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.

The Atacama Cosmology Telescope: A Measurement of the Primordial Power Spectrum

NASA Technical Reports Server (NTRS)

Hlozek, Renee; Dunkley, Joanna; Addison, Graeme; Appel, John William; Bond, J. Richard; Carvalho, C. Sofia; Das, Sudeep; Devlin, Mark J.; Duenner, Rolando; Essinger-Hileman, Thomas;

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:

Evidence for a Hard Ionizing Spectrum from a z = 6.11 Stellar Population

NASA Astrophysics Data System (ADS)

Mainali, Ramesh; Kollmeier, Juna A.; Stark, Daniel P.; Simcoe, Robert A.; Walth, Gregory; Newman, Andrew B.; Miller, Daniel R.

2017-02-01

We present the Magellan/FIRE detection of highly ionized C IV λ1550 and O III]λ1666 in a deep infrared spectrum of the z = 6.11 gravitationally lensed low-mass galaxy RXC J2248.7-4431-ID3, which has previously known Lyα. No corresponding emission is detected at the expected location of He II λ1640. The upper limit on He II, paired with detection of O III] and C IV, constrains possible ionization scenarios. Production of C IV and O III] requires ionizing photons of 2.5-3.5 Ryd, but once in that state their multiplet emission is powered by collisional excitation at lower energies (˜0.5 Ryd). As a pure recombination line, He II emission is powered by 4 Ryd ionizing photons. The data therefore require a spectrum with significant power at 3.5 Ryd but a rapid drop toward 4.0 Ryd. This hard spectrum with a steep drop is characteristic of low-metallicity stellar populations, and less consistent with soft AGN excitation, which features more 4 Ryd photons and hence higher He II flux. The conclusions based on ratios of metal line detections to helium non-detection are strengthened if the gas metallicity is low. RXJ2248-ID3 adds to the growing handful of reionization-era galaxies with UV emission line ratios distinct from the general z=2{--}3 population in a way that suggests hard ionizing spectra that do not necessarily originate in AGNs.

Power-Law Statistics of Driven Reconnection in the Magnetically Closed Corona

NASA Technical Reports Server (NTRS)

Klimchuk, J. A.; DeVore, C. R.; Knizhnik, K. J.; Uritskiy, V. M.

2018-01-01

Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere.

Signatures of Synchrotron: Low-cutoff X-ray emission and the hard X-ray spectrum of Cas A

NASA Astrophysics Data System (ADS)

Stage, Michael D.; Fedor, Emily Elizabeth; Martina-Hood, Hyourin

2018-06-01

In soft X-rays, bright, young Galactic remnants (Cas A, Kepler, Tycho, etc.) present thermal line emission and bremsstrahlung from ejecta, and synchrotron radiation from the shocks. Their hard X-ray spectra tend to be dominated by power-law sources. However, it can be non-trivial to discriminate between contributions from processes such as synchrotron and bremsstrahlung from nonthermally accelerated electrons, even though the energies of the electrons producing this radiation may be very different. Spatially-resolved spectroscopic analysis of 0.5-10 keV observations with, e.g., Chandracan provide leverage in identifying the processes and their locations. Previously, Stage & Allen (2006), Allen & Stage (2007) and Stage & Allen (2011) identified regions characterized by high-cutoff synchrotron radiation. Extrapolating synchrotron model fits to the emission in the Chandra band, they estimated the synchrotron contribution to the hard X-ray spectrum at about one-third the observed flux, fitting the balance with nonthermal bremsstrahlung emission produced by nonthermal electrons in the ejecta. Although it is unlikely this analysis missed regions of the highest-cutoff synchrotron emission, which supplies the bulk of the synchrotron above 15 keV, it may have missed regions of lower-cutoff emission, especially if they are near bright ejecta and the reverse shock. These regions cannot explain the emission at the highest energies (~50 keV), but may make significant contributions to the hard spectrum at lower energies (~10 keV). Using the technique described in Fedor, Martina-Hood & Stage (this meeting), we revisit the analysis to include regions that may be dominated by low-cutoff synchrotron, located in the interior of the remnant, and/or correlated with the reverse shock. Identifying X-ray emission from accelerated electrons associated with the reverse-shock would have important implications for synchrotron and non-thermal bremsstrahlung radiation above the 10 keV.

Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states

NASA Astrophysics Data System (ADS)

Dinani, Hossein T.; Berry, Dominic W.

2017-06-01

When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum 1 /|ω| p with p >1 , then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of 1 /N(p -1 )/p and 1 /N2 (p -1 )/(p +1 ) , respectively, where N is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of p =2 .

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.

The hard X-ray spectrum of NGC 5506 as seen by NuSTAR

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

Matt, G.; Balokovi , M.; Marinucci, A.

2015-01-14

NuSTAR observed the bright Compton-thin, narrow-line Seyfert 1 galaxy, NGC 5506, for about 56 ks. In agreement with past observations, the spectrum is well fitted by a power law with Γ ~ 1.9, a distant reflection component and narrow ionized iron lines. A relativistically blurred reflection component is not required by the data. When an exponential high-energy cutoff is added to the power law, a value of 720more » $$+130\\atop{-190}$$ keV (90 percent confidence level) is found. Even allowing for systematic uncertainties, we find a 3σ lower limit to the high-energy cutoff of 350 keV, the highest lower limit to the cutoff energy found so far in an AGN by NuSTAR.« less

Models of the hard X-ray spectrum of AM Herculis and implications for the accretion rate

NASA Technical Reports Server (NTRS)

Swank, J. H.; Fabian, A. C.; Ross, R. R.

1983-01-01

Phenomenological fits to the hard X-ray spectrum of AM Herculis left unexplained the high equivalent width (0.8 + or - 0.1 keV) of Fe K alpha emission. A purely thermal origin implies a much steeper spectrum than was observed. With Monte Carlo calculations, scattering and fluorescent line production in a cold or partially ionized accretion column of hard X-rays emitted at the base were investigated. The strength of the iron emission and the flat spectral continuum can be explained by the effects of fluorescence and absorption within the accretion column and the surface of the white dwarf on a thermal X-ray spectrum. Thomson optical depths across the column in the range 0.2 to 0.7 are acceptable. The accretion rate and gravitational power can be deduced from the optical depth across the column, if the column size is known, and, together with the observed hard X-ray and polarized light luminosities, imply a lower limit for the luminosity in the UV to soft X-ray range, for which the observations give model-dependent values. Estimates of the column size differ by a factor of 40. Small spot sizes and low luminosities would be consistent with the soft component being the expected reprocessed bremsstrahlung and cyclotron radiation, although the constraint of matching the spectrum confines one to solutions with fluxes exceeding 20% the Eddington limits.

On the origin of power-law X-ray spectra of active galactic nuclei

NASA Technical Reports Server (NTRS)

Schlosman, I.; Shaham, J.; Shaviv, G.

1984-01-01

In the present analytical model for a power law X-ray continuum production in active galactic nuclei, the dissipation of turbulent energy flux above the accretion disk forms an optically thin transition layer with an inverted temperature gradient. The emitted thermal radiation has a power law spectrum in the 0.1-100 keV range, with a photon energy spectral index gamma of about 0.4-1.0. Thermal X-ray contribution from the layer is 5-10 percent of the total disk luminosity. The gamma value of 0.75 is suggested as a 'natural' power law index for Seyfert galaxies and QSOs.

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.

Primordial power spectrum: a complete analysis with the WMAP nine-year data

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

Hazra, Dhiraj Kumar; Shafieloo, Arman; Souradeep, Tarun, E-mail: dhiraj@apctp.org, E-mail: arman@apctp.org, E-mail: tarun@iucaa.ernet.in

2013-07-01

We have improved further the error sensitive Richardson-Lucy deconvolution algorithm making it applicable directly on the un-binned measured angular power spectrum of Cosmic Microwave Background observations to reconstruct the form of the primordial power spectrum. This improvement makes the application of the method significantly more straight forward by removing some intermediate stages of analysis allowing a reconstruction of the primordial spectrum with higher efficiency and precision and with lower computational expenses. Applying the modified algorithm we fit the WMAP 9 year data using the optimized reconstructed form of the primordial spectrum with more than 300 improvement in χ{sup 2}{sub eff}more » with respect to the best fit power-law. This is clearly beyond the reach of other alternative approaches and reflects the efficiency of the proposed method in the reconstruction process and allow us to look for any possible feature in the primordial spectrum projected in the CMB data. Though the proposed method allow us to look at various possibilities for the form of the primordial spectrum, all having good fit to the data, proper error-analysis is needed to test for consistency of theoretical models since, along with possible physical artefacts, most of the features in the reconstructed spectrum might be arising from fitting noises in the CMB data. Reconstructed error-band for the form of the primordial spectrum using many realizations of the data, all bootstrapped and based on WMAP 9 year data, shows proper consistency of power-law form of the primordial spectrum with the WMAP 9 data at all wave numbers. Including WMAP polarization data in to the analysis have not improved much our results due to its low quality but we expect Planck data will allow us to make a full analysis on CMB observations on both temperature and polarization separately and in combination.« less

Power law cosmology model comparison with CMB scale information

NASA Astrophysics Data System (ADS)

Tutusaus, Isaac; Lamine, Brahim; Blanchard, Alain; Dupays, Arnaud; Zolnierowski, Yves; Cohen-Tanugi, Johann; Ealet, Anne; Escoffier, Stéphanie; Le Fèvre, Olivier; Ilić, Stéphane; Pisani, Alice; Plaszczynski, Stéphane; Sakr, Ziad; Salvatelli, Valentina; Schücker, Thomas; Tilquin, André; Virey, Jean-Marc

2016-11-01

Despite the ability of the cosmological concordance model (Λ CDM ) to describe the cosmological observations exceedingly well, power law expansion of the Universe scale radius, R (t )∝tn, has been proposed as an alternative framework. We examine here these models, analyzing their ability to fit cosmological data using robust model comparison criteria. Type Ia supernovae (SNIa), baryonic acoustic oscillations (BAO) and acoustic scale information from the cosmic microwave background (CMB) have been used. We find that SNIa data either alone or combined with BAO can be well reproduced by both Λ CDM and power law expansion models with n ˜1.5 , while the constant expansion rate model (n =1 ) is clearly disfavored. Allowing for some redshift evolution in the SNIa luminosity essentially removes any clear preference for a specific model. The CMB data are well known to provide the most stringent constraints on standard cosmological models, in particular, through the position of the first peak of the temperature angular power spectrum, corresponding to the sound horizon at recombination, a scale physically related to the BAO scale. Models with n ≥1 lead to a divergence of the sound horizon and do not naturally provide the relevant scales for the BAO and the CMB. We retain an empirical footing to overcome this issue: we let the data choose the preferred values for these scales, while we recompute the ionization history in power law models, to obtain the distance to the CMB. In doing so, we find that the scale coming from the BAO data is not consistent with the observed position of the first peak of the CMB temperature angular power spectrum for any power law cosmology. Therefore, we conclude that when the three standard probes (SNIa, BAO, and CMB) are combined, the Λ CDM model is very strongly favored over any of these alternative models, which are then essentially ruled out.

SHOCKS Impulse-Jerk(I-J) Plasticity/Fracture Burst Acoustic-Emission(BAE) NON:``1''/ ω -``Noise'' Power-Law; Universality Power-Spectrum is I-J Time-Series Fourier-Transform: 1687 < < < 1988: VERY-LONG PRE-``Bak''!!!

NASA Astrophysics Data System (ADS)

Chavira, Aldo; Gregson, Victor, Jr.; Green, Sidney; Siegel, Edward

2011-06-01

SHOCKS impulse-jerk(I-J) [apply strain/impulse to get stress/jerk ],{VS. NON-shocks[apply stress to get strain]}, 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 A.-E. Symp. (76);Acta Met.25,383(77); JMMM 7, 312(78)] NON: ``1''/ ω -``Noise'' Zipf(NON-Pareto); power-law ; universality power-spectrum is manifestly-demonstrated in ONLY ``PURE''-MATHS way to be nothing but d[F(t)=m(t)a(t)=Newton's (3rd) Law of Motion=(I-J)]/dt I-Jderivative d(I-J)/dt=dF(t)/dt=[m(t)da(t)/dt+a(t)dm(t)/dt] REdiscovery!!! A/Siegel NON-shock PHYSICS derivation fails!!!; ''PURE''-MATHS: dF(t)/dt=d2p(t)/dt2=[m(t)da(t)/dt+a(t)dm(t)/dt] TRIPLE-integral [VS. NON -shocks F = ma time-series DOUBLE-integral] Dichotomy: s(t) = [v0+(1/2)a(t)t2+EXTRA-TERM(S)], {VS. s(t) = [v0t+(1/2) at2]}, integral-transform formally defines power-spectrum Dichotomy:

Contribution of strong discontinuities to the power spectrum of the solar wind.

PubMed

Borovsky, Joseph E

2010-09-10

Eight and a half years of magnetic field measurements (2(22) samples) from the ACE spacecraft in the solar wind at 1 A.U. are analyzed. Strong (large-rotation-angle) discontinuities in the solar wind are collected and measured. An artificial time series is created that preserves the timing and amplitudes of the discontinuities. The power spectral density of the discontinuity series is calculated and compared with the power spectral density of the solar-wind magnetic field. The strong discontinuities produce a power-law spectrum in the "inertial subrange" with a spectral index near the Kolmogorov -5/3 index. The discontinuity spectrum contains about half of the power of the full solar-wind magnetic field over this "inertial subrange." Warnings are issued about the significant contribution of discontinuities to the spectrum of the solar wind, complicating interpretation of spectral power and spectral indices.

Hard X-ray spectrum of Cygnus X-1

NASA Technical Reports Server (NTRS)

Nolan, P. L.; Gruber, D. E.; Knight, F. K.; Matteson, J. L.; Rothschild, R. E.; Marshall, F. E.; Levine, A. M.; Primini, F. A.

1981-01-01

Long-term measurements of the hard X-ray spectrum from 3 keV to 8 MeV of the black-hole candidate Cygnus X-1 in its low state are reported. Observations were made from October 26 to November 18, 1977 with the A2 (Cosmic X-ray) and A4 (Hard X-ray and Low-Energy Gamma-Ray) experiments on board HEAO 1 in the spacecraft's scanning mode. The measured spectrum below 200 keV is found to agree well with previous spectra which have been fit by a model of the Compton scattering of optical or UV photons in a very hot plasma of electron temperature 32.4 keV and optical depth 3.9 or 1.6 for spherical or disk geometry, respectively. At energies above 300 keV, however, flux excess is observed which may be accounted for by a distribution of electron temperatures from 15 to about 100 keV.

Variability of the Magnetic Field Power Spectrum in the Solar Wind at Electron Scales

NASA Astrophysics Data System (ADS)

Roberts, Owen Wyn; Alexandrova, O.; Kajdič, P.; Turc, L.; Perrone, D.; Escoubet, C. P.; Walsh, A.

