamazepine–saccharin (CBZ-SAC) and carbamazepine–salicylic acid (CBZ-SLC) cocrystals were performed at varied pH and surfactant concentrations above the critical stabilization concentration (CSC), where the cocrystals were thermodynamically stable. The findings in this work demonstrate that the pH dependent dissolution behavior of cocrystals with ionizable components is dependent on interfacial pH. This mass transport analysis demonstrates the importance of pH, cocrystal solubility, diffusivity, and micellar solubilization on the dissolution rates of cocrystals. PMID:26877267
Mechanistic Analysis of Cocrystal Dissolution as a Function of pH and Micellar Solubilization.

PubMed

Cao, Fengjuan; Amidon, Gordon L; Rodriguez-Hornedo, Nair; Amidon, Gregory E

2016-03-07

The purpose of this work is to provide a mechanistic understanding of the dissolution behavior of cocrystals under the influence of ionization and micellar solubilization. Mass transport models were developed by applying Fick's law of diffusion to dissolution with simultaneous chemical reactions in the hydrodynamic boundary layer adjacent to the dissolving cocrystal surface to predict the pH at the dissolving solid-liquid interface (i.e., interfacial pH) and the flux of cocrystals. To evaluate the predictive power of these models, dissolution studies of carbamazepine-saccharin (CBZ-SAC) and carbamazepine-salicylic acid (CBZ-SLC) cocrystals were performed at varied pH and surfactant concentrations above the critical stabilization concentration (CSC), where the cocrystals were thermodynamically stable. The findings in this work demonstrate that the pH dependent dissolution behavior of cocrystals with ionizable components is dependent on interfacial pH. This mass transport analysis demonstrates the importance of pH, cocrystal solubility, diffusivity, and micellar solubilization on the dissolution rates of cocrystals.
Characterization of Fish Sauce Aroma Impact Compounds Using GC-MS, SPME-Osme-GCO, and Stevens' Power Law Exponents

USDA-ARS?s Scientific Manuscript database

The objectives of this study were to characterize volatile compounds and to determine the characteristic aromas associated with impact compounds in 4 fish sauces using solid-phase micro-extraction, gas chromatography-mass spectrometry, Osme, and gas chromatography olfactometry (SPME-Osme-GCO) couple...
Mechanical Properties of Mass Concrete at Early Ages

DTIC Science & Technology

1991-08-01

I.............. 15 WES UMAT Time-Dependent Material Properties Model.........15: CHAPTER IV: EXPERIMENTAL PROGRAM.................................. 17...Equationi.......................................41 WES UMAT Creep, Eqtation .................................. 42 Bazant Sinh-Double Power Law...and All ......... 42 7 UMAT Creep Equation Coefficients for Mixtures A2 and All .... 43 8 SDPL Creep Constants for Mixtures A2 and All
Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

NASA Astrophysics Data System (ADS)

Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun

2015-01-01

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass meff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation νt and change in spectral index for scalar perturbation νst to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of ns=0.96 by having a non-zero value of effective mass of the inflaton field m2eff/H2. The analysis with WP + Planck likelihood shows a non-zero detection of m2eff/H2 with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m2eff/H2 = -0.0237 ± 0.0135 which is consistent with zero.
Western Area Power Administration combined power system financial statements September 30, 1994 and 1993 and management overview and performance measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marwick, P.

1994-12-31

The attached report presents the results of the independent certified public accountant`s audit of the Department of Energy`s Western Area Power Administration`s (Western) combined financial statements as of September 30, 1994. The auditors have expressed an unqualified opinion on Western`s 1994 statements. Their reports on Western`s internal control structure and on compliance with laws and regulations are also provided. Western was established in December 1977, and has the responsibility for the Federal electric power marketing and transmission functions in 15 central and western states. Western markets power, as required by existing law, at the lowest possible rates consistent with soundmore » business principles to recover the costs of operation and capital invested in power facilities.« less
Development of a solid propellant viscoelastic dynamic model

NASA Technical Reports Server (NTRS)

Hufferd, W. L.; Fitzgerald, J. E.

1976-01-01

The results of a one year study to develop a dynamic response model for the Space Shuttle Solid Rocket Motor (SRM) propellant are presented. An extensive literature survey was conducted, from which it was concluded that the only significant variables affecting the dynamic response of the SRM propellant are temperature and frequency. Based on this study, and experimental data on propellants related to the SRM propellant, a dynamic constitutive model was developed in the form of a simple power law with temperature incorporated in the form of a modified power law. A computer program was generated which performs a least-squares curve-fit of laboratory data to determine the model parameters and it calculates dynamic moduli at any desired temperature and frequency. Additional studies investigated dynamic scaling laws and the extent of coupling between the SRM propellant and motor cases. It was found, in agreement with other investigations, that the propellant provides all of the mass and damping characteristics whereas the case provides all of the stiffness.
The languages of health in general practice electronic patient records: a Zipf's law analysis.

PubMed

Kalankesh, Leila R; New, John P; Baker, Patricia G; Brass, Andy

2014-01-10

Natural human languages show a power law behaviour in which word frequency (in any large enough corpus) is inversely proportional to word rank - Zipf's law. We have therefore asked whether similar power law behaviours could be seen in data from electronic patient records. In order to examine this question, anonymised data were obtained from all general practices in Salford covering a seven year period and captured in the form of Read codes. It was found that data for patient diagnoses and procedures followed Zipf's law. However, the medication data behaved very differently, looking much more like a referential index. We also observed differences in the statistical behaviour of the language used to describe patient diagnosis as a function of an anonymised GP practice identifier. This works demonstrate that data from electronic patient records does follow Zipf's law. We also found significant differences in Zipf's law behaviour in data from different GP practices. This suggests that computational linguistic techniques could become a useful additional tool to help understand and monitor the data quality of health records.
Dynamics of Longitudinal Impact in the Variable Cross-Section Rods

NASA Astrophysics Data System (ADS)

Stepanov, R.; Romenskyi, D.; Tsarenko, S.

2018-03-01

Dynamics of longitudinal impact in rods of variable cross-section is considered. Rods of various configurations are used as elements of power pulse systems. There is no single method to the construction of a mathematical model of longitudinal impact on rods. The creation of a general method for constructing a mathematical model of longitudinal impact for rods of variable cross-section is the goal of the article. An elastic rod is considered with a cross-sectional area varying in powers of law from the longitudinal coordinate. The solution of the wave equation is obtained using the Fourier method. Special functions are introduced on the basis of recurrence relations for Bessel functions for solving boundary value problems. The expression for the square of the norm is obtained taking into account the orthogonality property of the eigen functions with weight. For example, the impact of an inelastic mass along the wide end of a conical rod is considered. The expressions for the displacements, forces and stresses of the rod sections are obtained for the cases of sudden velocity communication and the application of force. The proposed mathematical model makes it possible to carry out investigations of the stress-strain state in rods of variable and constant cross-section for various conditions of dynamic effects.
Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model

NASA Astrophysics Data System (ADS)

Das, Subir K.

2017-01-01

Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.
Globular cluster formation and evolution in the context of cosmological galaxy assembly: open questions

NASA Astrophysics Data System (ADS)

Forbes, Duncan A.; Bastian, Nate; Gieles, Mark; Crain, Robert A.; Kruijssen, J. M. Diederik; Larsen, Søren S.; Ploeckinger, Sylvia; Agertz, Oscar; Trenti, Michele; Ferguson, Annette M. N.; Pfeffer, Joel; Gnedin, Oleg Y.

2018-02-01

We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state of the art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages greater than or equal to 12.5 Gyr and formed around the time of reionization. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z˜6 with the James Webb Space Telescope (JWST) promise further insight. GCs are known to host multiple populations of stars with variations in their chemical abundances. Recently, such multiple populations have been detected in ˜2 Gyr old compact, massive star clusters. This suggests a common, single pathway for the formation of GCs at high and low redshift. The shape of the initial mass function for GCs remains unknown; however, for massive galaxies a power-law mass function is favoured. Significant progress has been made recently modelling GC formation in the context of galaxy formation, with success in reproducing many of the observed GC-galaxy scaling relations.
Globular cluster formation and evolution in the context of cosmological galaxy assembly: open questions.

PubMed

Forbes, Duncan A; Bastian, Nate; Gieles, Mark; Crain, Robert A; Kruijssen, J M Diederik; Larsen, Søren S; Ploeckinger, Sylvia; Agertz, Oscar; Trenti, Michele; Ferguson, Annette M N; Pfeffer, Joel; Gnedin, Oleg Y

2018-02-01

We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state of the art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages greater than or equal to 12.5 Gyr and formed around the time of reionization. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z ∼6 with the James Webb Space Telescope (JWST) promise further insight. GCs are known to host multiple populations of stars with variations in their chemical abundances. Recently, such multiple populations have been detected in ∼2 Gyr old compact, massive star clusters. This suggests a common, single pathway for the formation of GCs at high and low redshift. The shape of the initial mass function for GCs remains unknown; however, for massive galaxies a power-law mass function is favoured. Significant progress has been made recently modelling GC formation in the context of galaxy formation, with success in reproducing many of the observed GC-galaxy scaling relations.
Globular cluster formation and evolution in the context of cosmological galaxy assembly: open questions

PubMed Central

Bastian, Nate; Gieles, Mark; Crain, Robert A.; Kruijssen, J. M. Diederik; Larsen, Søren S.; Ploeckinger, Sylvia; Agertz, Oscar; Trenti, Michele; Ferguson, Annette M. N.; Pfeffer, Joel; Gnedin, Oleg Y.

2018-01-01

We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state of the art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages greater than or equal to 12.5 Gyr and formed around the time of reionization. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z∼6 with the James Webb Space Telescope (JWST) promise further insight. GCs are known to host multiple populations of stars with variations in their chemical abundances. Recently, such multiple populations have been detected in ∼2 Gyr old compact, massive star clusters. This suggests a common, single pathway for the formation of GCs at high and low redshift. The shape of the initial mass function for GCs remains unknown; however, for massive galaxies a power-law mass function is favoured. Significant progress has been made recently modelling GC formation in the context of galaxy formation, with success in reproducing many of the observed GC-galaxy scaling relations. PMID:29507511
Mothers-in-law and daughters-in-law: Intergenerational relations within the Chinese family in Taiwan.

PubMed

Gallin, R S

1986-03-01

This paper examines the relations of mothers-in-law and daughters-in-law in a Taiwanese village that has changed over the past 25 years from an economic system based primarily on agriculture to one founded predominantly on off-farm employment. Using ethnographic data, it explores Amoss and Harrell's (1980: 5) proposition that the position of old people is a function of a 'cost/contribution balance' compounded by resources controlled. It concludes that economic development shifts power between women in different generations.
Long-time tail in the two-wave model

NASA Astrophysics Data System (ADS)

Hatori, T.; Abe, Y.; Irie, H.; Kaufman, A. N.

1984-07-01

The velocity time correlation function is found, both theoretically and numerically, to decay with the power law for the chaotic orbit governed by a Hamiltonian, H = v to 2nd power/2 - Mcosx - Pcos k(x-t) , M, P and k are the parameters.
Kennicutt-Schmidt Law in the Central Region of NGC 4321 as Seen by ALMA

PubMed Central

Azeez, Jazeel H.; Hwang, C.-Y.; Abidin, Zamri Z.; Ibrahim, Zainol A.

2016-01-01

We present the Atacama Large Millimeter/Sub-millimeter Array (ALMA) cycle-0 science verification data of the CO(1–0) line emission in the central region of NGC 4321 (also known as M100) at the distance of 17.1 Mpc and VLA, L-band data of HI of the same galaxy. We have drawn the center area of M100 in the 12CO(J = 1–0) line with the resolution of (3.87″ × 2.53″) as viewed by ALMA, along with HI and Spitzer 8 and 3.6 μm data. The relationship between the surface density of molecular gas mass ∑H2 and that of star formation rate ∑SFR has been investigated, in addition to the relationship between the surface density of the neutral atomic hydrogen mass and that of ∑SFR (Kennicutt–Schmidt law) in this galaxy with a high spatial resolution. The results indicate that a significant correlation exists between the SFR surface density and the molecular gas mass density in the ~2 kpc region. The power-law index has been determined for three regions: center, upper and lower arms. The value of this index in the center region is 1.13, which follows the traditional (K-S) law and indicates that the molecular gas is affected by star formation. PMID:27247251
Inter-relationship between scaling exponents for describing self-similar river networks

NASA Astrophysics Data System (ADS)

Yang, Soohyun; Paik, Kyungrock

2015-04-01

Natural river networks show well-known self-similar characteristics. Such characteristics are represented by various power-law relationships, e.g., between upstream length and drainage area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream area (exponent É) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these power-law exponents are within narrow ranges. Power-law is also found in the relationship between drainage density (the total stream length divided by the total basin area) and specified source area (the minimum drainage area to form a stream head) (exponent η) (Moussa and Bocquillon, 1996). Considering that above three scaling relationships all refer to fundamental measures of 'length' and 'area' of a given drainage basin, it is natural to hypothesize plausible inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996) demonstrated the relationship between É and h. In this study, we expand this to a more general É-η-h relationship. We approach É-η relationship in an analytical manner while η-h relationship is demonstrated for six study basins in Korea. Detailed analysis and implications will be presented. References Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1), 157-172. Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo, A. (1996). On Hack's Law. Water Resources Research, 32(11), 3367-3374. Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power law distributions of discharge mass and energy in river basins. Water Resources Research, 28(4), 1089-1093.
Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2017-10-01

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to 3 / 2, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.
BANYAN. IX. The Initial Mass Function and Planetary-mass Object Space Density of the TW HYA Association

NASA Astrophysics Data System (ADS)

Gagné, Jonathan; Faherty, Jacqueline K.; Mamajek, Eric E.; Malo, Lison; Doyon, René; Filippazzo, Joseph C.; Weinberger, Alycia J.; Donaldson, Jessica K.; Lépine, Sébastien; Lafrenière, David; Artigau, Étienne; Burgasser, Adam J.; Looper, Dagny; Boucher, Anne; Beletsky, Yuri; Camnasio, Sara; Brunette, Charles; Arboit, Geneviève

2017-02-01

A determination of the initial mass function (IMF) of the current, incomplete census of the 10 Myr-old TW Hya association (TWA) is presented. This census is built from a literature compilation supplemented with new spectra and 17 new radial velocities from ongoing membership surveys, as well as a reanalysis of Hipparcos data that confirmed HR 4334 (A2 Vn) as a member. Although the dominant uncertainty in the IMF remains census incompleteness, a detailed statistical treatment is carried out to make the IMF determination independent of binning while accounting for small number statistics. The currently known high-likelihood members are fitted by a log-normal distribution with a central mass of {0.21}-0.06+0.11 M ⊙ and a characteristic width of {0.8}-0.1+0.2 dex in the 12 M Jup-2 M ⊙ range, whereas a Salpeter power law with α ={2.2}-0.5+1.1 best describes the IMF slope in the 0.1-2 M ⊙ range. This characteristic width is higher than other young associations, which may be due to incompleteness in the current census of low-mass TWA stars. A tentative overpopulation of isolated planetary-mass members similar to 2MASS J11472421-2040204 and 2MASS J11193254-1137466 is identified: this indicates that there might be as many as {10}-5+13 similar members of TWA with hot-start model-dependent masses estimated at ˜5-7 M Jup, most of which would be too faint to be detected in 2MASS. Our new radial velocity measurements corroborate the membership of 2MASS J11472421-2040204, and secure TWA 28 (M8.5 γ), TWA 29 (M9.5 γ), and TWA 33 (M4.5 e) as members. The discovery of 2MASS J09553336-0208403, a young L7-type interloper unrelated to TWA, is also presented.
A deterministic width function model

NASA Astrophysics Data System (ADS)

Puente, C. E.; Sivakumar, B.

Use of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions.
AN ANALYSIS OF THE SHAPES OF INTERSTELLAR EXTINCTION CURVES. VI. THE NEAR-IR EXTINCTION LAW

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fitzpatrick, E. L.; Massa, D.

We combine new observations from the Hubble Space Telescope's Advanced Camera of Survey with existing data to investigate the wavelength dependence of near-IR (NIR) extinction. Previous studies suggest a power law form for NIR extinction, with a 'universal' value of the exponent, although some recent observations indicate that significant sight line-to-sight line variability may exist. We show that a power-law model for the NIR extinction provides an excellent fit to most extinction curves, but that the value of the power, {beta}, varies significantly from sight line to sight line. Therefore, it seems that a 'universal NIR extinction law' is notmore » possible. Instead, we find that as {beta} decreases, R(V) {identical_to} A(V)/E(B - V) tends to increase, suggesting that NIR extinction curves which have been considered 'peculiar' may, in fact, be typical for different R(V) values. We show that the power-law parameters can depend on the wavelength interval used to derive them, with the {beta} increasing as longer wavelengths are included. This result implies that extrapolating power-law fits to determine R(V) is unreliable. To avoid this problem, we adopt a different functional form for NIR extinction. This new form mimics a power law whose exponent increases with wavelength, has only two free parameters, can fit all of our curves over a longer wavelength baseline and to higher precision, and produces R(V) values which are consistent with independent estimates and commonly used methods for estimating R(V). Furthermore, unlike the power-law model, it gives R(V)s that are independent of the wavelength interval used to derive them. It also suggests that the relation R(V) = -1.36 E(K-V)/(E(B-V)) - 0.79 can estimate R(V) to {+-}0.12. Finally, we use model extinction curves to show that our extinction curves are in accord with theoretical expectations, and demonstrate how large samples of observational quantities can provide useful constraints on the grain properties.« less
On the Nature of the mHz X-Ray QPOs from ULX M82 X-1: Evidence for Timing-Spectral (anti) Correlation

NASA Technical Reports Server (NTRS)

Pasham, Dheeraj R.; Strohmayer, Tod E.