2017-12-01

At electron scales, the power spectrum of solar-wind magnetic fluctuations can be highly variable and the dissipation mechanisms of the magnetic energy into the various particle species is under debate. In this paper, we investigate data from the Cluster mission’s STAFF Search Coil magnetometer when the level of turbulence is sufficiently high that the morphology of the power spectrum at electron scales can be investigated. The Cluster spacecraft sample a disturbed interval of plasma where two streams of solar wind interact. Meanwhile, several discontinuities (coherent structures) are seen in the large-scale magnetic field, while at small scales several intermittent bursts of wave activity (whistler waves) are present. Several different morphologies of the power spectrum can be identified: (1) two power laws separated by a break, (2) an exponential cutoff near the Taylor shifted electron scales, and (3) strong spectral knees at the Taylor shifted electron scales. These different morphologies are investigated by using wavelet coherence, showing that, in this interval, a clear break and strong spectral knees are features that are associated with sporadic quasi parallel propagating whistler waves, even for short times. On the other hand, when no signatures of whistler waves at ∼ 0.1{--}0.2{f}{ce} are present, a clear break is difficult to find and the spectrum is often more characteristic of a power law with an exponential cutoff.

Diffusion with stochastic resetting at power-law times.

PubMed

Nagar, Apoorva; Gupta, Shamik

2016-06-01

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α<1, to one that is time independent for α>1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.

Power-law X-ray and gamma-ray emission from relativistic thermal plasmas

NASA Technical Reports Server (NTRS)

Zdziarski, A. A.

1985-01-01

A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.

NON-Shock-Plasticity/Fracture Burst Acoustic-Emission(BAE) ``1''/f -``Noise'' Power-Spectrum(PS) 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

2015-06-01

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. 5,383(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 3rd Law of Motion F = ma REdiscovery!!! (aka ``Bak''(1988)-``SOC'':1687 <<<1988: 1988-1687 =301-years!!! PHYSICS:F =ma cross-multiplied as 1/m =a/F =OUTPUT/INPUT = EFFECT/CAUSE =inverse-mass mechanical-susceptibility = χ (`` ω'') χ(`` ω'') ~(F.-D.thm.) ~P(`` ω'') ``noise'' power-spectrum; (``Max & Al show''): E ~ ω & E ~ (upper-limiting-speeds media) ~m. Thus: ω ~ E ~m Inverting: 1/ ω ~ 1/E ~1/m ~a/F = χ (`` 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 de?nes power-spectrum(PS): P(ω) ≡ ∫ s(t)e-iωtdt = ∫ [vot +(1/2)at2]e-iωtdt = vo ∫ a(t)e-iωtdt +(1/2)[a ≠a(t)] ∫t2e-iωtdt =vo(∂ / ∂ω) δ(ω) + (1/2)[a ≠a(t)](∂2/ ∂ω2) δ(ω) = vo/ω0 + (1/2)[a ≠a(t)]/ω 1 . 000 ...; uniform-velocity a =0 PS P(ω) = 1/ωo WHITE vs. uniform:-a>0a<0) PS P(ω) = 1/ω 1 . 000 ... pink/flicker/HYPERBOLICITY.

The Power Spectrum of Ionic Nanopore Currents: The Role of Ion Correlations.

PubMed

Zorkot, Mira; Golestanian, Ramin; Bonthuis, Douwe Jan

2016-04-13

We calculate the power spectrum of electric-field-driven ion transport through nanometer-scale membrane pores using both linearized mean-field theory and Langevin dynamics simulations. Remarkably, the linearized mean-field theory predicts a plateau in the power spectral density at low frequency ω, which is confirmed by the simulations at low ion concentration. At high ion concentration, however, the power spectral density follows a power law that is reminiscent of the 1/ω(α) dependence found experimentally at low frequency. On the basis of simulations with and without ion-ion interactions, we attribute the low-frequency power-law dependence to ion-ion correlations. We show that neither a static surface charge density, nor an increased pore length, nor an increased ion valency have a significant effect on the shape of the power spectral density at low frequency.

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W.

2002-01-01

A simple power law model consisting of a single spectral index, a 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 alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(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: (P1) 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 he 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 attained in practice are investigated. The ML technique is then extended to estimate spectra information from

The hard X-ray continuum of Cen a observed with INTEGRAL SPI

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

Burke, Mark J.; Jourdain, Elisabeth; Roques, Jean-Pierre

2014-05-20

We revisit the average hard X-ray spectrum from the active galactic nucleus (AGN) of Centaurus A (Cen A) using 10 yr worth of observations with INTEGRAL SPI. This source has the highest flux observed from any AGNs in the SPI bandpass (23 keV-8 MeV). The 10 year light curve of Cen A is presented, and hardness ratios confirm that the spectral shape changes very little despite the luminosity varying by a factor of a few. Primarily, we establish the presence of a reflection component in the average spectrum by demonstrating an excess between 20 and 60 keV, from extending themore » spectral shape observed at low energy to the SPI regime. The excess in Chandra HETGS and INTEGRAL SPI data is well described by reflection of the dominant power-law spectrum from a neutral, optically thick atmosphere. We find that the reprocessed emission contributes 20%-25% of the 23-100 keV flux. The existence of a cutoff at tens to hundreds of kiloelectron volts remains controversial. Using simulated spectra, we demonstrate that a high energy cutoff reproduces the observed spectral properties of Cen A more readily than a simple power law. However, we also show that such a cutoff is probably underestimated when neglecting (even modest) reflection, and for Cen A would be at energies >700 keV, with a confidence of >95%. This is atypically high for thermal Comptonizing plasmas observed in AGNs, and we propose that we are in fact modeling the more gradual change in spectral shape expected of synchrotron self-Compton spectra.« less

Signal detection in power-law noise: effect of spectrum exponents.

PubMed

Burgess, Arthur E; Judy, Philip F

2007-12-01

Many natural backgrounds have approximately isotropic power spectra of the power-law form, P(f)=K/f(beta), where f is radial frequency. For natural scenes and mammograms, the values of the exponent, beta, range from 1.5 to 3.5. The ideal observer model predicts that for signals with certain properties and backgrounds that can be treated as random noise, a plot of log (contrast threshold) versus log (signal size) will be linear with slope, m, given by: m=(beta-2)/2. This plot is referred to as a contrast-detail (CD) diagram. It is interesting that this predicts a detection threshold that is independent of signal size for beta equal to 2. We present two-alternative forced-choice (2AFC) detection results for human and channelized model observers of a simple signal in filtered noise with exponents from 1.5 to 3.5. The CD diagram results are in good agreement with the prediction of this equation.

A statistical spatial power spectrum of the Earth's lithospheric magnetic field

NASA Astrophysics Data System (ADS)

Thébault, E.; Vervelidou, F.

2015-05-01

The magnetic field of the Earth's lithosphere arises from rock magnetization contrasts that were shaped over geological times. The field can be described mathematically in spherical harmonics or with distributions of magnetization. We exploit this dual representation and assume that the lithospheric field is induced by spatially varying susceptibility values within a shell of constant thickness. By introducing a statistical assumption about the power spectrum of the susceptibility, we then derive a statistical expression for the spatial power spectrum of the crustal magnetic field for the spatial scales ranging from 60 to 2500 km. This expression depends on the mean induced magnetization, the thickness of the shell, and a power law exponent for the power spectrum of the susceptibility. We test the relevance of this form with a misfit analysis to the observational NGDC-720 lithospheric magnetic field model power spectrum. This allows us to estimate a mean global apparent induced magnetization value between 0.3 and 0.6 A m-1, a mean magnetic crustal thickness value between 23 and 30 km, and a root mean square for the field value between 190 and 205 nT at 95 per cent. These estimates are in good agreement with independent models of the crustal magnetization and of the seismic crustal thickness. We carry out the same analysis in the continental and oceanic domains separately. We complement the misfit analyses with a Kolmogorov-Smirnov goodness-of-fit test and we conclude that the observed power spectrum can be each time a sample of the statistical one.

Discovery of Diffuse Hard X-Ray Emission from the Vicinity of PSR J1648-4611 with Suzaku

NASA Astrophysics Data System (ADS)

Sakai, Michito; Matsumoto, Hironori; Haba, Yoshito; Kanou, Yasufumi; Miyamoto, Youhei

2013-06-01

We observed the pulsar PSR J1648-4611 with Suzaku. Two X-ray sources, Suzaku J1648-4610 (Src A) and Suzaku J1648-4615 (Src B), were found in the field of view. Src A is coincident with the pulsar PSR J1648-4611, which was also detected by the Fermi Gamma-ray Space Telescope. A hard-band image indicates that Src A is spatially extended. We found point sources in the vicinity of Src A by using a Chandra image of the same region, but the point sources have soft X-ray emission, and cannot explain the hard X-ray emission of Src A. The hard-band spectrum of Src A can be reproduced by a power-law model with a photon index of 2.0+0.9-0.7. The X-ray flux in the 2-10 keV band is 1.4 × 10-13 erg cm-2 s-1. The diffuse emission suggests a pulsar wind nebula around PSR J1648&"8211;4611, but the luminosity of Src A is much larger than that expected from the spin-down luminosity of the pulsar. Parts of the very-high-energy γ-ray emission of HESS J1646-458 may be powered by this pulsar wind nebula driven by PSR J1648-4611. Src B has soft emission, and its X-ray spectrum can be described by a power-law model with a photon index of 3.0+1.4-0.8. The X-ray flux in the 0.4-10 keV band is 6.4 × 10-14 erg s-1 cm-2. No counterpart for Src B has been found in the literature.

STATISTICAL STUDY of HARD X-RAY SPECTRAL CHARACTERISTICS OF SOLAR FLARES

NASA Astrophysics Data System (ADS)

Alaoui, M.; Krucker, S.; Saint-Hilaire, P.; Lin, R. P.

2009-12-01

We investigate the spectral characteristics of 75 solar flares at the hard X-ray peak time observed by RHESSI (Ramaty High Energy Solar Spectroscopic Imager) in the energy range 12-150keV. At energies above 40keV, the Hard X-ray emission is mostly produced by bremsstrahlung of suprathermal electrons as they interact with the ambient plasma in the chromosphere. The observed photon spectra therefore provide diagnostics of electron acceleration processes in Solar flares. We will present statistical results of spectral fitting using two models: a broken power law plus a thermal component which is a direct fit of the photon spectrum and a thick target model plus a thermal component which is a fit of the photon spectra with assumptions on the electrons emitting bremsstrahlung in the thick target approximation.

Airy pulse shaping using time-dependent power-law potentials

NASA Astrophysics Data System (ADS)

Han, Tianwen; Chen, Hao; Qin, Chengzhi; Li, Wenwan; Wang, Bing; Lu, Peixiang

2018-06-01

We investigate the temporal and spectral evolutions of finite-energy Airy pulses in the presence of power-law optical potentials. The potentials are generated by the time-dependent pumped light, which propagates together with the Airy pulses in a highly nonlinear optical fiber. We show that the intrinsic acceleration of Airy pulses can be modified by an external force that stems from a linear potential, and hence unidirectional frequency shift can be realized. When a triangle potential is employed, the pulse will exhibit self-splitting both in temporal and spectral domains. Additionally, as a parabolic potential is utilized, both the temporal waveform and frequency spectrum of the Airy pulse will exchange alternately between the Airy and Gaussian profiles. By using higher-order power-law potentials, we also realize both revival and antirevival effects for the Airy pulses. The study may find wide applications in pulse reshaping and spectral-temporal imaging for both optical communication and signal processing.

Hard Burst Emission from the Soft Gamma Repeater SGR 1900+14

NASA Technical Reports Server (NTRS)

Woods, Peter M.; Kouveliotou, Chryssa; VanParadijs, Jan; Briggs, Michael S.; Hurley, Kevin; Gogus, Ersin; Preece, Robert D.; Giblin, Timothy W.; Thompson, Christopher; Duncan, Robert C.

1999-01-01

We present evidence for burst emission from SGR 1900 + 14 with a power-law high-energy spectrum extending beyond 500 keV. Unlike previous detections of high-energy photons during bursts from soft gamma repeaters (SGRs), these emissions are not associated with extraordinarily bright flares. Not only is the emission hard, but the spectra are better fitted by D. Band's gamma-ray burst (GRB) function rather than by the traditional optically thin thermal bremsstrahlung model. We find that the spectral evolution within these hard events obeys a hardness/intensity anticorrelation. Temporally, these events are distinct from typical SGR burst emissions in that they are longer (approximately 1 s) and have relatively smooth profiles. Despite a difference in peak luminosity of approximately > 10(exp 11) between these bursts from SGR 1900 + 14 and cosmological GRBs, there are striking temporal and spectral similarities between the two kinds of bursts, aside from spectral evolution. We outline an interpretation of these events in the context of the magnetar model.

Discovery of hard-spectrum γ -ray emission from the BL Lacertae object 1ES 0414+009

DOE PAGES

Abramowski, A.

2012-02-01

1ES 0414 + 009 (z = 0.287) is a distant high-frequency-peaked BL Lac object, and has long been considered a likely emitter of very-high-energy (VHE, E > 100 GeV) γ-rays due to its high X-ray and radio flux. Observations in the VHE γ-ray band and across the electromagnetic spectrum can provide insights into the origin of highly energetic particles present in the source and the radiation processes at work. Because of the distance of the source, the γ-ray spectrum might provide further limits on the level of the extragalactic background light (EBL). Methods. We report observations made between October 2005more » and December 2009 with H.E.S.S., an array of four imaging atmospheric Cherenkov telescopes. Observations at high energies (HE, 100 MeV–100 GeV) with the Fermi-LAT instrument in the first 20 months of its operation are also reported. To complete the multi-wavelength picture, archival UV and X-ray observations with the Swift satellite and optical observations with the ATOM telescope are also used. Based on the observations with H.E.S.S., 1ES 0414 + 009 is detected for the first time in the VHE band. An excess of 224 events is measured, corresponding to a significance of 7.8σ. The photon spectrum of the source is well described by a power law, with photon index of ΓVHE = 3.45 ± 0.25stat ± 0.20syst. The integral flux above 200 GeV is (1.88 ± 0.20stat ± 0.38syst) × 10-12 cm-2 s-1. Observations with the Fermi-LAT in the first 20 months of operation show a flux between 200 MeV and 100 GeV of (2.3 ± 0.2stat) × 10-9 erg cm-2 s-1, and a spectrum well described by a power-law function with a photon index ΓHE = 1.85 ± 0.18. Swift/XRT observations show an X-ray flux between 2 and 10 keV of (0.8-1) × 10-11 erg cm-2 s-1, and a steep spectrum ΓX = (2.2-2.3). Combining X-ray with optical-UV data, a fit with a log-parabolic function locates the synchrotron peak around 0.1 keV. Although the GeV–TeV observations do not provide better constraints on the EBL

Hard X-ray Emission and Efficient Particle Acceleration by Supernova Remnants

NASA Astrophysics Data System (ADS)

Vink, Jacco

2009-05-01

I discuss the non-thermal X-ray emission from young supernova remnants. Over the last decade it has become clear from both X-ray and γ-ray observations that young supernovae accelerate particles up to 100 TeV. In soft X-rays the accelerated >10 TeV electrons produce synchrotron radiation, coming from narrow filaments located at the shock fronts. The width of these filaments shows that the magnetic fields are relatively high, thus providing evidence for magnetic field amplification. The synchrotron radiation of several remnants is known to extend into the hard X-ray regime. In particular Cas A, has a spectrum that appears as a power law up to almost 100 TeV. This is very surprising, as a steepening is expected going from the soft to the hard X-ray band. The spectrum is likely a result of many superimposed individual spectra, each steepening at different energies. This implies considerable spatial variation in hard X-rays, an obvious target for Simbol-X. The variations will be important to infer local shock acceleration properties, but also magnetic field fluctuations may cause spatial and temporal variations. Finally, I draw the attention to super bubbles and supernovae as sources of cosmic rays. As such they may be sources of hard X-ray emission. In particular, supernovae exploding inside the dense red supergiants winds of their progenitors ares promising candidates for hard X-ray emission.