2013-01-01

Using all the archival XMM-Newton X-ray (3-10 keV) observations of the ultraluminous X-ray source (ULX) M82 X-1 we searched for a correlation between its variable mHz quasi-periodic oscillation (QPO) frequency and its energy spectral power-law index. These quantities are known to correlate in stellar mass black holes (StMBHs) exhibiting Type-C QPOs (approx 0.2-15 Hz). The detection of such a correlation would strengthen the identification of its mHz QPOs as Type-C and enable a more reliable mass estimate by scaling its QPO frequencies to those of Type-C QPOs in StMBHs of known mass. We resolved the count rates of M82 X-1 and a nearby bright ULX (source 5/X42.3+59) through surface brightness modeling and identify observations in which M82 X-1 was at least as bright as source 5. Using only those observations, we detect QPOs in the frequency range of 36-210 mHz during which the energy spectral power-law index varied from 1.7-2.2. Interestingly, we find evidence for an anti-correlation (Pearsons correlation coefficient = -0.95) between the power-law index and the QPO centroid frequency. While such an anti-correlation is observed in StMBHs at high Type-C QPO frequencies (approx 5-15 Hz), the frequency range over which it holds in StMBHs is significantly smaller (factor of approx 1.5-3) than the QPO range reported here from M82 X-1 (factor of 6). However, it remains possible that contamination from source 5 can bias our result. Joint Chandra/XMM-Newton observations in the future can resolve this problem and confirm the timing-spectral anti-correlation reported here.
Reinstating the M31 X-Ray System RX J0042.3+4115 as a Black Hole X-Ray Binary and Compelling Evidence for an Extended Corona

NASA Astrophysics Data System (ADS)

Barnard, R.; Garcia, M. R.; Murray, S. S.

2011-12-01

The M31 X-ray source RX J0042.3+4115 was originally identified as a black hole (BH) binary because it displayed characteristic low-state variability at conspicuously high luminosities; unfortunately, this variability was later found to be artificial. However, analysis of 84 Chandra ACIS observations, a Hubble Space Telescope Advanced Camera for Surveys (ACS)/WFC observation, and a 60 ks XMM-Newton observation has supplied new evidence that RX J0042.3+4115 is indeed a BH binary. The brightest optical star within 3σ of the position of RXJ0042.3+4115 had a F435W (~B) magnitude of 25.4 ± 0.2; M B > -0.4, hence we find a low-mass donor likely. RX J0042.3+4115 was persistently bright over ~12 years. Spectral fits revealed characteristic BH binary states: a low/hard state at 2.08 ± 0.08 × 1038 erg s-1 and a steep power-law state at 2.41 ± 0.05 × 1038 erg s-1 (0.3-10 keV). The high-luminosity low state suggests a ~20 M ⊙ primary; this is high, but within the range of known stellar BH masses. The inner disk temperature during the steep power-law state is 2.24 ± 0.15 keV, high but strikingly similar to that of GRS 1915+105, the only known Galactic BH binary with a low-mass donor to be persistently bright. Therefore, RX J0042.3+4115 may be an analog for GRS 1915+105; however, other mechanisms may account for its behavior. We find compelling evidence for an extended corona during the steep power-law state, because compact corona models where the seed photons for Comptonization are tied to the inner disk temperature are rejected.
X-ray observations of black widow pulsars

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gentile, P. A.; McLaughlin, M. A.; Roberts, M. S. E.

2014-03-10

We describe the first X-ray observations of five short orbital period (P{sub B} < 1 day), γ-ray emitting, binary millisecond pulsars (MSPs). Four of these—PSRs J0023+0923, J1124–3653, J1810+1744, and J2256–1024—are 'black-widow' pulsars, with degenerate companions of mass <<0.1 M {sub ☉}, three of which exhibit radio eclipses. The fifth source, PSR J2215+5135, is an eclipsing 'redback' with a near Roche-lobe filling ∼0.2 solar mass non-degenerate companion. Data were taken using the Chandra X-Ray Observatory and covered a full binary orbit for each pulsar. Two pulsars, PSRs J2215+5135 and J2256–1024, show significant orbital variability while PSR J1124–3653 shows marginal orbital variability.more » The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses. This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays. The other two pulsars, PSRs J0023+0923 and J1810+1744, are fainter and do not demonstrate variability at a level we can detect in these data. All five spectra are fit with three separate models: a power-law model, a blackbody model, and a combined model with both power-law and blackbody components. The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component, with a large number of counts above 2 keV, which is additional evidence for the presence of intrabinary shock emission. This is similar to what has been detected in the low-mass X-ray binary to MSP transition object PSR J1023+0038.« less

Gravitational waves from vacuum first-order phase transitions: From the envelope to the lattice

NASA Astrophysics Data System (ADS)

Cutting, Daniel; Hindmarsh, Mark; Weir, David J.

2018-06-01

We conduct large scale numerical simulations of gravitational wave production at a first-order vacuum phase transition. We find a power law for the gravitational wave power spectrum at high wave number which falls off as k-1.5 rather than the k-1 produced by the envelope approximation. The peak of the power spectrum is shifted to slightly lower wave numbers from that of the envelope approximation. The envelope approximation reproduces our results for the peak power less well, agreeing only to within an order of magnitude. After the bubbles finish colliding, the scalar field oscillates around the true vacuum. An additional feature is produced in the UV of the gravitational wave power spectrum, and this continues to grow linearly until the end of our simulation. The additional feature peaks at a length scale close to the bubble wall thickness and is shown to have a negligible contribution to the energy in gravitational waves, providing the scalar field mass is much smaller than the Planck mass.
A simplified model to evaluate the effect of fluid rheology on non-Newtonian flow in variable aperture fractures

NASA Astrophysics Data System (ADS)

Felisa, Giada; Ciriello, Valentina; Longo, Sandro; Di Federico, Vittorio

2017-04-01

Modeling of non-Newtonian flow in fractured media is essential in hydraulic fracturing operations, largely used for optimal exploitation of oil, gas and thermal reservoirs. Complex fluids interact with pre-existing rock fractures also during drilling operations, enhanced oil recovery, environmental remediation, and other natural phenomena such as magma and sand intrusions, and mud volcanoes. A first step in the modeling effort is a detailed understanding of flow in a single fracture, as the fracture aperture is typically spatially variable. A large bibliography exists on Newtonian flow in single, variable aperture fractures. Ultimately, stochastic modeling of aperture variability at the single fracture scale leads to determination of the flowrate under a given pressure gradient as a function of the parameters describing the variability of the aperture field and the fluid rheological behaviour. From the flowrate, a flow, or 'hydraulic', aperture can then be derived. The equivalent flow aperture for non-Newtonian fluids of power-law nature in single, variable aperture fractures has been obtained in the past both for deterministic and stochastic variations. Detailed numerical modeling of power-law fluid flow in a variable aperture fracture demonstrated that pronounced channelization effects are associated to a nonlinear fluid rheology. The availability of an equivalent flow aperture as a function of the parameters describing the fluid rheology and the aperture variability is enticing, as it allows taking their interaction into account when modeling flow in fracture networks at a larger scale. A relevant issue in non-Newtonian fracture flow is the rheological nature of the fluid. The constitutive model routinely used for hydro-fracturing modeling is the simple, two-parameter power-law. Yet this model does not characterize real fluids at low and high shear rates, as it implies, for shear-thinning fluids, an apparent viscosity which becomes unbounded for zero shear rate and tends to zero for infinite shear rate. On the contrary, the four-parameter Carreau constitutive equation includes asymptotic values of the apparent viscosity at those limits; in turn, the Carreau rheological equation is well approximated by the more tractable truncated power-law model. Results for flow of such fluids between parallel walls are already available. This study extends the adoption of the truncated power-law model to variable aperture fractures, with the aim of understanding the joint influence of rheology and aperture spatial variability. The aperture variation, modeled within a stochastic or deterministic framework, is taken to be one-dimensional and perpendicular to the flow direction; for stochastic modeling, the influence of different distribution functions is examined. Results are then compared with those obtained for pure power-law fluids for different combinations of model parameters. It is seen that the adoption of the pure power law model leads to significant overestimation of the flowrate with respect to the truncated model, more so for large external pressure gradient and/or aperture variability.
Utsu aftershock productivity law explained from geometric operations on the permanent static stress field of mainshocks

NASA Astrophysics Data System (ADS)