Probing dark energy using convergence power spectrum and bi-spectrum

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

Dinda, Bikash R., E-mail: bikash@ctp-jamia.res.in

Weak lensing convergence statistics is a powerful tool to probe dark energy. Dark energy plays an important role to the structure formation and the effects can be detected through the convergence power spectrum, bi-spectrum etc. One of the most promising and simplest dark energy model is the ΛCDM . However, it is worth investigating different dark energy models with evolving equation of state of the dark energy. In this work, detectability of different dark energy models from ΛCDM model has been explored through convergence power spectrum and bi-spectrum.

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.

NuSTAR and XMM-Newton Observations of the Hard X- Ray Spectrum of Centaurus A

NASA Technical Reports Server (NTRS)

Furst, F.; Muller, C.; Madsen, K. K.; Lanz, L.; Rivers, E.; Brightman, M.; Arevalo, P.; Balokovic, M.; Beuchert, T.; Zhang, W.

2016-01-01

We present simultaneous XMM-Newton and Nuclear Spectroscopic Telescope Array (NuSTAR) observations spanning 3-78 keV of the nearest radio galaxy, Centaurus A (Cen A). The accretion geometry around the central engine in Cen A is still debated, and we investigate possible configurations using detailed X-ray spectral modeling. NuSTAR imaged the central region of Cen A with subarcminute resolution at X-ray energies above 10 keV for the first time, but found no evidence for an extended source or other off-nuclear point sources. The XMM-Newton and NuSTAR spectra agree well and can be described with an absorbed power law with a photon index Gamma = 1.8150 +/- 0.005 and a fluorescent Fe Kaline in good agreement with literature values. The spectrum is greater than 1 MeV. A thermal Comptonization continuum describes the data well, with parameters that agree with values measured by INTEGRAL, in particular an electron temperature kTe between approximately 100-300 keV and seed photon input temperatures between 5 and 50 eV. We do not find evidence for reflection or a broad iron line and put stringent upper limits of R is less than 0.01 on the reflection fraction and accretion disk illumination. We use archival Chandra data to estimate the contribution from diffuse emission, extra-nuclear point sources, and the outer X-ray jet to the observed NuSTAR and XMM-Newton X-ray spectra and find the contribution to be negligible. We discuss different scenarios for the physical origin of the observed hard X-ray spectrum and conclude that the inner disk is replaced by an advection-dominated accretion flow or that the X-rays are dominated by synchrotron self-Compton emission from the inner regions of the radio jet or a combination thereof.

Fractional power-law spatial dispersion in electrodynamics

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru; Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife; Trujillo, Juan J., E-mail: jtrujill@ullmat.es

2013-07-15

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s lawmore » and Debye’s screening for the media.« less

Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks.

PubMed

Cota, Wesley; Ferreira, Silvio C; Ódor, Géza

2016-03-01

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space λ(1)<λ<λ(2), suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at λ(2). We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at λ(c)=0. Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.

The Spectrum of Wind Power Fluctuations

NASA Astrophysics Data System (ADS)

Bandi, Mahesh

2016-11-01

Wind is a variable energy source whose fluctuations threaten electrical grid stability and complicate dynamical load balancing. The power generated by a wind turbine fluctuates due to the variable wind speed that blows past the turbine. Indeed, the spectrum of wind power fluctuations is widely believed to reflect the Kolmogorov spectrum; both vary with frequency f as f - 5 / 3. This variability decreases when aggregate power fluctuations from geographically distributed wind farms are averaged at the grid via a mechanism known as geographic smoothing. Neither the f - 5 / 3 wind power fluctuation spectrum nor the mechanism of geographic smoothing are understood. In this work, we explain the wind power fluctuation spectrum from the turbine through grid scales. The f - 5 / 3 wind power fluctuation spectrum results from the largest length scales of atmospheric turbulence of order 200 km influencing the small scales where individual turbines operate. This long-range influence spatially couples geographically distributed wind farms and synchronizes farm outputs over a range of frequencies and decreases with increasing inter-farm distance. Consequently, aggregate grid-scale power fluctuations remain correlated, and are smoothed until they reach a limiting f - 7 / 3 spectrum. This work was funded by the Collective Interactions Unit, OIST Graduate University, Japan.

Power-law decay exponents: A dynamical criterion for predicting thermalization

NASA Astrophysics Data System (ADS)

Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.

2017-01-01

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

Hard X-ray Emission from the M87 AGN Detected with NuSTAR

NASA Astrophysics Data System (ADS)

Wong, Ka-Wah; Nemmen, Rodrigo; Irwin, Jimmy; Lin, Dacheng

2018-01-01

M87 hosts a 3–6 billion solar mass black hole with a remarkable relativistic jet that has been regularly monitored in radio to TeV bands. However, hard X-ray emission above 10keV expected to primarily come from the jet or the accretion flow had never been detected from its unresolved X-ray core. We report NuSTAR detection up to 40 keV from the the central regions of M87. Together with simultaneous Chandra observations, we have constrained the dominant hard X-ray emission to be from its unresolved X-ray core, presumably in its quiescent state. The core spectrum is well fitted by a power-law. The measured flux density at 40keV is consistent with a jet origin, although emission from the advection-dominated accretion flow cannot be completely ruled out. The detected hard X-ray emission is significantly lower than that predicted by synchrotron self-Compton models introduced to explain emission above a GeV.

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.

Randomized Trial of Law Enforcement Training on Autism Spectrum Disorders

ERIC Educational Resources Information Center

Teagardin, Jill; Dixon, Dennis R.; Smith, Marlena N.; Granpeesheh, Doreen

2012-01-01

The core symptoms of autism spectrum disorders (ASD) are likely to affect interactions between law enforcement officers and persons with ASD. If law enforcement officers are not trained to identify and appropriately respond to persons with ASD, it is possible that officers may exacerbate a situation, resulting in unnecessary trauma, injury, or…

A Test of Thick-Target Nonuniform Ionization as an Explanation for Breaks in Solar Flare Hard X-Ray Spectra

NASA Technical Reports Server (NTRS)

Holman, gordon; Dennis Brian R.; Tolbert, Anne K.; Schwartz, Richard

2010-01-01

Solar nonthermal hard X-ray (HXR) flare spectra often cannot be fitted by a single power law, but rather require a downward break in the photon spectrum. A possible explanation for this spectral break is nonuniform ionization in the emission region. We have developed a computer code to calculate the photon spectrum from electrons with a power-law distribution injected into a thick-target in which the ionization decreases linearly from 100% to zero. We use the bremsstrahlung cross-section from Haug (1997), which closely approximates the full relativistic Bethe-Heitler cross-section, and compare photon spectra computed from this model with those obtained by Kontar, Brown and McArthur (2002), who used a step-function ionization model and the Kramers approximation to the cross-section. We find that for HXR spectra from a target with nonuniform ionization, the difference (Delta-gamma) between the power-law indexes above and below the break has an upper limit between approx.0.2 and 0.7 that depends on the power-law index delta of the injected electron distribution. A broken power-law spectrum with a. higher value of Delta-gamma cannot result from nonuniform ionization alone. The model is applied to spectra obtained around the peak times of 20 flares observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI from 2002 to 2004 to determine whether thick-target nonuniform ionization can explain the measured spectral breaks. A Monte Carlo method is used to determine the uncertainties of the best-fit parameters, especially on Delta-gamma. We find that 15 of the 20 flare spectra require a downward spectral break and that at least 6 of these could not be explained by nonuniform ionization alone because they had values of Delta-gamma with less than a 2.5% probability of being consistent with the computed upper limits from the model. The remaining 9 flare spectra, based on this criterion, are consistent with the nonuniform ionization model.

NuSTAR Results and Future Plans for Magnetar and Rotation-Powered Pulsar Observations

NASA Technical Reports Server (NTRS)

An, H.; Kaspi, V. M.; Archibald, R.; Bachetti, M.; Bhalerao, V.; Bellm, E. C.; Beloborodov, A. M.; Boggs, S. E.; Chakrabarty, D.; Christensen, F. E.;

Smart power. Great leaders know when hard power is not enough.

PubMed

Nye, Joseph S

2008-11-01

The next U.S. administration will face enormous challenges to world peace, the global economy, and the environment. Exercising military and economic muscle alone will not bring peace and prosperity. According to Nye, a former U.S. government official and a former dean at Harvard University's John F. Kennedy School of Government, the next president must be able to combine hard power, characterized by coercion, and what Nye calls "soft" power, which relies instead on attraction. The result is smart power, a tool great leaders use to mobilize people around agendas that look beyond current problems. Hard power is often necessary, Nye explains. In the 1990s, when the Taliban was providing refuge to Al Oaeda, President Clinton tried---and failed--to solve the problem diplomatically instead of destroying terrorist havens in Afghanistan. In other situations, however, soft power is more effective, though it has been too often overlooked. In Iraq, Nye argues, the use of soft power could draw young people toward something other than terrorism. "I think that there's an awakening to the need for soft power as people look at the crisis in the Middle East and begin to realize that hard power is not sufficient to resolve it," he says. Solving today's global problems will require smart power--a judicious blend of the other two powers. While there are notable examples of men who have used smart power--Teddy Roosevelt, for instance--it's much more difficult for women to lead with smart power, especially in the United States, where women feel pressure to prove that they are not "soft." Only by exercising smart power, Nye says, can the next president of the United States set a new tone for U.S. foreign policy in this century.

Power-laws in art

NASA Astrophysics Data System (ADS)

Etro, Federico; Stepanova, Elena

2018-09-01

We provide evidence of a cubic law of art prices that hints to a general pattern for the distribution of artistic talent. The persistence across heterogeneous markets from historical ones to contemporary art auctions of a power law in the distribution of the average price per artist suggests the possibility of a universal law for talent distribution. We explore scale-free networks of teacher-students to investigate the diffusion of talent over time.

Power laws in citation distributions: evidence from Scopus.

PubMed

Brzezinski, Michal

Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in "Physics and Astronomy". Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.

The Energy Spectrum of Solar Energetic Electrons

NASA Astrophysics Data System (ADS)

Wang, L.; Yang, L.; Krucker, S.; Wimmer-Schweingruber, R. F.; Bale, S. D.

2015-12-01

Here we present a statistical survey of the energy spectrum of solar energetic electron events (SEEs) observed by the WIND 3DP instrument from 1995 though 2014. For SEEs with the minimum energy below 10 keV and the maximum energy above 100 keV, ~85% (~2%) have a double-power-law energy spectrum with a steepening (hardening) above the break energy, while ~13% have a single-power-law energy spectrum at all energies. The average spectral index is ~2.4 below the energy break and is ~4.0 above the energy break. For SEEs detected only at energies <10 keV (>20 keV), they generally show a single-power-law spectrum with the average index of ~3.0 (~3.3). The spectrum of SEEs detected only below 10 keV appears to get harder with increasing solar activity, but the spectrum of SEEs with higher-energy electrons shows no clear correlation with solar activity. We will also investigate whether the observed energy spectrum of SEEs at 1 AU mainly reflects the electron acceleration at the Sun or the electron transport in the interplanetary medium.

Fermi observations of the very hard gamma-ray blazar PG 1553+113

DOE PAGES

Abdo, A. A.; Ackermann, M.; Ajello, M.; ...

2009-12-22

Here, we report the observations of PG 1553+113 during the first ~ 200 days of Fermi Gamma-ray Space Telescope science operations, from 2008 August 4 to 2009 February 22 (MJD 54682.7-54884.2). This is the first detailed study of PG 1553+113 in the GeV gamma-ray regime and it allows us to fill a gap of three decades in energy in its spectral energy distribution (SED). We find PG 1553+113 to be a steady source with a hard spectrum that is best fit by a simple power law in the Fermi energy band. We combine the Fermi data with archival radio, optical,more » X-ray, and very high energy (VHE) gamma-ray data to model its broadband SED and find that a simple, one-zone synchrotron self-Compton model provides a reasonable fit. PG 1553+113 has the softest VHE spectrum of all sources detected in that regime and, out of those with significant detections across the Fermi energy bandpass so far, the hardest spectrum in that energy regime. Thus, it has the largest spectral break of any gamma-ray source studied to date, which could be due to the absorption of the intrinsic gamma-ray spectrum by the extragalactic background light (EBL). Assuming this to be the case, we selected a model with a low level of EBL and used it to absorb the power-law spectrum from PG 1553+113 measured with Fermi (200 MeV-157 GeV) to find the redshift, which gave the best fit to the measured VHE data (90 GeV-1.1 TeV) for this parameterization of the EBL. We show that this redshift can be considered an upper limit on the distance to PG 1553+113.« less

Power-law regularities in human language

NASA Astrophysics Data System (ADS)

Mehri, Ali; Lashkari, Sahar Mohammadpour

2016-11-01

Complex structure of human language enables us to exchange very complicated information. This communication system obeys some common nonlinear statistical regularities. We investigate four important long-range features of human language. We perform our calculations for adopted works of seven famous litterateurs. Zipf's law and Heaps' law, which imply well-known power-law behaviors, are established in human language, showing a qualitative inverse relation with each other. Furthermore, the informational content associated with the words ordering, is measured by using an entropic metric. We also calculate fractal dimension of words in the text by using box counting method. The fractal dimension of each word, that is a positive value less than or equal to one, exhibits its spatial distribution in the text. Generally, we can claim that the Human language follows the mentioned power-law regularities. Power-law relations imply the existence of long-range correlations between the word types, to convey an especial idea.

QUASI-PERIODIC PULSATIONS IN SOLAR AND STELLAR FLARES: RE-EVALUATING THEIR NATURE IN THE CONTEXT OF POWER-LAW FLARE FOURIER SPECTRA

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

Inglis, A. R.; Ireland, J.; Dominique, M.

The nature of quasi-periodic pulsations (QPPs) in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPPs is needed. We adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power-law properties of flare signals. Using data from the PROBA2/Large Yield Radiometer, Fermi/Gamma-ray Burst Monitor, Nobeyama Radioheliograph, and Yohkoh/HXT instruments, we study a selection of flares from the literaturemore » identified as QPP events. Additionally, we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum. However, for the flare of 1998 May 8, strong evidence for an explicit oscillation with P ≈ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh/HXT data. We conclude that, most likely, many previously analyzed events in the literature may be similarly described by power laws in the flare Fourier power spectrum, without invoking a narrowband, oscillatory component. Hence the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.« less

Power Spectrum Analysis of Polarized Emission from the Canadian Galactic Plane Survey

NASA Astrophysics Data System (ADS)

Stutz, R. A.; Rosolowsky, E. W.; Kothes, R.; Landecker, T. L.

2014-05-01

Angular power spectra are calculated and presented for the entirety of the Canadian Galactic Plane Survey polarization data set at 1.4 GHz covering an area of 1060 deg2. The data analyzed are a combination of data from the 100 m Effelsberg Telescope, the 26 m Telescope at the Dominion Radio Astrophysical Observatory, and the Synthesis Telescope at the Dominion Radio Astrophysical Observatory, allowing all scales to be sampled down to arcminute resolution. The resulting power spectra cover multipoles from l ≈ 60 to l ≈ 104 and display both a power-law component at low multipoles and a flattening at high multipoles from point sources. We fit the power spectrum with a model that accounts for these components and instrumental effects. The resulting power-law indices are found to have a mode of 2.3, similar to previous results. However, there are significant regional variations in the index, defying attempts to characterize the emission with a single value. The power-law index is found to increase away from the Galactic plane. A transition from small-scale to large-scale structure is evident at b = 9°, associated with the disk-halo transition in a 15° region around l = 108°. Localized variations in the index are found toward H II regions and supernova remnants, but the interpretation of these variations is inconclusive. The power in the polarized emission is anticorrelated with bright thermal emission (traced by Hα emission) indicating that the thermal emission depolarizes background synchrotron emission.

ROTATIONAL- SHOCK(S) Impulse-Jerk(I-J) [VS. T=I α] Plasticity/Fracture Burst Acoustic-Emission(BAE) NON: ``1''/[f= ω]-``Noise'' Power-Law Power-Spectrum is T=I α DERIVATIVE I-J Time-Series Integral-Transform

NASA Astrophysics Data System (ADS)

Lewis, Thomas; Siegel, Edward

2011-06-01

ROTATIONAL-[``spin-up''/``spin-down'']-SHOCK(S)-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 A.-E. Symp.(76);Acta Met. 25,383(77);JMMM 7,312(78)] NON: ``1''/ ω noise'' Zipf-(Pareto); power-law universality power-spectrum; is manifestly-demonstrated in two distinct ways to be nothing but ROTATIONAL(in 2 OR 3-dimensions)ANGULAR-momentum Newton's 3rd Law of Motion T=I α=dJ/dt REdiscovery!!! A/Siegel PHYSICS derivation FAILS!!! ''PURE''-MATHS: dT(t)/dt=(dJ(t)/dt)2=[I(t)d α(t)/dt+ α(t)(t)dI(t)/dt TRIPLE-integral VS. T=I α DOUBLE-integral time-series(T-S) Dichotomy: θ(t)=[ϖ0 t + α(t) t 2 / 2 + EXTRA-TERM(S)] VS. θ(t)=[ϖ0 t + α(t) t 2 / 2 ] integral-transform formally defines power-spectrum Dichotomy: P(ω) =? θ(t)e-iωtdt=?[ϖ0 t + αt2 / 2 ]e-iωtdt=φ0?te-iωtdt+?{[ α ≠ α (t)]/2}t2eiωtdt= φ0 (ω) /d ω+{[a ≠a(t)]/2}d2 δ (ω) /dω2 =φ0 /ω0+{[ α ≠ α (t)]/2}/ω 1 . 000 ...: if α=0, then P(ω) 1/ω0, VS. if α ≠ α (t) ≠0, then P(ω) 1/ ω 1/ω 1 . 000 ...

Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

NASA Astrophysics Data System (ADS)

Walicka, A.

2018-02-01

In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

Production of hard X rays in a plasma focus

NASA Technical Reports Server (NTRS)

Newman, C. E.; Petrosian, V.

1975-01-01

A model of a plasma focus is examined wherein large axial electric fields are produced by an imploding current sheet during the final nanoseconds of the collapse phase and where the fields provide a mechanism for creating a beam of electrons of highly suprathermal energies. The expected bremsstrahlung radiation above 100 keV is calculated for such a beam, which has a power-law spectrum, both from electron-deuteron collisions in the focused plasma and when the beam reaches the wall of the device. It is concluded that, since the experimental results indicate little or no radiation above 100 keV originating in the walls, that the electrons in the beam must be decelerated after leaving the plasma and before reaching the wall. Comparisons with the results and the total energy of the device yield qualitative agreement with the expected angular distribution of hard X-rays and reasonable agreement with the total energy in accelerated electrons required to produce the observed total energy in hard X-rays by this mechanism.

Suzaku Detection of Diffuse Hard X-Ray Emission Outside Vela X

NASA Technical Reports Server (NTRS)

Katsuda, Satoru; Mori, Koji; Petre, Robert; Yamaguchi, Hiroya; Tsunemi, Hiroshi; Bocchino, Fabrizio; Bamba, Aya; Miceli, Marco; Hewitt, John W.; Temim, Tea;

Microwave and hard X-ray emissions during the impulsive phase of solar flares: Nonthermal electron spectrum and time delay

NASA Technical Reports Server (NTRS)

Gu, Ye-Ming; Li, Chung-Sheng

1986-01-01

On the basis of the summing-up and analysis of the observations and theories about the impulsive microwave and hard X-ray bursts, the correlations between these two kinds of emissions were investigated. It is shown that it is only possible to explain the optically-thin microwave spectrum and its relations with the hard X-ray spectrum by means of the nonthermal source model. A simple nonthermal trap model in the mildly-relativistic case can consistently explain the main characteristics of the spectrum and the relative time delays.

Systematic harmonic power laws inter-relating multiple fundamental constants

NASA Astrophysics Data System (ADS)

Chakeres, Donald; Buckhanan, Wayne; Andrianarijaona, Vola

2017-01-01

Power laws and harmonic systems are ubiquitous in physics. We hypothesize that 2, π, the electron, Bohr radius, Rydberg constant, neutron, fine structure constant, Higgs boson, top quark, kaons, pions, muon, Tau, W, and Z when scaled in a common single unit are all inter-related by systematic harmonic powers laws. This implies that if the power law is known it is possible to derive a fundamental constant's scale in the absence of any direct experimental data of that constant. This is true for the case of the hydrogen constants. We created a power law search engine computer program that randomly generated possible positive or negative powers searching when the product of logical groups of constants equals 1, confirming they are physically valid. For 2, π, and the hydrogen constants the search engine found Planck's constant, Coulomb's energy law, and the kinetic energy law. The product of ratios defined by two constants each was the standard general format. The search engine found systematic resonant power laws based on partial harmonic fraction powers of the neutron for all of the constants with products near 1, within their known experimental precision, when utilized with appropriate hydrogen constants. We conclude that multiple fundamental constants are inter-related within a harmonic power law system.

The speed-curvature power law of movements: a reappraisal.

PubMed

Zago, Myrka; Matic, Adam; Flash, Tamar; Gomez-Marin, Alex; Lacquaniti, Francesco

2018-01-01

Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

The time-domain behavior of power-law noises. [of many geophysical phenomena

NASA Technical Reports Server (NTRS)

Agnew, Duncan C.

1992-01-01

The power spectra of many geophysical phenomena are well approximated by a power-law dependence on frequency or wavenumber. A simple expression for the root-mean-square variability of a process with such a spectrum over an interval of time or space is derived. The resulting expression yields the powerlaw time dependence characteristic of fractal processes, but can be generalized to give the temporal variability for more general spectral behaviors. The method is applied to spectra of crustal strain (to show what size of strain events can be detected over periods of months to seconds) and of sea level (to show the difficulty of extracting long-term rates from short records).

A comparison of the thick-target model with stereo data on the height structure of solar hard X-ray bursts

NASA Technical Reports Server (NTRS)

Brown, J. C.; Carlaw, V. A.; Cromwell, D.; Kane, S. R.

1983-01-01

The thick target, hard solar X-ray source height structure is predicted for the case of a beam that is injected vertically downward, having a power law spectrum, being dominated by Coulomb collisional energy losses, and being structurally characterized by the ratio of hard X-ray flux from an upper part of the source to that from the entire source. These predictions are compared with the flux ratios at 150 and 350 keV which were observed by two spacecraft for five events in which the solar limb occults part of the source for one spacecraft. The energy dependence of the occultation ratio is found to be inconsistent with that predicted by the model, and it is concluded that noncollisional losses must be significant in beam dynamics.

Autism Spectrum Disorder and New Jersey Administrative Law Decisions: An Analysis of Case Law Involving Public School Students

ERIC Educational Resources Information Center

Barcadepone, Michael J.

2012-01-01

The purpose of this case study was to investigate existing New Jersey case law for the special education population classified as Autism Spectrum Disorder (ASD) and analyze New Jersey Administrative Law Judge (ALJ) decisions to identify why districts win or lose cases, adding to the limited body of research in New Jersey. In addition, the purpose…

Existence of k⁻¹ power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg's eddy viscosity.

PubMed

Katul, Gabriel G; Porporato, Amilcare; Nikora, Vladimir

2012-12-01

The existence of a "-1" power-law scaling at low wavenumbers in the longitudinal velocity spectrum of wall-bounded turbulence was explained by multiple mechanisms; however, experimental support has not been uniform across laboratory studies. This letter shows that Heisenberg's eddy viscosity approach can provide a theoretical framework that bridges these multiple mechanisms and explains the elusiveness of the "-1" power law in some experiments. Novel theoretical outcomes are conjectured about the role of intermittency and very-large scale motions in modifying the k⁻¹ scaling.

Local region power spectrum-based unfocused ship detection method in synthetic aperture radar images

NASA Astrophysics Data System (ADS)

Wei, Xiangfei; Wang, Xiaoqing; Chong, Jinsong

2018-01-01

Ships on synthetic aperture radar (SAR) images will be severely defocused and their energy will disperse into numerous resolution cells under long SAR integration time. Therefore, the image intensity of ships is weak and sometimes even overwhelmed by sea clutter on SAR image. Consequently, it is hard to detect the ships from SAR intensity images. A ship detection method based on local region power spectrum of SAR complex image is proposed. Although the energies of the ships are dispersed on SAR intensity images, their spectral energies are rather concentrated or will cause the power spectra of local areas of SAR images to deviate from that of sea surface background. Therefore, the key idea of the proposed method is to detect ships via the power spectra distortion of local areas of SAR images. The local region power spectrum of a moving target on SAR image is analyzed and the way to obtain the detection threshold through the probability density function (pdf) of the power spectrum is illustrated. Numerical P- and L-band airborne SAR ocean data are utilized and the detection results are also illustrated. Results show that the proposed method can well detect the unfocused ships, with a detection rate of 93.6% and a false-alarm rate of 8.6%. Moreover, by comparing with some other algorithms, it indicates that the proposed method performs better under long SAR integration time. Finally, the applicability of the proposed method and the way of parameters selection are also discussed.

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 Spectrum Density of Long-Term MAXI Data

NASA Astrophysics Data System (ADS)

Sugimoto, Juri; Mihara, Tatehiro; Sugizaki, Mutsumi; Serino, Motoko; Kitamoto, Shunji; Sato, Ryousuke; Ueda, Yoshihiro; Ueno, Shiro

Monitor of All-sky X-ray Image (MAXI) on the International Space Station has been observing the X-ray sky since 2009 August 15. It has accumulated the X-ray data for about four years, so far. X-ray objects are usually variable and their variability can be studied by the power spectrum density (PSD) of the X-ray light curves. We applied our method to calculate PSDs of several kinds of objects observed with MAXI. We obtained significant PSDs from 16 Seyfert galaxies. For blackhole binary Cygnus X-1 there was a difference in the shape of PSD between the hard state and the soft state. For high mass X-ray binaries, Cen X-3, SMC X-1, and LMC X-4, there were several peaks in the PSD corresponding to the orbital period and the superorbital period.

Alternative Fuels Data Center: CNG Powers Law Enforcement in Arkansas

Science.gov Websites

CNG Powers Law Enforcement in Arkansas to someone by E-mail Share Alternative Fuels Data Center : CNG Powers Law Enforcement in Arkansas on Facebook Tweet about Alternative Fuels Data Center: CNG Powers Law Enforcement in Arkansas on Twitter Bookmark Alternative Fuels Data Center: CNG Powers Law

HESS J1427-608: An Unusual Hard, Unbroken Gamma-Ray Spectrum in a Very Wide Energy Range

NASA Astrophysics Data System (ADS)

Guo, Xiao-Lei; Xin, Yu-Liang; Liao, Neng-Hui; Yuan, Qiang; Gao, Wei-Hong; He, Hao-Ning; Fan, Yi-Zhong; Liu, Si-Ming

2017-01-01

We report the detection of a GeV γ-ray source that spatially overlaps and is thus very likely associated with the unidentified very high energy (VHE) γ-ray source HESS J1427-608 with the Pass 8 data recorded by the Fermi Large Area Telescope. The photon spectrum of this source is best described by a power law with an index of 1.85 ± 0.17 in the energy range of 3-500 GeV, and the measured flux connects smoothly with that of HESS J1427-608 at a few hundred gigaelectronvolts. This source shows no significant extension and time variation. The broadband GeV to TeV emission over four decades of energies can be well fitted by a single power-law function with an index of 2.0, without obvious indication of spectral cutoff toward high energies. Such a result implies that HESS J1427-608 may be a PeV particle accelerator. We discuss the possible nature of HESS J1427-608 according to the multiwavelength spectral fittings. Given the relatively large errors, either a leptonic or a hadronic model can explain the multiwavelength data from radio to VHE γ-rays. The inferred magnetic field strength is a few micro-Gauss, which is smaller than the typical values of supernova remnants (SNRs) and is consistent with some pulsar wind nebulae (PWNe). On the other hand, the flat γ-ray spectrum is slightly different from typical PWNe but is similar to that of some known SNRs.

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.

Nature of the atmospheric dynamics on Venus from power spectrum analysis of Mariner 10 images

NASA Technical Reports Server (NTRS)

Travis, L. D.