Mignan, Arnaud

2018-03-01

The aftershock productivity law is an exponential function of the form K ∝ exp(αM), with K being the number of aftershocks triggered by a given mainshock of magnitude M and α ≈ ln(10) being the productivity parameter. This law remains empirical in nature although it has also been retrieved in static stress simulations. Here, we parameterize this law using the solid seismicity postulate (SSP), the basis of a geometrical theory of seismicity where seismicity patterns are described by mathematical expressions obtained from geometric operations on a permanent static stress field. We first test the SSP that relates seismicity density to a static stress step function. We show that it yields a power exponent q = 1.96 ± 0.01 for the power-law spatial linear density distribution of aftershocks, once uniform noise is added to the static stress field, in agreement with observations. We then recover the exponential function of the productivity law with a break in scaling obtained between small and large M, with α = 1.5ln(10) and ln(10), respectively, in agreement with results from previous static stress simulations. Possible biases of aftershock selection, proven to exist in epidemic-type aftershock sequence (ETAS) simulations, may explain the lack of break in scaling observed in seismicity catalogues. The existence of the theoretical kink, however, remains to be proven. Finally, we describe how to estimate the solid seismicity parameters (activation density δ+, aftershock solid envelope r∗ and background stress amplitude range Δo∗) for large M values.
Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

PubMed

Salje, Ekhard K H; Planes, Antoni; Vives, Eduard

2017-10-01

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.
Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

NASA Astrophysics Data System (ADS)

Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

2018-04-01

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.
The first experimental confirmation of the fractional kinetics containing the complex-power-law exponents: Dielectric measurements of polymerization reactions

NASA Astrophysics Data System (ADS)

Nigmatullin, R. R.; Arbuzov, A. A.; Salehli, F.; Giz, A.; Bayrak, I.; Catalgil-Giz, H.

2007-01-01

For the first time we achieved incontestable evidence that the real process of dielectric relaxation during the polymerization reaction of polyvinylpyrrolidone (PVP) is described in terms of the fractional kinetic equations containing complex-power-law exponents. The possibility of the existence of the fractional kinetics containing non-integer complex-power-law exponents follows from the general theory of dielectric relaxation that has been suggested recently by one of the authors (R.R.N). Based on the physical/geometrical meaning of the fractional integral with complex exponents there is a possibility to develop a general theory of dielectric relaxation based on the self-similar (fractal) character of the reduced (averaged) microprocesses that take place in the mesoscale region. This theory contains some essential predictions related to existence of the non-integer power-law kinetics and the results of this paper can be considered as the first confirmation of existence of the kinetic phenomena that are described by fractional derivatives with complex-power-law exponents. We want to stress here that with the help of a new complex fitting function for the complex permittivity it becomes possible to describe the whole process for real and imaginary parts simultaneously throughout the admissible frequency range (30 Hz-13 MHz). The fitting parameters obtained for the complex permittivity function for three temperatures (70, 90 and 110 °C) confirm in general the picture of reaction that was known qualitatively before. They also reveal some new features, which improve the interpretation of the whole polymerization process. We hope that these first results obtained in the paper will serve as a good stimulus for other researches to find the traces of the existence of new fractional kinetics in other relaxation processes unrelated to the dielectric relaxation. These results should lead to the reconsideration and generalization of irreversibility and kinetic phenomena that can take place for many linear non-equilibrium systems.
Optimal trajectories for hypersonic launch vehicles

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Bowles, Jeffrey V.; Whittaker, Thomas

1994-01-01

In this paper, we derive a near-optimal guidance law for the ascent trajectory from earth surface to earth orbit of a hypersonic, dual-mode propulsion, lifting vehicle. Of interest are both the optical flight path and the optimal operation of the propulsion system. The guidance law is developed from the energy-state approximation of the equations of motion. Because liquid hydrogen fueled hypersonic aircraft are volume sensitive, as well as weight sensitive, the cost functional is a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize gross take-off weight for a given payload mass and volume in orbit.
Probing features in the primordial perturbation spectrum with large-scale structure data

NASA Astrophysics Data System (ADS)

L'Huillier, Benjamin; Shafieloo, Arman; Hazra, Dhiraj Kumar; Smoot, George F.; Starobinsky, Alexei A.

2018-06-01

The form of the primordial power spectrum (PPS) of cosmological scalar (matter density) perturbations is not yet constrained satisfactorily in spite of the tremendous amount of information from the Cosmic Microwave Background (CMB) data. While a smooth power-law-like form of the PPS is consistent with the CMB data, some PPSs with small non-smooth features at large scales can also fit the CMB temperature and polarization data with similar statistical evidence. Future CMB surveys cannot help distinguish all such models due to the cosmic variance at large angular scales. In this paper, we study how well we can differentiate between such featured forms of the PPS not otherwise distinguishable using CMB data. We ran 15 N-body DESI-like simulations of these models to explore this approach. Showing that statistics such as the halo mass function and the two-point correlation function are not able to distinguish these models in a DESI-like survey, we advocate to avoid reducing the dimensionality of the problem by demonstrating that the use of a simple three-dimensional count-in-cell density field can be much more effective for the purpose of model distinction.
Beyond the Band Function Paradigm : a New Model for GRB Prompt Emission and Possible Impact in Cosmology

NASA Astrophysics Data System (ADS)

Guiriec, Sylvain

Gamma Ray Bursts (GRBs) are the most violent phenomenons in the Universe. They are associated with the birth of stellar mass black holes either from the collapse of hypermassive stars or the merger of compact objects. The Fireball model is the most popular scenario to explain GRBs. In this theoretical framework, GRB central engines release collimated, bipolar and highly relativistic jets mainly composed of electrons, positrons, photons, and a small amount of baryons. During the first phase of the Fireball model, charged particles are accelerated and release non-thermal radiations. The Fireball model also predicts a thermal like component coming from the jet photosphere. This first phase would be responsible for the GRB prompt emission observed by gamma ray telescopes such as Fermi/GBM in the keV-MeV energy range and which is the only phase discussed in this talk. Until now, GRB prompt emission spectra were considered as adequately fitted with the empirical Band function, which is a smoothly broken power law. However, its parameters are very often incompatible with the Fireball model predictions for both the thermal and non-thermal components. We will see that observation with the Fermi Gamma Ray Space Telescope break the paradigm of the Band function and that deviations from this function exists in many GRBs. Those deviations are adequately fitted with an additional thermal-like component -that we consider as the jet photosphere- and/or an additional power law. Importantly, with the three components together, theory and observations are much more in agreement. We will also see how this new model for prompt emission spectra may have an impact beyond the physics of GRBs. Indeed, this work may confirm a relation between the hardness of the GRB prompt emission and its luminosity which may be used to scale GRBs as standard-like candles for use in cosmology.
A Simple, Efficient and Effective Modeling Approach to Determine Baseflow Based on Concentration-Discharge Relationships

NASA Astrophysics Data System (ADS)

Liu, F.; Miller, M. P.; Conklin, M. H.

2017-12-01

Concentration-discharge relationships in streamflow are a precursor for diagnosing endmember mixing. With a strong power-law relationship between concentration and discharge, previous studies have shown that conservative solute concentrations in streamflow can be explained by mixing of two endmembers, i.e., quick runoff (QR) and baseflow (BF). This current study showed that the unique concentration-discharge power-law curve provides two characteristic values of solute concentrations at extremely high and low flows and these envelope values can be used to aid two-endmember mixing models. In an example conducted in the Upper Colorado River Basin (UCRB), daily specific conductance (SC) and discharge were strongly correlated by a power-law function on both rising and falling limbs from 1983 to 2015 (R2 > 0.9 for all years). The high envelope SC value in each year was directly used to characterize baseflow for that year, while the low envelope SC value was adjusted to represent quick runoff, a collective term for surface runoff and responsive shallow subsurface runoff. The peak flow was considered to be dominated by QR with only a small portion of BF. The ratio of minimum to maximum flows was used to calibrate the low envelope SC value. This ratio represents the least fraction of baseflow to total flow at the peak flow, as baseflow increases with total flow based on published studies. The SC value at the peak flow was considered to be a mixture of QR and BF with the minimum/maximum flow ratio as baseflow fraction and thus SC value in QR was determined with a mass balance equation. The baseflow fractions determined in two-endmember mixing models by this characterization of QR from 1983 to 2011 match those by Miller et al. [2014] very well (R2 = 0.96, slope = 1.07, intercept = -0.13). Baseflow fractions were slightly under-estimated by this approach mainly due to the fact that responsive shallow subsurface runoff was considered to be part of quick flow in this study rather than part of baseflow. This approach provides a simple, efficient and effective modeling tool for estimating baseflow without requiring any samples from endmembers in catchments with a strong power-law relation.
Solid earth as a recycling systems and the lateral growth of Precambrian North America

NASA Technical Reports Server (NTRS)