1978-01-01

Power spectrum analysis of Mariner 10 images for planetary zonal wavenumbers no less than 3 and for latitudes in the range 55 deg S to 25 deg N yields spectra which show a systematic and apparently significant variation with latitude. Accordingly, average spectra are determined for three latitude zones: an equatorial region, a midlatitude region, and an intermediate zone. A comparison of the results for Venus with brightness distribution spectra for terrestrial clouds reveals similarities between the Venus midlatitude region spectrum and that for the equatorial region of the earth. The only indication of a departure from a general power law behavior for the Venus spectra is a flattening of the equatorial spectrum in the region of wavenumbers 3 and 4. The characteristics of the Venus image spectra appear to be compatible with the interpretation that the observable clouds lie in a region of high static stability with the inertial eddy motions corresponding to two-dimensional turbulence.

Power-law spatial dispersion from fractional Liouville equation

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

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

Power-law versus log-law in wall-bounded turbulence: A large-eddy simulation perspective

NASA Astrophysics Data System (ADS)

Cheng, W.; Samtaney, R.

2014-01-01

The debate whether the mean streamwise velocity in wall-bounded turbulent flows obeys a log-law or a power-law scaling originated over two decades ago, and continues to ferment in recent years. As experiments and direct numerical simulation can not provide sufficient clues, in this study we present an insight into this debate from a large-eddy simulation (LES) viewpoint. The LES organically combines state-of-the-art models (the stretched-vortex model and inflow rescaling method) with a virtual-wall model derived under different scaling law assumptions (the log-law or the power-law by George and Castillo ["Zero-pressure-gradient turbulent boundary layer," Appl. Mech. Rev. 50, 689 (1997)]). Comparison of LES results for Reθ ranging from 105 to 1011 for zero-pressure-gradient turbulent boundary layer flows are carried out for the mean streamwise velocity, its gradient and its scaled gradient. Our results provide strong evidence that for both sets of modeling assumption (log law or power law), the turbulence gravitates naturally towards the log-law scaling at extremely large Reynolds numbers.

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.

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.

Power-law creep and residual stresses in carbopol microgels

NASA Astrophysics Data System (ADS)

Lidon, Pierre; Manneville, Sebastien

We report on the interplay between creep and residual stresses in carbopol microgels. When a constant shear stress σ is applied below the yield stress σc, the strain is shown to increase as a power law of time, γ (t) =γ0 +(t / τ) α , with and exponent α ~= 0 . 38 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some characteristic value of about σc / 10 , the microgels experience a more complex creep behavior that we link to the existence of residual stresses and to weak aging of the system after preshear. The influence of the preshear protocol, of boundary conditions and of microgel concentration on residual stresses is investigated. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.

X-ray nova MAXI J1828-249. Evolution of the broadband spectrum during its 2013-2014 outburst

NASA Astrophysics Data System (ADS)

Grebenev, S. A.; Prosvetov, A. V.; Burenin, R. A.; Krivonos, R. A.; Mescheryakov, A. V.

2016-02-01

Based on data from the SWIFT, INTEGRAL, MAXI/ISS orbital observatories, and the ground-based RTT-150 telescope, we have investigated the broadband (from the optical to the hard X-ray bands) spectrum of the X-ray nova MAXI J1828-249 and its evolution during the outburst of the source in 2013-2014. The optical and infrared emissions from the nova are shown to be largely determined by the extension of the power-law component responsible for the hard X-ray emission. The contribution from the outer cold regions of the accretion disk, even if the X-ray heating of its surface is taken into account, turns out to be moderate during the source's "high" state (when a soft blackbody emission component is observed in the X-ray spectrum) and is virtually absent during its "low" ("hard") state. This result suggests that much of the optical and infrared emissions from such systems originates in the same region of main energy release where their hard X-ray emission is formed. This can be the Compton or synchro-Compton radiation from a high-temperature plasma in the central accretion disk region puffed up by instabilities, the synchrotron radiation from a hot corona above the disk, or the synchrotron radiation from its relativistic jets.

DETECTION OF VERY HARD γ -RAY SPECTRUM FROM THE TEV BLAZAR MRK 501

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

Shukla, A.; Chitnis, V. R.; Acharya, B. S.

2016-12-01

The occasional hardening of the GeV-to-TeV spectrum observed from the blazar Mrk 501 has reopened the debate on the physical origin of radiation and particle acceleration processes in TeV blazars. We have used the ∼7 years of Fermi -LAT data to search for the time intervals with unusually hard spectra from the nearby TeV blazar Mrk 501. We detected hard spectral components above 10 GeV with photon index <1.5 at a significance level of more than 5 sigma on 17 occasions, each with 30 day integration time. The photon index of the hardest component reached a value of 0.89 ± 0.29. We interpretmore » these hard spectra as signatures of intermittent injection of sharply peaked and localized particle distributions from the base of the jet.« less

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.

Scaling for hard-sphere colloidal glasses near jamming

NASA Astrophysics Data System (ADS)

Zargar, Rojman; DeGiuli, Eric; Bonn, Daniel

2016-12-01

Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the density of states, shear modulus, and mean-squared displacement (MSD) in a hard-sphere colloidal glass. Scaling the frequency with the boson-peak frequency, we find that the density of states at different volume fractions all collapse on a single master curve, which obeys a power law in terms of the scaled frequency. Below the boson peak, the exponent is consistent with theoretical results obtained by real-space and phase-space approaches to understanding amorphous solids. We find that the shear modulus and the MSD are nearly inversely proportional, and show a singular power-law dependence on the distance from random close packing. Our results are in very good agreement with the theoretical predictions.

HESS J1427−608: AN UNUSUAL HARD, UNBROKEN γ -RAY SPECTRUM IN A VERY WIDE ENERGY RANGE

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

Guo, Xiao-Lei; Gao, Wei-Hong; Xin, Yu-Liang

2017-01-20

We report the detection of a GeV γ -ray source that spatially overlaps and is thus very likely associated with the unidentified very high energy (VHE) γ -ray source HESS J1427−608 with the Pass 8 data recorded by the Fermi Large Area Telescope . The photon spectrum of this source is best described by a power law with an index of 1.85 ± 0.17 in the energy range of 3–500 GeV, and the measured flux connects smoothly with that of HESS J1427−608 at a few hundred gigaelectronvolts. This source shows no significant extension and time variation. The broadband GeV tomore » TeV emission over four decades of energies can be well fitted by a single power-law function with an index of 2.0, without obvious indication of spectral cutoff toward high energies. Such a result implies that HESS J1427−608 may be a PeV particle accelerator. We discuss the possible nature of HESS J1427−608 according to the multiwavelength spectral fittings. Given the relatively large errors, either a leptonic or a hadronic model can explain the multiwavelength data from radio to VHE γ -rays. The inferred magnetic field strength is a few micro-Gauss, which is smaller than the typical values of supernova remnants (SNRs) and is consistent with some pulsar wind nebulae (PWNe). On the other hand, the flat γ -ray spectrum is slightly different from typical PWNe but is similar to that of some known SNRs.« less

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

General 2.5 power law of metallic glasses

PubMed Central

Zeng, Qiaoshi; Lin, Yu; Liu, Yijin; Zeng, Zhidan; Shi, Crystal Y.; Zhang, Bo; Lou, Hongbo; Sinogeikin, Stanislav V.; Kono, Yoshio; Kenney-Benson, Curtis; Park, Changyong; Yang, Wenge; Wang, Weihua; Sheng, Hongwei; Mao, Ho-kwang; Mao, Wendy L.

2016-01-01

Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its “disordered” structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous “composition” change of 4f-localized “big Ce” to 4f-itinerant “small Ce,” indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs. PMID:26831105

Punctuated equilibrium and power law in economic dynamics

NASA Astrophysics Data System (ADS)

Gupta, Abhijit Kar

2012-02-01

This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called 'feedback' was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of 'fitness' and 'selection' in the present model of economic evolution.

Robust model comparison disfavors power law cosmology

NASA Astrophysics Data System (ADS)

Shafer, Daniel L.

2015-05-01

Late-time power law expansion has been proposed as an alternative to the standard cosmological model and shown to be consistent with some low-redshift data. We test power law expansion against the standard flat Λ CDM cosmology using goodness-of-fit and model comparison criteria. We consider type Ia supernova (SN Ia) data from two current compilations (JLA and Union2.1) along with a current set of baryon acoustic oscillation (BAO) measurements that includes the high-redshift Lyman-α forest measurements from BOSS quasars. We find that neither power law expansion nor Λ CDM is strongly preferred over the other when the SN Ia and BAO data are analyzed separately but that power law expansion is strongly disfavored by the combination. We treat the Rh=c t cosmology (a constant rate of expansion) separately and find that it is conclusively disfavored by all combinations of data that include SN Ia observations and a poor overall fit when systematic errors in the SN Ia measurements are ignored, despite a recent claim to the contrary. We discuss this claim and some concerns regarding hidden model dependence in the SN Ia data.

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

NASA Astrophysics Data System (ADS)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

Power-law relaxation in human violent conflicts

NASA Astrophysics Data System (ADS)

Picoli, Sergio; Antonio, Fernando J.; Itami, Andreia S.; Mendes, Renio S.

2017-08-01

We study relaxation patterns of violent conflicts after bursts of activity. Data were obtained from available catalogs on the conflicts in Iraq, Afghanistan and Northern Ireland. We find several examples in each catalog for which the observed relaxation curves can be well described by an asymptotic power-law decay (the analog of the Omori's law in geophysics). The power-law exponents are robust, nearly independent of the conflict. We also discuss the exogenous or endogenous nature of the shocks. Our results suggest that violent conflicts share with earthquakes and other natural and social phenomena a common feature in the dynamics of aftershocks.

29 CFR 102.35 - Duties and powers of administrative law judges; stipulations of cases to administrative law...

Code of Federal Regulations, 2010 CFR

2010-07-01

... 29 Labor 2 2010-07-01 2010-07-01 false Duties and powers of administrative law judges; stipulations of cases to administrative law judges or to the Board; assignment and powers of settlement judges... Practices 1 Hearings § 102.35 Duties and powers of administrative law judges; stipulations of cases to...

Deformation of a Capsule in a Power-Law Shear Flow

PubMed Central

2016-01-01

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values. PMID:27840656

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816

On the Linearly-Balanced Kinetic Energy Spectrum

NASA Technical Reports Server (NTRS)

Lu, Huei,-Iin; Robertson, F. R.

1999-01-01

It is well known that the earth's atmospheric motion can generally be characterized by the two dimensional quasi-geostrophic approximation, in which the constraints on global integrals of kinetic energy, entrophy and potential vorticity play very important roles in redistributing the wave energy among different scales of motion. Assuming the hypothesis of Kolmogrov's local isotropy, derived a -3 power law of the equilibrium two-dimensional kinetic energy spectrum that entails constant vorticity and zero energy flows from the energy-containing wave number up to the viscous cutoff. In his three dimensional quasi-geostrophic theory, showed that the spectrum function of the vertical scale turbulence - expressible in terms of the available potential energy - possesses the same power law as the two dimensional kinetic energy spectrum. As the slope of kinetic energy spectrum in the inertial range is theoretically related to the predictability of the synoptic scales (Lorenz, 1969), many general circulation models includes a horizontal diffusion to provide reasonable kinetic energy spectra, although the actual power law exhibited in the atmospheric general circulation is controversial. Note that in either the atmospheric modeling or the observational analyses, the proper choice of wave number Index to represent the turbulence scale Is the degree of the Legendre polynomial.

Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

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.

Beyond the power law: Uncovering stylized facts in interbank networks

NASA Astrophysics Data System (ADS)

Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen

2015-06-01

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.

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.

On the structure and phase transitions of power-law Poissonian ensembles

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Oshanin, Gleb

2012-10-01

Power-law Poissonian ensembles are Poisson processes that are defined on the positive half-line, and that are governed by power-law intensities. Power-law Poissonian ensembles are stochastic objects of fundamental significance; they uniquely display an array of fractal features and they uniquely generate a span of important applications. In this paper we apply three different methods—oligarchic analysis, Lorenzian analysis and heterogeneity analysis—to explore power-law Poissonian ensembles. The amalgamation of these analyses, combined with the topology of power-law Poissonian ensembles, establishes a detailed and multi-faceted picture of the statistical structure and the statistical phase transitions of these elemental ensembles.

Cascade model of gamma-ray bursts: Power-law and annihilation-line components

NASA Technical Reports Server (NTRS)

Harding, A. K.; Sturrock, P. A.; Daugherty, J. K.

1988-01-01

If, in a neutron star magnetosphere, an electron is accelerated to an energy of 10 to the 11th or 12th power eV by an electric field parallel to the magnetic field, motion of the electron along the curved field line leads to a cascade of gamma rays and electron-positron pairs. This process is believed to occur in radio pulsars and gamma ray burst sources. Results are presented from numerical simulations of the radiation and photon annihilation pair production processes, using a computer code previously developed for the study of radio pulsars. A range of values of initial energy of a primary electron was considered along with initial injection position, and magnetic dipole moment of the neutron star. The resulting spectra was found to exhibit complex forms that are typically power law over a substantial range of photon energy, and typically include a dip in the spectrum near the electron gyro-frequency at the injection point. The results of a number of models are compared with data for the 5 Mar., 1979 gamma ray burst. A good fit was found to the gamma ray part of the spectrum, including the equivalent width of the annihilation line.

Can power-law scaling and neuronal avalanches arise from stochastic dynamics?

PubMed

Touboul, Jonathan; Destexhe, Alain

2010-02-11

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain activity and show that event size distributions defined as negative LFP peaks can be close to power-law distributions. However, this result is not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov-Smirnov test. Similar power-law scaling is observed for surrogate signals, suggesting that power-law scaling may be a generic property of thresholded stochastic processes. We next investigate this problem analytically, and show that, indeed, stochastic processes can produce spurious power-law scaling without the presence of underlying self-organized criticality. However, this power-law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov-Smirnov test. The same analysis was also performed on an artificial network known to display self-organized criticality. In this case, both the graphical representations and the rigorous statistical analysis reveal with no ambiguity that the avalanche size is distributed as a power-law. We conclude that logarithmic representations can lead to spurious power-law scaling induced by the stochastic nature of the phenomenon. This apparent power-law scaling does not constitute a proof of self-organized criticality, which should be demonstrated by more stringent statistical tests.

VERITAS Observations of Six Bright, Hard-Spectrum Fermi-LAT Blazars

NASA Technical Reports Server (NTRS)

E. Aliu; Archambault, S.; Arlen, T.; Aune, T.; Beilicke, M.; Benbow, W.; Boettcher, M.; Bouvier, A.; Buckley, J. H.; Bugaev, V.;

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

Resolving the Crab Nebula with Direct Hard X-Ray Imaging

NASA Technical Reports Server (NTRS)

Swartz, Douglas A.; Ramsey, Brian D.; Tennant, Allyn F.; Dietz, Kurtis L.; Apple, Jeff A.; Gaskin, Jessica A.; Weisskopf, Martin

2008-01-01

We report the first direct hard (25--60 keV) X-ray imaging observation of the Crab Nebula that resolves structure to approximately 0.25 pc. The observation was performed over a 1.4 hour period during a balloon flight from Ft. Sumner, NM, on 2007 May 27. The source was detected in the energy band above the atmospheric cutoff at approx.25 keV and below the mirror graze angle cutoff at approx.60 keV. The image shows elongation about 25 degrees E of N in the direction along the plane of the torus (and perpendicular to the jet axis) with a slight surface-brightness enhancement NE of the pulsar. The spectrum within a 1.7 arcminute radius region centered on the Crab pulsar can be fitted with a Gamma=2 power law absorbed by an atmospheric column consistent with the balloon altitude at the time of observation.

Peptide kinetics from picoseconds to microseconds using boxed molecular dynamics: Power law rate coefficients in cyclisation reactions

NASA Astrophysics Data System (ADS)

Shalashilin, Dmitrii V.; Beddard, Godfrey S.; Paci, Emanuele; Glowacki, David R.

2012-10-01

Molecular dynamics (MD) methods are increasingly widespread, but simulation of rare events in complex molecular systems remains a challenge. We recently introduced the boxed molecular dynamics (BXD) method, which accelerates rare events, and simultaneously provides both kinetic and thermodynamic information. We illustrate how the BXD method may be used to obtain high-resolution kinetic data from explicit MD simulations, spanning picoseconds to microseconds. The method is applied to investigate the loop formation dynamics and kinetics of cyclisation for a range of polypeptides, and recovers a power law dependence of the instantaneous rate coefficient over six orders of magnitude in time, in good agreement with experimental observations. Analysis of our BXD results shows that this power law behaviour arises when there is a broad and nearly uniform spectrum of reaction rate coefficients. For the systems investigated in this work, where the free energy surfaces have relatively small barriers, the kinetics is very sensitive to the initial conditions: strongly non-equilibrium conditions give rise to power law kinetics, while equilibrium initial conditions result in a rate coefficient with only a weak dependence on time. These results suggest that BXD may offer us a powerful and general algorithm for describing kinetics and thermodynamics in chemical and biochemical systems.

NuSTAR Hard X-Ray Observations of the Energetic Millisecond Pulsars PSR B1821-24, PSR B1937+21, and PSR J0218+4232

NASA Astrophysics Data System (ADS)

Gotthelf, E. V.; Bogdanov, S.

2017-08-01

We present Nuclear Spectroscopic Telescope Array (NuSTAR) hard X-ray timing and spectroscopy of the three exceptionally energetic rotation-powered millisecond pulsars PSRs B1821-24, B1937+21, and J0218+4232. By correcting for the frequency and phase drifts of the NuSTAR onboard clock, we are able to recover the intrinsic hard X-ray pulse profiles of all three pulsars with a resolution down to ≤slant 15 μ {{s}}. The substantial reduction of background emission relative to previous broadband X-ray observations allows us to detect for the first time pulsed emission up to ˜50 keV, ˜20 keV, and ˜25 keV for the three pulsars, respectively. We conduct phase-resolved spectroscopy in the 0.5-79 keV range for all three objects, obtaining the best measurements yet of the broadband spectral shape and high-energy pulsed emission to date. We find extensions of the same power-law continua seen at lower energies, with no conclusive evidence for a spectral turnover or break. Extrapolation of the X-ray power-law spectrum to higher energies reveals that a turnover in the 100 keV to 100 MeV range is required to accommodate the high-energy γ-ray emission observed with Fermi-LAT, similar to the spectral energy distribution observed for the Crab pulsar.

NuSTAR Hard X-ray Observations of the Energetic Millisecond Pulsars PSR B1821-24, PSR B1937+21, and PSR J0218+4232

NASA Astrophysics Data System (ADS)

Gotthelf, Eric V.; Bogdanov, Slavko

2017-08-01

We present NuSTAR hard X-ray timing and spectroscopy of the three exceptionally energetic rotation-powered millisecond pulsars PSRs B1821-24, B1937+21, and J0218+4232. By correcting for frequency and phase drifts of the NuSTAR on-board clock we are able to recover the intrinsic hard X-ray pulse profiles of all three pulsars with a resolution down to <15 ms. The substantial reduction of background emission relative to previous broad-band X-ray observations allows us to detect for the first time pulsed emission up to ~50 keV, ~20 keV, and ~25 keV, for the three pulsars, respectively. We conduct phase-resolved spectroscopy in the 0.5 - 79 keV range for all three objects, obtaining the best yet measurements of the broad-band spectral shape and high-energy pulsed emission to date. We find extensions of the same power-law continua seen at lower energies, with no conclusive evidence for a spectral turnover or break. Extrapolation of the X-ray power-law spectrum to higher energies reveals that a turnover in the 100 keV to 100 MeV range is required to accommodate the high energy gamma-ray emission observed with Fermi LAT, similar to the broad-band spectral energy distribution observed for the Crab pulsar.

Renormalization group approach to power-law modeling of complex metabolic networks.

PubMed

Hernández-Bermejo, Benito

2010-08-07

In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations. Copyright 2010 Elsevier Ltd. All rights reserved.

Power Spectrum of Atmospheric Scintillation for the Deep Space Network Goldstone Ka-Band Downlink

NASA Technical Reports Server (NTRS)

Ho, C.; Wheelon, A.

2004-01-01

Dynamic signal fluctuations due to atmospheric scintillations may impair the Ka-band (around 32-GHz) link sensitivities for a low-margin Deep Space Network (DSN) receiving system. The ranges of frequency and power of the fast fluctuating signals (time scale less than 1 min) are theoretically investigated using the spatial covariance and turbulence theory. Scintillation power spectrum solutions are derived for both a point receiver and a finite-aperture receiver. The aperture-smoothing frequency ((omega(sub s)), corner frequency ((omega(sub c)), and damping rate are introduced to define the shape of the spectrum for a finite-aperture antenna. The emphasis is put on quantitatively describing the aperture-smoothing effects and graphically estimating the corner frequency for a large aperture receiver. Power spectral shapes are analyzed parametrically in detail through both low- and high-frequency approximations. It is found that aperture-averaging effects become significant when the transverse correlation length of the scintillation is smaller than the antenna radius. The upper frequency or corner frequency for a finite-aperture receiver is controlled by both the Fresnel frequency and aperture-smoothing frequency. Above the aperture-smoothing frequency, the spectrum rolls off at a much faster rate of exp (-omega(sup 2)/omega(sup 2, sub s), rather than omega(sup -8/3), which is customary for a point receiver. However, a relatively higher receiver noise level can mask the fast falling-off shape and make it hard to be identified. We also predict that when the effective antenna radius a(sub r) less than or = 6 m, the corner frequency of its power spectrum becomes the same as that for a point receiver. The aperture-smoothing effects are not obvious. We have applied these solutions to the scenario of a DSN Goldstone 34-m-diameter antenna and predicted the power spectrum shape for the receiving station. The maximum corner frequency for the receiver (with omega(sub s) = 0

X-ray spectrum and variability of the quasar PG 1211+143

NASA Technical Reports Server (NTRS)

Yaqoob, Tahir; Serlemitsos, Peter; Mushotzky, Richard; Madejski, Greg; Turner, T. Jane; Kunieda, Hideyo

1994-01-01

We present preliminary results of an ASCA observation of the classic soft-excess quasar PG 1211+143. The overall ASCA spectrum can be characterized by a blackbody with a temperature of approximately 125 eV (quasar frame) and a power law with photon index of approximately 2. Simultaneous ROSAT data are suggestive of further steepening of the spectrum just below the ASCA band. Comparison with previous observations shows that the soft flux in the 0.1-2 keV band varies by at least a factor of approximately 16, scaling roughly as the square of the hard flux in the 2-10 keV band over a timescale of approximately 13.5 yr. We also find evidence of short-term amplitude variability of up to a factor of approximately 2 on a timescale of approximately 2 x 10(exp 4) sec, in both the soft and hard flux so that the soft and hard photons are likely to originate from the same, compact, region. The data rule out variable absorption (cold or ionized) as the origin of the soft excess, favoring an intrinsic emission component. However, we argue against optically thin emission for the 'blue bump' in PG 1211+143. The large amplitude soft X-ray variability may be indicative of variations in the effective temperature, or peak, of the soft component. There is only marginal evidence for Fe K line emission between 6-7 keV in the quasar frame.

On the universality of power laws for tokamak plasma predictions

NASA Astrophysics Data System (ADS)

Garcia, J.; Cambon, D.; Contributors, JET

2018-02-01

Significant deviations from well established power laws for the thermal energy confinement time, obtained from extensive databases analysis as the IPB98(y,2), have been recently reported in dedicated power scans. In order to illuminate the adequacy, validity and universality of power laws as tools for predicting plasma performance, a simplified analysis has been carried out in the framework of a minimal modeling for heat transport which is, however, able to account for the interplay between turbulence and collinear effects with the input power known to play a role in experiments with significant deviations from such power laws. Whereas at low powers, the usual scaling laws are recovered with little influence of other plasma parameters, resulting in a robust power low exponent, at high power it is shown how the exponents obtained are extremely sensitive to the heating deposition, the q-profile or even the sampling or the number of points considered due to highly non-linear behavior of the heat transport. In particular circumstances, even a minimum of the thermal energy confinement time with the input power can be obtained, which means that the approach of the energy confinement time as a power law might be intrinsically invalid. Therefore plasma predictions with a power law approximation with a constant exponent obtained from a regression of a broad range of powers and other plasma parameters which can non-linearly affect and suppress heat transport, can lead to misleading results suggesting that this approach should be taken cautiously and its results continuously compared with modeling which can properly capture the underline physics, as gyrokinetic simulations.

Kant on causal laws and powers.

PubMed

Henschen, Tobias

2014-12-01

The aim of the paper is threefold. Its first aim is to defend Eric Watkins's claim that for Kant, a cause is not an event but a causal power: a power that is borne by a substance, and that, when active, brings about its effect, i.e. a change of the states of another substance, by generating a continuous flow of intermediate states of that substance. The second aim of the paper is to argue against Watkins that the Kantian concept of causal power is not the pre-critical concept of real ground but the category of causality, and that Kant holds with Hume that causal laws cannot be inferred non-inductively (that he accordingly has no intention to show in the Second analogy or elsewhere that events fall under causal laws). The third aim of the paper is to compare the Kantian position on causality with central tenets of contemporary powers ontology: it argues that unlike the variants endorsed by contemporary powers theorists, the Kantian variants of these tenets are resistant to objections that neo-Humeans raise to these tenets.

NuSTAR Detection of a Hard X-Ray Source in the Supernova Remnant-molecular Cloud Interaction Site of IC 443

NASA Astrophysics Data System (ADS)

Zhang, Shuo; Tang, Xiaping; Zhang, Xiao; Sun, Lei; Gotthelf, Eric V.; Zhang, Zhi-Yu; Li, Hui; Cheng, Allen; Pasham, Dheeraj; Baganoff, Frederick K.; Perez, Kerstin; Hailey, Charles J.; Mori, Kaya

2018-06-01

We report on a broadband study of a complex X-ray source (1SAX J0618.0+2227) associated with the interaction site of the supernova remnant (SNR) IC 443 and ambient molecular cloud (MC) using NuSTAR, XMM-Newton, and Chandra observations. Its X-ray spectrum is composed of both thermal and nonthermal components. The thermal component can be equally well represented by either a thin plasma model with kT = 0.19 keV or a blackbody model with kT = 0.11 keV. The nonthermal component can be fit with either a power law with Γ ∼ 1.7 or a cutoff power law with Γ ∼ 1.5 and a cutoff energy at E cut ∼ 18 keV. Using the newly obtained NuSTAR data set, we test three possible scenarios for isolated X-ray sources in the SNR–MC interaction site: (1) a pulsar wind nebula (PWN); (2) an SNR ejecta fragment; and (3) a shocked molecular clump. We conclude that this source is most likely composed of an SNR ejecta (or a PWN) and surrounding shocked molecular clumps. The nature of this hard X-ray source in the SNR–MC interaction site of IC 443 may shed light on unidentified X-ray sources with hard X-ray spectra in rich environments for star-forming regions, such as the Galactic center.

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.

First NuSTAR observations of the BL Lac - type blazar PKS 2155-304: constraints on the jet content and distribution of radiating particles

NASA Astrophysics Data System (ADS)

Madejski, Grzegorz; Nalewajko, Krzysztof; Madsen, Kristin; Chiang, James; Balokovic, Mislav; Paneque, David; Furniss, Amy; NuSTAR Team

2017-01-01

Current scenarios for emission mechanisms operating in relativistic jets in AGN involve synchrotron emission for the radio through UV spectrum, and inverse Compton for hard X-rays through γ-rays, but the particle content of relativistic jets - whether they are dominated by proton-electron, or e +/e- plasma - has not been established. Our first hard X-ray observations with NuSTAR of the BL Lac type blazar PKS 2155-304, augmented by XMM-Newton data, reveal the 0.5-60 keV spectrum as best-described by a soft power law component dominating below 10 keV (photon index of 3 at 2 keV), and a hard power-law tail (index 2), dominating in the 20-60 keV range. The hard X-ray tail can be smoothly joined to the quasi-simultaneous Fermi/LAT γ-ray spectrum by a synchrotron self-Compton component produced by an electron distribution with index p =2.2. The jet content needs to (globally) obey charge neutrality; assuming that the power-law electron distribution extends down to the Lorentz factor of 1, and one proton per electron, yields an unrealistically high total jet power of 1047 erg/s. This can be reduced by two orders of magnitude by considering a significant presence of e +/e- pairs with lepton-to-proton ratio of at least 30.

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 spectrum analysis for defect screening in integrated circuit devices

DOEpatents

Tangyunyong, Paiboon; Cole Jr., Edward I.; Stein, David J.

2011-12-01

A device sample is screened for defects using its power spectrum in response to a dynamic stimulus. The device sample receives a time-varying electrical signal. The power spectrum of the device sample is measured at one of the pins of the device sample. A defect in the device sample can be identified based on results of comparing the power spectrum with one or more power spectra of the device that have a known defect status.

Increased Service Use Among Children With Autism Spectrum Disorder Associated With Mental Health Parity Law.