Veizer, Jan

1988-01-01

If plotted on mass vs time diagrams, geologic entities (for example, continental and oceanic crust, sediments, and mineral resources) display an exponential (power law) relationship, with entity per unit time increasing toward the present. This relationship is consistent with the concept of recycling and can be simulated mathematically. The approach is based on the plate tectonic theory and considers area-age or mass-age distributions of crystalline basement and sediments for major global tectonic realms. Each tectonic realm is characterized by a specific lifespan, which is an inverse function of its recycling rate. The estimated average half-area of half-mass ages are given. The corresponding parameters for continental crust are 690 Ma for K/Ar, and approximately 1200 Ma for Rb/St and U-Th/Pb dating pairs. Tectonic diversity preserved in the geologic record is therefore a function of time, with oceanic tectonic realms, because of their rapid recycling, underrepresented in the rocks older than approximately 300 Ma. The Sm/Nd isotopic systematic of sediments suggest that, for a near steady-state post-Archean sedimentary mass, recycling is approximately 90 + or - 5 percent cannibalistic. This yields an estimated upper limit on crust-mantle exchange via sediment subduction of approximately 1.1 + or - 0.5 x 10 g a(sup -1) considerably less than demanded by isotopic constraints. The discrepancy may indicate the existence of additional loci, such as orogenic belts, for significant crust-mantle interaction.
Ionization compression impact on dense gas distribution and star formation. Probability density functions around H II regions as seen by Herschel

NASA Astrophysics Data System (ADS)

Tremblin, P.; Schneider, N.; Minier, V.; Didelon, P.; Hill, T.; Anderson, L. D.; Motte, F.; Zavagno, A.; André, Ph.; Arzoumanian, D.; Audit, E.; Benedettini, M.; Bontemps, S.; Csengeri, T.; Di Francesco, J.; Giannini, T.; Hennemann, M.; Nguyen Luong, Q.; Marston, A. P.; Peretto, N.; Rivera-Ingraham, A.; Russeil, D.; Rygl, K. L. J.; Spinoglio, L.; White, G. J.

2014-04-01

Aims: Ionization feedback should impact the probability distribution function (PDF) of the column density of cold dust around the ionized gas. We aim to quantify this effect and discuss its potential link to the core and initial mass function (CMF/IMF). Methods: We used Herschel column density maps of several regions observed within the HOBYS key program in a systematic way: M 16, the Rosette and Vela C molecular clouds, and the RCW 120 H ii region. We computed the PDFs in concentric disks around the main ionizing sources, determined their properties, and discuss the effect of ionization pressure on the distribution of the column density. Results: We fitted the column density PDFs of all clouds with two lognormal distributions, since they present a "double-peak" or an enlarged shape in the PDF. Our interpretation is that the lowest part of the column density distribution describes the turbulent molecular gas, while the second peak corresponds to a compression zone induced by the expansion of the ionized gas into the turbulent molecular cloud. Such a double peak is not visible for all clouds associated with ionization fronts, but it depends on the relative importance of ionization pressure and turbulent ram pressure. A power-law tail is present for higher column densities, which are generally ascribed to the effect of gravity. The condensations at the edge of the ionized gas have a steep compressed radial profile, sometimes recognizable in the flattening of the power-law tail. This could lead to an unambiguous criterion that is able to disentangle triggered star formation from pre-existing star formation. Conclusions: In the context of the gravo-turbulent scenario for the origin of the CMF/IMF, the double-peaked or enlarged shape of the PDF may affect the formation of objects at both the low-mass and the high-mass ends of the CMF/IMF. In particular, a broader PDF is required by the gravo-turbulent scenario to fit the IMF properly with a reasonable initial Mach number for the molecular cloud. Since other physical processes (e.g., the equation of state and the variations among the core properties) have already been said to broaden the PDF, the relative importance of the different effects remains an open question. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.
Physical analysis of an electric resistor heating

NASA Astrophysics Data System (ADS)

Perea Martins, J. E. M.

2018-05-01

This work describes a simple experiment to measure the resistor temperature as a function of the applied power and proves that it is an efficient way to introduce some important physical concepts in classroom, including the Joule’s first law, hot-spot temperature, thermal resistance, thermal dissipation constant, time constant and the Newton’s law of cooling.
Coalescence of Drops of a Power-law Fluid

NASA Astrophysics Data System (ADS)

Kamat, Pritish; Thete, Sumeet; Basaran, Osman

2014-11-01

Drop coalescence is crucial in a host of industrial, household, and natural processes that involve dispersions. Coalescence is a rate-controlling process in breaking emulsions and strongly influences drop-size-distributions in sprays. In a continuum approach, coalescence begins by the formation of a microscopic, non-slender bridge connecting the two drops. Indefinitely large axial curvature at the neck results in local lowering of pressure that drives fluid from the bulk of the drops toward the neck, thereby causing the bridge radius r (t) and height z (t) to increase in time t. The coalescence of Newtonian drops in air has heretofore been thoroughly studied. Here, we extend these earlier studies by analyzing the coalescence of drops of power-law fluids because many fluids encountered in real applications, including cosmetic creams, shampoos, grease, and paint, exhibit power-law (deformation-rate thinning) rheology. On account of the non-slender geometry of the liquid bridge connecting the two drops (z << r) , we analyze the resulting free surface flow problem by numerical simulation. Among other results, we present and discuss the nature of flows and scaling behaviors for r and z as functions of the initial viscosity and power-law index (0 < n <= 1) .
Scale-free avalanche dynamics in the stock market

NASA Astrophysics Data System (ADS)

Bartolozzi, M.; Leinweber, D. B.; Thomas, A. W.

2006-10-01

Self-organized criticality (SOC) has been claimed to play an important role in many natural and social systems. In the present work we empirically investigate the relevance of this theory to stock-market dynamics. Avalanches in stock-market indices are identified using a multi-scale wavelet-filtering analysis designed to remove Gaussian noise from the index. Here, new methods are developed to identify the optimal filtering parameters which maximize the noise removal. The filtered time series is reconstructed and compared with the original time series. A statistical analysis of both high-frequency Nasdaq E-mini Futures and daily Dow Jones data is performed. The results of this new analysis confirm earlier results revealing a robust power-law behaviour in the probability distribution function of the sizes, duration and laminar times between avalanches. This power-law behaviour holds the potential to be established as a stylized fact of stock market indices in general. While the memory process, implied by the power-law distribution of the laminar times, is not consistent with classical models for SOC, we note that a power-law distribution of the laminar times cannot be used to rule out self-organized critical behaviour.
The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

NASA Astrophysics Data System (ADS)

Garavaglia, Alessandro; van der Hofstad, Remco; Woeginger, Gerhard

2017-09-01

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.
THE STAR FORMATION HISTORY OF MASS-SELECTED GALAXIES IN THE COSMOS FIELD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karim, A.; Schinnerer, E.; Sargent, M. T.

2011-04-01

We explore the redshift evolution of the specific star formation rate (SSFR) for galaxies of different stellar mass by drawing on a deep 3.6 {mu}m selected sample of >10{sup 5} galaxies in the 2 deg{sup 2} COSMOS field. The average star formation rate (SFR) for subsets of these galaxies is estimated with stacked 1.4 GHz radio continuum emission. We separately consider the total sample and a subset of galaxies that shows evidence for substantive recent star formation in the rest-frame optical spectral energy distributions. At redshifts 0.2 < z < 3 both populations show a strong and mass-independent decrease inmore » their SSFR toward the present epoch. It is best described by a power law (1 + z) {sup n}, where n {approx} 4.3 for all galaxies and n {approx} 3.5 for star-forming (SF) sources. The decrease appears to have started at z>2, at least for high-mass (M{sub *} {approx}> 4 x 10{sup 10} M{sub sun}) systems where our conclusions are most robust. Our data show that there is a tight correlation with power-law dependence, SSFR {proportional_to} M{sub *} {sup {beta},} between SSFR and stellar mass at all epochs. The relation tends to flatten below M{sub *} {approx} 10{sup 10} M{sub sun} if quiescent galaxies are included; if they are excluded from the analysis a shallow index {beta}{sub SFG} {approx} -0.4 fits the correlation. On average, higher mass objects always have lower SSFRs, also among SF galaxies. At z>1.5 there is tentative evidence for an upper threshold in SSFR that an average galaxy cannot exceed, possibly due to gravitationally limited molecular gas accretion. It is suggested by a flattening of the SSFR-M{sub *} relation (also for SF sources), but affects massive (>10{sup 10} M{sub sun}) galaxies only at the highest redshifts. Since z = 1.5 there thus is no direct evidence that galaxies of higher mass experience a more rapid waning of their SSFR than lower mass SF systems. In this sense, the data rule out any strong 'downsizing' in the SSFR. We combine our results with recent measurements of the galaxy (stellar) mass function in order to determine the characteristic mass of an SF galaxy: we find that since z {approx} 3 the majority of all new stars were always formed in galaxies of M{sub *} = 10{sup 10.6{+-}0.4} M{sub sun}. In this sense, too, there is no 'downsizing'. Finally, our analysis constitutes the most extensive SFR density determination with a single technique out to z = 3. Recent Herschel results are consistent with our results, but rely on far smaller samples.« less
Development Status of a Power Processing Unit for Low Power Ion Thrusters

NASA Technical Reports Server (NTRS)

Pinero, Luis R.; Bowers, Glen E.; Lafontaine, Eric M.

2000-01-01

An advanced breadboard Power Processing Unit (PPU) for a low power ion propulsion system incorporating mass reduction techniques was designed and fabricated. As a result of similar output current requirements, the discharge supply was also used to provide the neutralizer heater and discharge heater functions by using three relays to switch the output connections. This multi-function supply reduces to four the number of power converters needed to produce the required six electrical outputs. Switching frequencies of 20 and 50 kHz were chosen as a compromise between the size of the magnetic components and switching losses. The advanced breadboard PPU is capable of a maximum total output power of 0.47 kW. Its component mass is 0.65 kg and its total mass 1.9 kg. The total efficiency at full power is 0.89.
Pair production rates in mildly relativistic, magnetized plasmas

NASA Technical Reports Server (NTRS)

Burns, M. L.; Harding, A. K.

1984-01-01

Electron-positron pairs may be produced by either one or two photons in the presence of a strong magnetic field. In magnetized plasmas with temperatures kT approximately sq mc, both of these processes may be important and could be competitive. The rates of one-photon and two-photon pair production by photons with Maxwellian, thermal bremsstrahlung, thermal synchrotron and power law spectra are calculated as a function of temperature or power law index and field strength. This allows a comparison of the two rates and a determination of the conditions under which each process may be a significant source of pairs in astrophysical plasmas. It is found that for photon densities n(gamma) or = 10 to the 25th power/cu cm and magnetic field strengths B or = 10 to the 12th power G, one-photon pair production dominates at kT approximately sq mc for a Maxwellian, at kT approximately 2 sq mc for a thermal bremsstrahlung spectrum, at all temperatures for a thermal synchrotron spectrum, and for power law spectra with indices s approximately 4.
Mapping power-law rheology of living cells using multi-frequency force modulation atomic force microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takahashi, Ryosuke; Okajima, Takaharu, E-mail: okajima@ist.hokudai.ac.jp

We present multi-frequency force modulation atomic force microscopy (AFM) for mapping the complex shear modulus G* of living cells as a function of frequency over the range of 50–500 Hz in the same measurement time as the single-frequency force modulation measurement. The AFM technique enables us to reconstruct image maps of rheological parameters, which exhibit a frequency-dependent power-law behavior with respect to G{sup *}. These quantitative rheological measurements reveal a large spatial variation in G* in this frequency range for single cells. Moreover, we find that the reconstructed images of the power-law rheological parameters are much different from those obtained inmore » force-curve or single-frequency force modulation measurements. This indicates that the former provide information about intracellular mechanical structures of the cells that are usually not resolved with the conventional force measurement methods.« less

Slow domain reconfiguration causes power-law kinetics in a two-state enzyme.

PubMed

Grossman-Haham, Iris; Rosenblum, Gabriel; Namani, Trishool; Hofmann, Hagen

2018-01-16

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.
The star-forming content of the W3 giant molecular cloud

NASA Astrophysics Data System (ADS)

Moore, T. J. T.; Bretherton, D. E.; Fujiyoshi, T.; Ridge, N. A.; Allsopp, J.; Hoare, M. G.; Lumsden, S. L.; Richer, J. S.

2007-08-01

We have surveyed a ˜0.9 square degree area of the W3 giant molecular cloud (GMC) and star-forming region in the 850-μm continuum, using the Submillimetre Common-User Bolometer Array on the James Clerk Maxwell Telescope. A complete sample of 316 dense clumps were detected with a mass range from around 13 to 2500 M⊙. Part of the W3 GMC is subject to an interaction with the H ii region and fast stellar winds generated by the nearby W4 OB association. We find that the fraction of total gas mass in dense, 850-μm traced structures is significantly altered by this interaction, being around 5-13 per cent in the undisturbed cloud but ˜25-37 per cent in the feedback-affected region. The mass distribution in the detected clump sample depends somewhat on assumptions of dust temperature and is not a simple, single power law but contains significant structure at intermediate masses. This structure is likely to be due to crowding of sources near or below the spatial resolution of the observations. There is little evidence of any difference between the index of the high-mass end of the clump mass function in the compressed region and in the unaffected cloud. The consequences of these results are discussed in terms of current models of triggered star formation.
Population is the main driver of war group size and conflict casualties.

PubMed

Oka, Rahul C; Kissel, Marc; Golitko, Mark; Sheridan, Susan Guise; Kim, Nam C; Fuentes, Agustín

2017-12-26

The proportions of individuals involved in intergroup coalitional conflict, measured by war group size (W), conflict casualties (C), and overall group conflict deaths (G), have declined with respect to growing populations, implying that states are less violent than small-scale societies. We argue that these trends are better explained by scaling laws shared by both past and contemporary societies regardless of social organization, where group population (P) directly determines W and indirectly determines C and G. W is shown to be a power law function of P with scaling exponent X [demographic conflict investment (DCI)]. C is shown to be a power law function of W with scaling exponent Y [conflict lethality (CL)]. G is shown to be a power law function of P with scaling exponent Z [group conflict mortality (GCM)]. Results show that, while W/P and G/P decrease as expected with increasing P, C/W increases with growing W. Small-scale societies show higher but more variance in DCI and CL than contemporary states. We find no significant differences in DCI or CL between small-scale societies and contemporary states undergoing drafts or conflict, after accounting for variance and scale. We calculate relative measures of DCI and CL applicable to all societies that can be tracked over time for one or multiple actors. In light of the recent global emergence of populist, nationalist, and sectarian violence, our comparison-focused approach to DCI and CL will enable better models and analysis of the landscapes of violence in the 21st century. Copyright © 2017 the Author(s). Published by PNAS.
Population is the main driver of war group size and conflict casualties

PubMed Central

Oka, Rahul C.; Kissel, Marc; Golitko, Mark; Sheridan, Susan Guise; Kim, Nam C.; Fuentes, Agustín

2017-01-01

The proportions of individuals involved in intergroup coalitional conflict, measured by war group size (W), conflict casualties (C), and overall group conflict deaths (G), have declined with respect to growing populations, implying that states are less violent than small-scale societies. We argue that these trends are better explained by scaling laws shared by both past and contemporary societies regardless of social organization, where group population (P) directly determines W and indirectly determines C and G. W is shown to be a power law function of P with scaling exponent X [demographic conflict investment (DCI)]. C is shown to be a power law function of W with scaling exponent Y [conflict lethality (CL)]. G is shown to be a power law function of P with scaling exponent Z [group conflict mortality (GCM)]. Results show that, while W/P and G/P decrease as expected with increasing P, C/W increases with growing W. Small-scale societies show higher but more variance in DCI and CL than contemporary states. We find no significant differences in DCI or CL between small-scale societies and contemporary states undergoing drafts or conflict, after accounting for variance and scale. We calculate relative measures of DCI and CL applicable to all societies that can be tracked over time for one or multiple actors. In light of the recent global emergence of populist, nationalist, and sectarian violence, our comparison-focused approach to DCI and CL will enable better models and analysis of the landscapes of violence in the 21st century. PMID:29229847
Ultrashort-Pulse Child-Langmuir Law in the Quantum and Relativistic Regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ang, L. K.; Zhang, P.

This Letter presents a consistent quantum and relativistic model of short-pulse Child-Langmuir (CL) law, of which the pulse length {tau} is less than the electron transit time in a gap of spacing D and voltage V. The classical value of the short-pulse CL law is enhanced by a large factor due to quantum effects when the pulse length and the size of the beam are, respectively, in femtosecond duration and nanometer scale. At high voltage larger than the electron rest mass, relativistic effects will suppress the enhancement of short-pulse CL law, which is confirmed by particle-in-cell simulation. When the pulsemore » length is much shorter than the gap transit time, the current density is proportional to V, and to the inverse power of D and {tau}.« less
RESOLVE and ECO: The Halo Mass-dependent Shape of Galaxy Stellar and Baryonic Mass Functions

NASA Astrophysics Data System (ADS)

Eckert, Kathleen D.; Kannappan, Sheila J.; Stark, David V.; Moffett, Amanda J.; Berlind, Andreas A.; Norris, Mark A.