PubMed

Stuart, Elizabeth A; McGinty, Emma E; Kalb, Luther; Huskamp, Haiden A; Busch, Susan H; Gibson, Teresa B; Goldman, Howard; Barry, Colleen L

2017-02-01

Health care services for children with autism spectrum disorder are often expensive and frequently not covered under private health insurance. The 2008 Paul Wellstone and Pete Domenici Mental Health Parity and Addiction Equity Act was viewed as a possible means of improving access by eliminating differences between behavioral health and medical/surgical benefits. We examined whether the legislation was associated with increased use of and spending on mental health care and functional services for children with autism spectrum disorder compared to the period prior to implementation of the law. We used nationwide health insurance commercial group claims data to examine trends in service use and spending among children with autism spectrum disorder before and after implementation of the law. For such children, implementation was associated with increased use of both mental health and non-mental health services. These increases in use were not associated with higher out-of-pocket spending, which suggests that the law improved financial protection for families. Project HOPE—The People-to-People Health Foundation, Inc.

Avalanches and power-law behaviour in lung inflation

NASA Astrophysics Data System (ADS)

Suki, Béla; Barabási, Albert-László; Hantos, Zoltán; Peták, Ferenc; Stanley, H. Eugene

1994-04-01

WHEN lungs are emptied during exhalation, peripheral airways close up1. For people with lung disease, they may not reopen for a significant portion of inhalation, impairing gas exchange2,3. A knowledge of the mechanisms that govern reinflation of collapsed regions of lungs is therefore central to the development of ventilation strategies for combating respiratory problems. Here we report measurements of the terminal airway resistance, Rt , during the opening of isolated dog lungs. When inflated by a constant flow, Rt decreases in discrete jumps. We find that the probability distribution of the sizes of the jumps and of the time intervals between them exhibit power-law behaviour over two decades. We develop a model of the inflation process in which 'avalanches' of airway openings are seen-with power-law distributions of both the size of avalanches and the time intervals between them-which agree quantitatively with those seen experimentally, and are reminiscent of the power-law behaviour observed for self-organized critical systems4. Thus power-law distributions, arising from avalanches associated with threshold phenomena propagating down a branching tree structure, appear to govern the recruitment of terminal airspaces.

Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems.

PubMed

Riser, Roman; Osipov, Vladimir Al; Kanzieper, Eugene

2017-05-19

We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→∞ limit of the exact solution furnishes the main result of this study-a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.

Estimating the Crustal Power Spectrum From Vector Magsat Data: Crustal Power Spectrum

NASA Technical Reports Server (NTRS)

Lowe, David A. J.; Parker, Robert L.; Purucker, Michael E.; Constable, Catherine G.

2000-01-01

The Earth's magnetic field can be subdivided into core and crustal components and we seek to characterize the crustal part through its spatial power spectrum (R(sub l)). We process vector Magsat data to isolate the crustal field and then invert power spectral densities of flight-local components along-track for R(sub l) following O'Brien et al. [1999]. Our model (LPPC) is accurate up to approximately degree 45 (lambda=900 km) - this is the resolution limit of our data and suggests that global crustal anomaly maps constructed from vector Magsat data should not contain features with wavelengths less than 900 km. We find continental power spectra to be greater than oceanic ones and attribute this to the relative thicknesses of continental and oceanic crust.

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

An observation of the Galactic center hard X-ray source, 1E 1740.7-2942, with the Caltech coded-aperture telescope

NASA Technical Reports Server (NTRS)

Heindl, William A.; Cook, Walter R.; Grunsfeld, John M.; Palmer, David M.; Prince, Thomas A.; Schindler, Stephen M.; Stone, Edward C.

1993-01-01

The Galactic center region hard X-ray source IE 1740.7-2942 has been observed with the Caltech Gamma-Ray Imaging Payload (GRIP) from Alice Springs, Australia, on 1988 April 12 and on 1989 April 3 and 4. We report here results from the 1989 measurements based on 14 hr of observation of the Galactic center region. The observations showed IE 1740.7-2942 to be in its normal state, having a spectrum between 35 and 200 keV characterized by a power law with an exponent of -2.2 +/- 0.3 and flux at 100 keV of (7.0 +/- 0.7) x 10 exp -5 sq cm s keV. No flux was detected above 200 keV. A search for time variability in the spectrum of IE 1740.7-2942 on one hour time scales showed no evidence for variability.

Association between power law coefficients of the anatomical noise power spectrum and lesion detectability in breast imaging modalities

NASA Astrophysics Data System (ADS)

Chen, Lin; Abbey, Craig K.; Boone, John M.

2013-03-01

Previous research has demonstrated that a parameter extracted from a power function fit to the anatomical noise power spectrum, β, may be predictive of breast mass lesion detectability in x-ray based medical images of the breast. In this investigation, the value of β was compared with a number of other more widely used parameters, in order to determine the relationship between β and these other parameters. This study made use of breast CT data sets, acquired on two breast CT systems developed in our laboratory. A total of 185 breast data sets in 183 women were used, and only the unaffected breast was used (where no lesion was suspected). The anatomical noise power spectrum computed from two-dimensional region of interests (ROIs), was fit to a power function (NPS(f) = α f-β), and the exponent parameter (β) was determined using log/log linear regression. Breast density for each of the volume data sets was characterized in previous work. The breast CT data sets analyzed in this study were part of a previous study which evaluated the receiver operating characteristic (ROC) curve performance using simulated spherical lesions and a pre-whitened matched filter computer observer. This ROC information was used to compute the detectability index as well as the sensitivity at 95% specificity. The fractal dimension was computed from the same ROIs which were used for the assessment of β. The value of β was compared to breast density, detectability index, sensitivity, and fractal dimension, and the slope of these relationships was investigated to assess statistical significance from zero slope. A statistically significant non-zero slope was considered to be a positive association in this investigation. All comparisons between β and breast density, detectability index, sensitivity at 95% specificity, and fractal dimension demonstrated statistically significant association with p < 0.001 in all cases. The value of β was also found to be associated with patient age and

High energy power-law tail in X-ray binaries and bulk Comptonization due to an outflow from a disk

NASA Astrophysics Data System (ADS)

Kumar, Nagendra

2018-02-01

We study the high energy power-law tail emission of X-ray binaries (XRBs) by a bulk Comptonization process which is usually observed in the very high soft (VHS) state of black hole (BH) XRBs and the high soft (HS) state of the neutron star (NS) and BH XRBs. Earlier, to generate the power-law tail in bulk Comptonization framework, a free-fall converging flow into BH or NS had been considered as a bulk region. In this work, for a bulk region we consider mainly an outflow geometry from the accretion disk which is bounded by a torus surrounding the compact object. We have two choices for an outflow geometry: (i) collimated flow and (ii) conical flow of opening angle θ _b and the axis is perpendicular to the disk. We also consider an azimuthal velocity of the torus fluids as a bulk motion where the fluids are rotating around the compact object (a torus flow). We find that the power-law tail can be generated in a torus flow having large optical depth and bulk speed (>0.75 c), and in conical flow with θ _b > ˜ 30° for a low value of Comptonizing medium temperature. Particularly, in conical flow the low opening angle is more favourable to generate the power-law tail in both the HS state and the VHS state. We notice that when the outflow is collimated, then the emergent spectrum does not have power-law component for a low Comptonizing medium temperature.

Nonthermal electron-positron pairs and the break in the hard X-ray spectrum of NGC 4151

NASA Technical Reports Server (NTRS)

Coppi, Paolo S.; Zdziarski, Andrzej A.

1992-01-01

The recent observation by the detectors on board Granat of a spectral steepening above about 50 keV imposes a constraint on possible emission models for NGC 4151. This steepening, for example, is not well fitted by an exponential rollover characteristic of a purely thermal model, or by a Compton-downscattered power law. We find that this spectral behavior is consistent with that produced by a photon-starved nonthermal pair plasma with high compactness. This is the first quantitative test of the nonthermal pair plasma model against broad-band X-ray/gamma-ray observations. Above 200 keV or so, the nonthermal pair plasma model predicts an upturn in the spectrum, and a thermal annihilation feature around 511 keV. Such spectral behavior should be looked for with GRO.

The effect of stochastic re-acceleration on the energy spectrum of shock-accelerated protons

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

Afanasiev, Alexandr; Vainio, Rami; Kocharov, Leon

2014-07-20

The energy spectra of particles in gradual solar energetic particle (SEP) events do not always have a power-law form attributed to the diffusive shock acceleration mechanism. In particular, the observed spectra in major SEP events can take the form of a broken (double) power law. In this paper, we study the effect of a process that can modify the power-law spectral form produced by the diffusive shock acceleration: the stochastic re-acceleration of energetic protons by enhanced Alfvénic turbulence in the downstream region of a shock wave. There are arguments suggesting that this process can be important when the shock propagatesmore » in the corona. We consider a coronal magnetic loop traversed by a shock and perform Monte Carlo simulations of interactions of shock-accelerated protons with Alfvén waves in the loop. The wave-particle interactions are treated self-consistently, so the finiteness of the available turbulent energy is taken into account. The initial energy spectrum of particles is taken to be a power law. The simulations reveal that the stochastic re-acceleration leads either to the formation of a spectrum that is described in a wide energy range by a power law (although the resulting power-law index is different from the initial one) or to a broken power-law spectrum. The resulting spectral form is determined by the ratio of the energy density of shock-accelerated protons to the wave energy density in the shock's downstream region.« less

Evapotranspiration Power Law in Self-Organized and Human-Managed Ecosystems

NASA Astrophysics Data System (ADS)

Zeng, R.; Cai, X.

2017-12-01

Natural systems display a profound degree of self-organization, often apparent even to the untrained eye. However, in this age of increased coupling among human and natural systems, it is unclear to what degree natural organization principles continue to govern human-managed landscapes. Here we present an emerging characteristic of terrestrial evapotranspiration (ET), one of the key components of the water cycle and energy budget, adhered to by both naturally organized and intensively managed landscapes. We find that ET variance and ET mean for ecosystems throughout the world with diverse climate conditions, vegetation structures, and land covers and land uses organize themselves according to a specific power law curve. From multi-source observations, the ET power law curve stands true through varying spatial scales, from field to region. Moreover, a phenomenon of similar ecosystems gravitating toward particular segments of the power law curve, suggests that the feature of self-optimization of ecosystems establishes the ET power law together with climatic conditions. Perhaps surprisingly, we find that landscapes persistently follow the power law curve even upon human-induced transition from rain-fed to irrigated agriculture in the American High Plains and from wetland to agricultural land in American Midwest. As such, the ET power law can be an informative tool for predicting consequences of anthropogenic disturbances to the hydrologic cycle and understanding constraints to sustainable land use.

Surprises from a Deep ASCA Spectrum of the Broad Absorption Line Quasar PHL 5200

NASA Technical Reports Server (NTRS)

Mathur, Smita; Matt, G.; Green, P. J.; Elvis, M.; Singh, K. P.

2002-01-01

We present a deep (approx. 85 ks) ASCA observation of the prototype broad absorption line quasar (BALQSO) PHL 5200. This is the best X-ray spectrum of a BALQSO yet. We find the following: (1) The source is not intrinsically X-ray weak. (2) The line-of-sight absorption is very strong, with N(sub H) = 5 x 10(exp 23)/sq cm. (3) The absorber does not cover the source completely; the covering fraction is approx. 90%. This is consistent with the large optical polarization observed in this source, implying multiple lines of sight. The most surprising result of this observation is that (4) the spectrum of this BALQSO is not exactly similar to other radio-quiet quasars. The hard X-ray spectrum of PHL 5200 is steep, with the power-law spectral index alpha approx. 1.5. This is similar to the steepest hard X-ray slopes observed so far. At low redshifts, such steep slopes are observed in narrow-line Seyfert 1 (NLS1) galaxies, believed to be accreting at a high Eddington rate. This observation strengthens the analogy between BALQSOs and NLS1 galaxies and supports the hypothesis that BALQSOs represent an early evolutionary state of quasars. It is well accepted that the orientation to the line of sight determines the appearance of a quasar: age seems to play a significant role as well.

VERITAS Observations of Six Bright, Hard-Spectrum Fermi-LAT Blazars

DOE PAGES

Aliu, E.; Archambault, S.; Arlen, T.; ...

2012-10-25

In this paper, we report on VERITAS very high energy (VHE; E ≥ 100 GeV) observations of six blazars selected from the Fermi Large Area Telescope First Source Catalog (1FGL). The gamma-ray emission from 1FGL sources was extrapolated up to the VHE band, taking gamma-ray absorption by the extragalactic background light into account. This allowed the selection of six bright, hard-spectrum blazars that were good candidate TeV emitters. Spectroscopic redshift measurements were attempted with the Keck Telescope for the targets without Sloan Digital Sky Survey spectroscopic data. No VHE emission is detected during the observations of the six sources describedmore » here. Corresponding TeV upper limits are presented, along with contemporaneous Fermi observations and non-concurrent Swift UVOT and X-Ray Telescope data. The blazar broadband spectral energy distributions (SEDs) are assembled and modeled with a single-zone synchrotron self-Compton model. Finally, the SED built for each of the six blazars shows a synchrotron peak bordering between the intermediate- and high-spectrum-peak classifications, with four of the six resulting in particle-dominated emission regions.« less

Constraints on cosmological parameters in power-law cosmology

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

Rani, Sarita; Singh, J.K.; Altaibayeva, A.

In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H{sub 0} (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not withmore » H(z) data. However, the constraints obtained on and i.e. H{sub 0} average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → −1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.« less

Do wealth distributions follow power laws? Evidence from ‘rich lists’

NASA Astrophysics Data System (ADS)

Brzezinski, Michal

2014-07-01

We use data on the wealth of the richest persons taken from the 'rich lists' provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012, and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.

On syntheses of the X-ray background with power-law sources

NASA Technical Reports Server (NTRS)

Dezotti, G.; Boldt, E. A.; Cavaliere, A.; Danese, L.; Franceschini, A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.

1981-01-01

The conditions under which the combined emission from power law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit sleeper spectra at higher energies.

On syntheses of the X-ray background with power-law sources

NASA Astrophysics Data System (ADS)

De Zotti, G.; Boldt, E. A.; Cavaliere, A.; Danese, L.; Franceschini, A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.

1981-08-01

The conditions under which the combined emission from power law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit sleeper spectra at higher energies.

[Effects of noise and music on EEG power spectrum].

PubMed

Yuan, Q; Liu, X H; Li, D C; Wang, H L; Liu, Y S

2000-12-01

Objective. To observe the effect of noise and music on EEG power spectrum. Method. 12 healthy male pilots aged 30 +/- 0.58 years served as the subjects. Dynamic EEG from 16 regions was recorded during quiet, under noise or when listening to music using Oxford MR95 Holter recorder. Changes of EEG power spectrum of delta, theta, alpha1, alpha2, beta1 and beta2, frequency components in 16 regions were analyzed. Result. The total alpha1 power was significantly decreased, while the total theta power was significantly increased when listening to music; It implies that the interhemispheric transmission of information in the frontotemporal areas might be involved. Conclusion. The changes of the EEG power spectrum were closely related to man's emotions; relaxation was associated with music; Individual difference exists in the influence of sound on EEG.