2016-06-01

In this work, we present galaxy stellar and baryonic (stars plus cold gas) mass functions (SMF and BMF) and their halo mass dependence for two volume-limited data sets. The first, RESOLVE-B, coincides with the Stripe 82 footprint and is extremely complete down to baryonic mass M bary ˜ 109.1 M ⊙, probing the gas-rich dwarf regime below M bary ˜ 1010 M ⊙. The second, ECO, covers a ˜40× larger volume (containing RESOLVE-A) and is complete to M bary ˜ 109.4 M ⊙. To construct the SMF and BMF we implement a new “cross-bin sampling” technique with Monte Carlo sampling from the full likelihood distributions of stellar or baryonic mass. Our SMFs exhibit the “plateau” feature starting below M star ˜ 1010 M ⊙ that has been described in prior work. However, the BMF fills in this feature and rises as a straight power law below ˜1010 M ⊙, as gas-dominated galaxies become the majority of the population. Nonetheless, the low-mass slope of the BMF is not as steep as that of the theoretical dark matter halo MF. Moreover, we assign group halo masses by abundance matching, finding that the SMF and BMF, separated into four physically motivated halo mass regimes, reveal complex structure underlying the simple shape of the overall MFs. In particular, the satellite MFs are depressed below the central galaxy MF “humps” in groups with mass <1013.5 M ⊙ yet rise steeply in clusters. Our results suggest that satellite destruction and stripping are active from the point of nascent group formation. We show that the key role of groups in shaping MFs enables reconstruction of a given survey’s SMF or BMF based on its group halo mass distribution.
RESOLVE AND ECO: THE HALO MASS-DEPENDENT SHAPE OF GALAXY STELLAR AND BARYONIC MASS FUNCTIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eckert, Kathleen D.; Kannappan, Sheila J.; Stark, David V.

2016-06-20

In this work, we present galaxy stellar and baryonic (stars plus cold gas) mass functions (SMF and BMF) and their halo mass dependence for two volume-limited data sets. The first, RESOLVE-B, coincides with the Stripe 82 footprint and is extremely complete down to baryonic mass M {sub bary} ∼ 10{sup 9.1} M {sub ⊙}, probing the gas-rich dwarf regime below M {sub bary} ∼ 10{sup 10} M {sub ⊙}. The second, ECO, covers a ∼40× larger volume (containing RESOLVE-A) and is complete to M {sub bary} ∼ 10{sup 9.4} M {sub ⊙}. To construct the SMF and BMF we implementmore » a new “cross-bin sampling” technique with Monte Carlo sampling from the full likelihood distributions of stellar or baryonic mass. Our SMFs exhibit the “plateau” feature starting below M {sub star} ∼ 10{sup 10} M {sub ⊙} that has been described in prior work. However, the BMF fills in this feature and rises as a straight power law below ∼10{sup 10} M {sub ⊙}, as gas-dominated galaxies become the majority of the population. Nonetheless, the low-mass slope of the BMF is not as steep as that of the theoretical dark matter halo MF. Moreover, we assign group halo masses by abundance matching, finding that the SMF and BMF, separated into four physically motivated halo mass regimes, reveal complex structure underlying the simple shape of the overall MFs. In particular, the satellite MFs are depressed below the central galaxy MF “humps” in groups with mass <10{sup 13.5} M {sub ⊙} yet rise steeply in clusters. Our results suggest that satellite destruction and stripping are active from the point of nascent group formation. We show that the key role of groups in shaping MFs enables reconstruction of a given survey’s SMF or BMF based on its group halo mass distribution.« less
BINARY FORMATION MECHANISMS: CONSTRAINTS FROM THE COMPANION MASS RATIO DISTRIBUTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reggiani, Maddalena M.; Meyer, Michael R., E-mail: reggiani@phys.ethz.ch

2011-09-01

We present a statistical comparison of the mass ratio distribution of companions, as observed in different multiplicity surveys, to the most recent estimate of the single-object mass function. The main goal of our analysis is to test whether or not the observed companion mass ratio distribution (CMRD) as a function of primary star mass and star formation environment is consistent with having been drawn from the field star initial mass function (IMF). We consider samples of companions for M dwarfs, solar-type stars, and intermediate-mass stars, both in the field as well as clusters or associations, and compare them with populationsmore » of binaries generated by random pairing from the assumed IMF for a fixed primary mass. With regard to the field we can reject the hypothesis that the CMRD was drawn from the IMF for different primary mass ranges: the observed CMRDs show a larger number of equal-mass systems than predicted by the IMF. This is in agreement with fragmentation theories of binary formation. For the open clusters {alpha} Persei and the Pleiades we also reject the IMF random-pairing hypothesis. Concerning young star-forming regions, currently we can rule out a connection between the CMRD and the field IMF in Taurus but not in Chamaeleon I. Larger and different samples are needed to better constrain the result as a function of the environment. We also consider other companion mass functions and we compare them with observations. Moreover the CMRD both in the field and clusters or associations appears to be independent of separation in the range covered by the observations. Combining therefore the CMRDs of M (1-2400 AU) and G (28-1590 AU) primaries in the field and intermediate-mass primary binaries in Sco OB2 (29-1612 AU) for mass ratios, q = M{sub 2}/M{sub 1}, from 0.2 to 1, we find that the best chi-square fit follows a power law dN/dq{proportional_to}q {sup {beta}}, with {beta} = -0.50 {+-} 0.29, consistent with previous results. Finally, we note that the Kolmogorov-Smirnov test gives a {approx}1% probability of the observed CMRD in the Pleiades and Taurus being consistent with that observed for solar-type primaries in the field over comparable primary mass range. This highlights the value of using CMRDs to understand which star formation events contribute most to the field.« less
Weighted Flow Algorithms (WFA) for stochastic particle coagulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

DeVille, R.E.L., E-mail: rdeville@illinois.edu; Riemer, N., E-mail: nriemer@illinois.edu; West, M., E-mail: mwest@illinois.edu

2011-09-20

Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to the recently-developed particle-resolved model PartMC-MOSAIC and present the mathematical formalism of these Weighted Flow Algorithms (WFA) for particle coagulation and growth. We apply this to an urban plume scenario that simulates a particle population undergoing emission of different particle types, dilution, coagulation and aerosol chemistry along a Lagrangianmore » trajectory. We quantify the performance of the Weighted Flow Algorithm for number and mass-based quantities of relevance for atmospheric sciences applications.« less
Yields of projectile fragments in sulphur-emulsion interactions at 3.7 A GeV

NASA Astrophysics Data System (ADS)

Kamel, S.; Osman, W.; Fayed, M.

2017-05-01

This work presents the basic characteristics of singly, doubly and heavily charged projectile fragments (PFs) emitted in inelastic interactions of 32S ions with photo-emulsion nuclei at Dubna energy (3.7 A GeV). Our experimental data are compared with the corresponding data for other projectiles at the same incident energy. The study of mean multiplicities of different charged PFs against the projectile mass shows a power-law relationship. The multiplicity distributions of singly and doubly charged PFs have been fitted well with a Gaussian distribution function. The yields of PFs broken up from the interactions of 32S projectile nuclei with different target nuclei are studied. The beam energy dependence in terms of the various order moments is studied as well.
Weighted Flow Algorithms (WFA) for stochastic particle coagulation

NASA Astrophysics Data System (ADS)

DeVille, R. E. L.; Riemer, N.; West, M.

2011-09-01

Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to the recently-developed particle-resolved model PartMC-MOSAIC and present the mathematical formalism of these Weighted Flow Algorithms (WFA) for particle coagulation and growth. We apply this to an urban plume scenario that simulates a particle population undergoing emission of different particle types, dilution, coagulation and aerosol chemistry along a Lagrangian trajectory. We quantify the performance of the Weighted Flow Algorithm for number and mass-based quantities of relevance for atmospheric sciences applications.
Statistical characteristics of dynamics for population migration driven by the economic interests

NASA Astrophysics Data System (ADS)

Huo, Jie; Wang, Xu-Ming; Zhao, Ning; Hao, Rui

2016-06-01

Population migration typically occurs under some constraints, which can deeply affect the structure of a society and some other related aspects. Therefore, it is critical to investigate the characteristics of population migration. Data from the China Statistical Yearbook indicate that the regional gross domestic product per capita relates to the population size via a linear or power-law relation. In addition, the distribution of population migration sizes or relative migration strength introduced here is dominated by a shifted power-law relation. To reveal the mechanism that creates the aforementioned distributions, a dynamic model is proposed based on the population migration rule that migration is facilitated by higher financial gains and abated by fewer employment opportunities at the destination, considering the migration cost as a function of the migration distance. The calculated results indicate that the distribution of the relative migration strength is governed by a shifted power-law relation, and that the distribution of migration distances is dominated by a truncated power-law relation. These results suggest the use of a power-law to fit a distribution may be not always suitable. Additionally, from the modeling framework, one can infer that it is the randomness and determinacy that jointly create the scaling characteristics of the distributions. The calculation also demonstrates that the network formed by active nodes, representing the immigration and emigration regions, usually evolves from an ordered state with a non-uniform structure to a disordered state with a uniform structure, which is evidenced by the increasing structural entropy.
Star formation in the outskirts of DDO 154: a top-light IMF in a nearly dormant disc

NASA Astrophysics Data System (ADS)

Watts, Adam B.; Meurer, Gerhardt R.; Lagos, Claudia D. P.; Bruzzese, Sarah M.; Kroupa, Pavel; Jerabkova, Tereza

2018-07-01

We present optical photometry of Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS)/Wide Field Camera (WFC) data of the resolved stellar populations in the outer disc of the dwarf irregular galaxy DDO 154. The photometry reveals that young main sequence (MS) stars are almost absent from the outermost H I disc. Instead, most are clustered near the main stellar component of the galaxy. We constrain the stellar initial mass function (IMF) by comparing the luminosity function of the MS stars to simulated stellar populations, assuming a constant star formation rate over the dynamical time-scale. The best-fitting IMF is deficient in high-mass stars compared to a canonical Kroupa IMF, with a best-fitting slope α = -2.45 and upper mass limit MU = 16 M⊙. This top-light IMF is consistent with predictions of the integrated galactic IMF theory. Combining the HST images with H I data from The H I Nearby Galaxy Survey (THINGS), we determine the star formation law (SFL) in the outer disc. The fit has a power-law exponent N = 2.92 ± 0.22 and zero-point A = 4.47 ± 0.65 × 10-7 M⊙ yr-1 kpc-2. This is depressed compared to the Kennicutt-Schmidt SFL, but consistent with weak star formation observed in diffuse H I environments. Extrapolating the SFL over the outer disc implies that there could be significant star formation occurring that is not detectable in H α. Last, we determine the Toomre stability parameter Q of the outer disc of DDO 154 using the THINGS H I rotation curve and velocity dispersion map. 72 per cent of the H I in our field has Q ≤ 4 and this incorporates 96 per cent of the observed MS stars. Hence, 28 per cent of the H I in the field is largely dormant.
Hot Molecular Gas in the Circumnuclear Disk

NASA Astrophysics Data System (ADS)

Mills, Elisabeth A. C.; Togi, Aditya; Kaufman, Michael

2017-12-01

We present an analysis of archival Infrared Space Observatory observations of H2 for three 14\\prime\\prime × 20\\prime\\prime pointings in the central 3 pc of the Galaxy: toward the southwest region and northeast region of the Galactic center circumnuclear disk (CND), and toward the supermassive black hole Sgr A*. We detect pure rotational lines from 0-0 S(0) to S(13), as well as a number of rovibrationally excited transitions. Using the pure rotational lines, we perform both fits to a discrete temperature distribution (measuring up to three temperature components with T = 500-600 K, T = 1250-1350 K, and T > 2600 K) and fits to a continuous temperature distribution, assuming a power-law distribution of temperatures. We measure power-law indices of n = 3.22 for the northeast region and n = 2.83 for the southwest region. These indices are lower than those measured for other galaxies or other Galactic center clouds, indicating a larger fraction of gas at high temperatures. We also test whether extrapolating this temperature distribution can yield a reasonable estimate of the total molecular mass, as has been recently done for H2 observations in other galaxies. Extrapolating to a cutoff temperature of 50 K in the southwest (northeast) region, we would measure 32% (140%) of the total molecular gas mass inferred from the dust emission, and 26% (125%) of the total molecular gas mass inferred from the CO emission. Ultimately, the inconsistency of the masses inferred in this way suggests that a simple application of this method cannot yield a reliable estimate of the mass of the CND.
TWELVE AND A HALF YEARS OF OBSERVATIONS OF CENTAURUS A WITH THE ROSSI X-RAY TIMING EXPLORER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rothschild, R. E.; Markowitz, A.; Rivers, E.

2011-05-20

The Rossi X-ray Timing Explorer (RXTE) has observed the nearest radio galaxy, Centaurus A (Cen A), in 13 intervals from 1996 August to 2009 February over the 3-200 keV band. Spectra accumulated over the 13 intervals were well described with an absorbed power law and an iron line. Cutoff power laws and Compton reflection from cold matter did not provide a better description. For the 2009 January observation, we set a lower limit on the cutoff energy at over 2 MeV. The power spectral density function was generated from RXTE/All Sky Monitor and Proportional Counter Array data as well asmore » an XMM-Newton long look, and clear evidence for a break at 18{sup +18}{sub -7} days (68% conf.) was seen. Given Cen A's high black hole mass and very low value of L{sub X}/L{sub Edd}, the break was a factor of 17{sup +36}{sub -13} times higher than the break frequency predicted by the McHardy et al. relation, which was empirically derived for a sample of objects, which are radio-quiet and accreting at relatively high values of L{sub bol}/L{sub Edd}. We have interpreted our observations in the context of a clumpy molecular torus. The variability characteristics and the broadband spectral energy distribution, when compared to Seyferts, imply that the bright hard X-ray continuum emission may originate at the base of the jet, yet from behind the absorbing line-of-sight material, in contrast to what is commonly observed from blazars.« less
Public Health Law Reform

PubMed Central

Gostin, Lawrence O.

2001-01-01

Public health law reform is necessary because existing statutes are outdated, contain multiple layers of regulation, and are inconsistent. A model law would define the mission and functions of public health agencies, provide a full range of flexible powers, specify clear criteria and procedures for activities, and provide protections for privacy and against discrimination. The law reform process provides an opportunity for public health agencies to draw attention to their resource needs and achievements and to form ties with constituency groups and enduring relations with the legislative branch of government. Ultimately, the law should become a catalyst, rather than an impediment, to reinvigorating the public health system. PMID:11527757
Public health law reform.

PubMed

Gostin, L O

2001-09-01

Public health law reform is necessary because existing statutes are outdated, contain multiple layers of regulation, and are inconsistent. A model law would define the mission and functions of public health agen cies, provide a full range of flexible powers, specify clear criteria and procedures for activities, and provide protections for privacy and against discrimination. The law reform process provides an opportunity for public health agencies to draw attention to their resource needs and achievements and to form ties with constituency groups and enduring relations with the legislative branch of government. Ultimately, the law should become a catalyst, rather than an impediment, to reinvigorating the public health system.
Weak lensing mass map and peak statistics in Canada-France-Hawaii Telescope Stripe 82 survey

NASA Astrophysics Data System (ADS)

Shan, Huan Yuan; Kneib, Jean-Paul; Comparat, Johan; Jullo, Eric; Charbonnier, Aldée; Erben, Thomas; Makler, Martin; Moraes, Bruno; Van Waerbeke, Ludovic; Courbin, Frédéric; Meylan, Georges; Tao, Charling; Taylor, James E.

2014-08-01

We present a weak lensing mass map covering ˜124 deg2 of the Canada-France-Hawaii Telescope Stripe 82 Survey (CS82). We study the statistics of rare peaks in the map, including peak abundance, the peak-peak correlation functions and the tangential-shear profiles around peaks. We find that the abundance of peaks detected in CS82 is consistent with predictions from a Λ cold dark matter cosmological model, once noise effects are properly included. The correlation functions of peaks with different signal-to-noise ratio (SNR) are well described by power laws, and there is a clear cross-correlation between the Sloan Digital Sky Survey III/Constant Mass galaxies and high SNR peaks. The tangential-shear profiles around peaks increase with peak SNR. We fit analytical models to the tangential-shear profiles, including a projected singular isothermal sphere (SIS) model and a projected Navarro, Frenk & White (NFW) model, plus a two-halo term. For the high SNR peaks, the SIS model is rejected at ˜3σ. The NFW model plus a two-halo term gives more acceptable fits to the data. Some peaks match the positions of optically detected clusters, while others are relatively dark. Comparing dark and matched peaks, we find a difference in lensing signal of a factor of 2, suggesting that about half of the dark peaks are false detections.
Neural representations of kinematic laws of motion: evidence for action-perception coupling.

PubMed

Dayan, Eran; Casile, Antonino; Levit-Binnun, Nava; Giese, Martin A; Hendler, Talma; Flash, Tamar

2007-12-18

Behavioral and modeling studies have established that curved and drawing human hand movements obey the 2/3 power law, which dictates a strong coupling between movement curvature and velocity. Human motion perception seems to reflect this constraint. The functional MRI study reported here demonstrates that the brain's response to this law of motion is much stronger and more widespread than to other types of motion. Compliance with this law is reflected in the activation of a large network of brain areas subserving motor production, visual motion processing, and action observation functions. Hence, these results strongly support the notion of similar neural coding for motion perception and production. These findings suggest that cortical motion representations are optimally tuned to the kinematic and geometrical invariants characterizing biological actions.
Engines with ideal efficiency and nonzero power for sublinear transport laws

NASA Astrophysics Data System (ADS)

Koning, Jesper; Indekeu, Joseph O.

2016-11-01

It is known that an engine with ideal efficiency (η = 1 for a chemical engine and e = eCarnot for a thermal one) has zero power because a reversible cycle takes an infinite time. However, at least from a theoretical point of view, it is possible to conceive (irreversible) engines with nonzero power that can reach ideal efficiency. Here this is achieved by replacing the usual linear transport law by a sublinear one and taking the step-function limit for the particle current (chemical engine) or heat current (thermal engine) versus the applied force. It is shown that in taking this limit exact thermodynamic inequalities relating the currents to the entropy production are not violated.

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