Vortex clustering and universal scaling laws in two-dimensional quantum turbulence.

PubMed

Skaugen, Audun; Angheluta, Luiza

2016-03-01

We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal -5/3 scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The -5/3 scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a -5/3 exponent.

Temperature profile and equipartition law in a Langevin harmonic chain

NASA Astrophysics Data System (ADS)

Kim, Sangrak

2017-09-01

Temperature profile in a Langevin harmonic chain is explicitly derived and the validity of the equipartition law is checked. First, we point out that the temperature profile in previous studies does not agree with the equipartition law: In thermal equilibrium, the temperature profile deviates from the same temperature distribution against the equipartition law, particularly at the ends of the chain. The matrix connecting temperatures of the heat reservoirs and the temperatures of the harmonic oscillators turns out to be a probability matrix. By explicitly calculating the power spectrum of the probability matrix, we will show that the discrepancy comes from the neglect of the power spectrum in higher frequency ω, which is in decay mode, and related with the imaginary number of wave number q.

Power spectrum of dark matter substructure in strong gravitational lenses

NASA Astrophysics Data System (ADS)

Diaz Rivero, Ana; Cyr-Racine, Francis-Yan; Dvorkin, Cora

2018-01-01

Studying the smallest self-bound dark matter structure in our Universe can yield important clues about the fundamental particle nature of dark matter. Galaxy-scale strong gravitational lensing provides a unique way to detect and characterize dark matter substructures at cosmological distances from the Milky Way. Within the cold dark matter (CDM) paradigm, the number of low-mass subhalos within lens galaxies is expected to be large, implying that their contribution to the lensing convergence field is approximately Gaussian and could thus be described by their power spectrum. We develop here a general formalism to compute from first principles the substructure convergence power spectrum for different populations of dark matter subhalos. As an example, we apply our framework to two distinct subhalo populations: a truncated Navarro-Frenk-White subhalo population motivated by standard CDM, and a truncated cored subhalo population motivated by self-interacting dark matter (SIDM). We study in detail how the subhalo abundance, mass function, internal density profile, and concentration affect the amplitude and shape of the substructure power spectrum. We determine that the power spectrum is mostly sensitive to a specific combination of the subhalo abundance and moments of the mass function, as well as to the average tidal truncation scale of the largest subhalos included in the analysis. Interestingly, we show that the asymptotic slope of the substructure power spectrum at large wave number reflects the internal density profile of the subhalos. In particular, the SIDM power spectrum exhibits a characteristic steepening at large wave number absent in the CDM power spectrum, opening the possibility of using this observable, if at all measurable, to discern between these two scenarios.

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

The High Energy X-ray Spectrum of 4U1700-37 Observed from OSO-8

NASA Technical Reports Server (NTRS)

Dolan, J. F.; Coe, M. J.; Crannell, C. J.; Dennis, B. R.; Frost, K. J.; Maurer, G. S.; Orwig, L. E.

1979-01-01

The most intense hard X-ray source in the confused region in Scorpius is identified as 4U1700-37. The 3.4-day modulation is seen above 20 keV with the intensity during eclipse being consistent with zero flux. The photon-number spectrum from 20 to 150 keV is well represented by a single power law with a photo-number spectral index of -2.77 + or - 0.35 or by a thermal bremsstrahlung spectrum with kT = 27 96.8-min X-ray modulation previously reported at lower energies. Despite the difficulties in reconciling both the lack of periodic modulation in the emitted X-radiation and the orbital dynamics of the system with theories of the evolution and physical properties of neutron stars, the observed properties of 4U1700-37 are all consistent with the source being a spherically accreting neutron star rather than a black hole.

The bias of the log power spectrum for discrete surveys

NASA Astrophysics Data System (ADS)

Repp, Andrew; Szapudi, István

2018-03-01

A primary goal of galaxy surveys is to tighten constraints on cosmological parameters, and the power spectrum P(k) is the standard means of doing so. However, at translinear scales P(k) is blind to much of these surveys' information - information which the log density power spectrum recovers. For discrete fields (such as the galaxy density), A* denotes the statistic analogous to the log density: A* is a `sufficient statistic' in that its power spectrum (and mean) capture virtually all of a discrete survey's information. However, the power spectrum of A* is biased with respect to the corresponding log spectrum for continuous fields, and to use P_{A^*}(k) to constrain the values of cosmological parameters, we require some means of predicting this bias. Here, we present a prescription for doing so; for Euclid-like surveys (with cubical cells 16h-1 Mpc across) our bias prescription's error is less than 3 per cent. This prediction will facilitate optimal utilization of the information in future galaxy surveys.

Particle acceleration model for the broad-band baseline spectrum of the Crab nebula

NASA Astrophysics Data System (ADS)

Fraschetti, F.; Pohl, M.

2017-11-01

We develop a simple one-zone model of the steady-state Crab nebula spectrum encompassing both the radio/soft X-ray and the GeV/multi-TeV observations. By solving the transport equation for GeV-TeV electrons injected at the wind termination shock as a log-parabola momentum distribution and evolved via energy losses, we determine analytically the resulting differential energy spectrum of photons. We find an impressive agreement with the observed spectrum of synchrotron emission, and the synchrotron self-Compton component reproduces the previously unexplained broad 200-GeV peak that matches the Fermi/Large Area Telescope (LAT) data beyond 1 GeV with the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) data. We determine the parameters of the single log-parabola electron injection distribution, in contrast with multiple broken power-law electron spectra proposed in the literature. The resulting photon differential spectrum provides a natural interpretation of the deviation from power law customarily fitted with empirical multiple broken power laws. Our model can be applied to the radio-to-multi-TeV spectrum of a variety of astrophysical outflows, including pulsar wind nebulae and supernova remnants, as well as to interplanetary shocks.

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.

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.

Joint resonant CMB power spectrum and bispectrum estimation

NASA Astrophysics Data System (ADS)

Meerburg, P. Daniel; Münchmeyer, Moritz; Wandelt, Benjamin

2016-02-01

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multivariate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multifrequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows us to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.

A robust power spectrum split cancellation-based spectrum sensing method for cognitive radio systems

NASA Astrophysics Data System (ADS)

Qi, Pei-Han; Li, Zan; Si, Jiang-Bo; Gao, Rui

2014-12-01

Spectrum sensing is an essential component to realize the cognitive radio, and the requirement for real-time spectrum sensing in the case of lacking prior information, fading channel, and noise uncertainty, indeed poses a major challenge to the classical spectrum sensing algorithms. Based on the stochastic properties of scalar transformation of power spectral density (PSD), a novel spectrum sensing algorithm, referred to as the power spectral density split cancellation method (PSC), is proposed in this paper. The PSC makes use of a scalar value as a test statistic, which is the ratio of each subband power to the full band power. Besides, by exploiting the asymptotic normality and independence of Fourier transform, the distribution of the ratio and the mathematical expressions for the probabilities of false alarm and detection in different channel models are derived. Further, the exact closed-form expression of decision threshold is calculated in accordance with Neyman—Pearson criterion. Analytical and simulation results show that the PSC is invulnerable to noise uncertainty, and can achive excellent detection performance without prior knowledge in additive white Gaussian noise and flat slow fading channels. In addition, the PSC benefits from a low computational cost, which can be completed in microseconds.

Scaling laws of aquatic locomotion

NASA Astrophysics Data System (ADS)

Sun, BoHua

2017-10-01

In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion C D( Re)2 = ( Sw)2 and its corresponding log law and power law. For power scaling law, ( Sw)2 = β n Re 2-1/ n , which is valid within the full spectrum of the Reynolds number Re = UL/ν from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw = ωAL/ν as Re ∝ ( Sw)σ, with σ = 2 for creeping flows, σ = 4=3 for laminar flows, σ = 10=9 and σ = 14=13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(ln Re+1:287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer's gait A; ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number

Angular power spectrum of galaxies in the 2MASS Redshift Survey

NASA Astrophysics Data System (ADS)

Ando, Shin'ichiro; Benoit-Lévy, Aurélien; Komatsu, Eiichiro

2018-02-01

We present the measurement and interpretation of the angular power spectrum of nearby galaxies in the 2MASS Redshift Survey catalogue with spectroscopic redshifts up to z ≈ 0.1. We detect the angular power spectrum up to a multipole of ℓ ≈ 1000. We find that the measured power spectrum is dominated by galaxies living inside nearby galaxy clusters and groups. We use the halo occupation distribution (HOD) formalism to model the power spectrum, obtaining a fit with reasonable parameters. These HOD parameters are in agreement with the 2MASS galaxy distribution we measure towards the known nearby galaxy clusters, confirming validity of our analysis.

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 MURCHISON WIDEFIELD ARRAY 21 cm POWER SPECTRUM ANALYSIS METHODOLOGY

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

Jacobs, Daniel C.; Beardsley, A. P.; Bowman, Judd D.

2016-07-10

We present the 21 cm power spectrum analysis approach of the Murchison Widefield Array Epoch of Reionization project. In this paper, we compare the outputs of multiple pipelines for the purpose of validating statistical limits cosmological hydrogen at redshifts between 6 and 12. Multiple independent data calibration and reduction pipelines are used to make power spectrum limits on a fiducial night of data. Comparing the outputs of imaging and power spectrum stages highlights differences in calibration, foreground subtraction, and power spectrum calculation. The power spectra found using these different methods span a space defined by the various tradeoffs between speed,more » accuracy, and systematic control. Lessons learned from comparing the pipelines range from the algorithmic to the prosaically mundane; all demonstrate the many pitfalls of neglecting reproducibility. We briefly discuss the way these different methods attempt to handle the question of evaluating a significant detection in the presence of foregrounds.« less

Stretched exponentials and power laws in granular avalanching

NASA Astrophysics Data System (ADS)

Head, D. A.; Rodgers, G. J.

1999-02-01

We introduce a model for granular surface flow which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion.

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.

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.

Power-law distribution in Japanese racetrack betting

NASA Astrophysics Data System (ADS)

Ichinomiya, Takashi

2006-08-01

Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)∝1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.

Robust Statistical Detection of Power-Law Cross-Correlation.

PubMed

Blythe, Duncan A J; Nikulin, Vadim V; Müller, Klaus-Robert

2016-06-02

We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram.

Robust Statistical Detection of Power-Law Cross-Correlation

PubMed Central

Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert

2016-01-01

We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630

First Year Wilkinson Microwave Anisotropy Probe(WMAP)Observations: The Angular Power Spectrum

NASA Technical Reports Server (NTRS)

Hinshaw, G.; Spergel, D. N.; Verde, L.; Hill, R. S.; Meyer, S. S.; Barnes, C.; Bennett, C. L.; Halpern, M.; Jarosik, N.; Kogut, A.

2003-01-01

We present the angular power spectrum derived from the first-year Wilkinson Microwave Anisotropy Probe (WMAP) sky maps. We study a variety of power spectrum estimation methods and data combinations and demonstrate that the results are robust. The data are modestly contaminated by diffuse Galactic foreground emission, but we show that a simple Galactic template model is sufficient to remove the signal. Point sources produce a modest contamination in the low frequency data. After masking approximately 700 known bright sources from the maps, we estimate residual sources contribute approximately 3500 mu sq Kappa at 41 GHz, and approximately 130 mu sq Kappa at 94 GHz, to the power spectrum [iota(iota + 1)C(sub iota)/2pi] at iota = 1000. Systematic errors are negligible compared to the (modest) level of foreground emission. Our best estimate of the power spectrum is derived from 28 cross-power spectra of statistically independent channels. The final spectrum is essentially independent of the noise properties of an individual radiometer. The resulting spectrum provides a definitive measurement of the CMB power spectrum, with uncertainties limited by cosmic variance, up to iota approximately 350. The spectrum clearly exhibits a first acoustic peak at iota = 220 and a second acoustic peak at iota approximately 540, and it provides strong support for adiabatic initial conditions. Researchers have analyzed the CT(sup Epsilon) power spectrum, and present evidence for a relatively high optical depth, and an early period of cosmic reionization. Among other things, this implies that the temperature power spectrum has been suppressed by approximately 30% on degree angular scales, due to secondary scattering.

Maximum Renyi entropy principle for systems with power-law Hamiltonians.

PubMed

Bashkirov, A G

2004-09-24

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0power-law part. Such a picture corresponds to some observed phenomena.

Power Spectrum Analysis of BNL Decay-Rate Data

DTIC Science & Technology

2010-01-01

1/31 Power Spectrum Analysis of BNL Decay-Rate Data P.A. Sturrocka,*, J.B. Buncherb, E. Fischbachb, J.T. Gruenwaldb, D. Javorsek...Power Spectrum Analysis of BNL Decay-Rate Data 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e...spectra in the rotational search band formed from BNL data and from ACRIM total solar irradiance data. Since rotation rate estimates derived from

[Restoration filtering based on projection power spectrum for single-photon emission computed tomography].

PubMed

Kubo, N

1995-04-01

To improve the quality of single-photon emission computed tomographic (SPECT) images, a restoration filter has been developed. This filter was designed according to practical "least squares filter" theory. It is necessary to know the object power spectrum and the noise power spectrum. The power spectrum is estimated from the power spectrum of a projection, when the high-frequency power spectrum of a projection is adequately approximated as a polynomial exponential expression. A study of the restoration with the filter based on a projection power spectrum was conducted, and compared with that of the "Butterworth" filtering method (cut-off frequency of 0.15 cycles/pixel), and "Wiener" filtering (signal-to-noise power spectrum ratio was a constant). Normalized mean-squared errors (NMSE) of the phantom, two line sources located in a 99mTc filled cylinder, were used. NMSE of the "Butterworth" filter, "Wiener" filter, and filtering based on a power spectrum were 0.77, 0.83, and 0.76 respectively. Clinically, brain SPECT images utilizing this new restoration filter improved the contrast. Thus, this filter may be useful in diagnosis of SPECT images.

Physics of the saturation of particle acceleration in relativistic magnetic reconnection

NASA Astrophysics Data System (ADS)

Kagan, Daniel; Nakar, Ehud; Piran, Tsvi

2018-05-01

We investigate the saturation of particle acceleration in relativistic reconnection using two-dimensional particle-in-cell simulations at various magnetizations σ. We find that the particle energy spectrum produced in reconnection quickly saturates as a hard power law that cuts off at γ ≈ 4σ, confirming previous work. Using particle tracing, we find that particle acceleration by the reconnection electric field in X-points determines the shape of the particle energy spectrum. By analysing the current sheet structure, we show that physical cause of saturation is the spontaneous formation of secondary magnetic islands that can disrupt particle acceleration. By comparing the size of acceleration regions to the typical distance between disruptive islands, we show that the maximum Lorentz factor produced in reconnection is γ ≈ 5σ, which is very close to what we find in our particle energy spectra. We also show that the dynamic range in Lorentz factor of the power-law spectrum in reconnection is ≤40. The hardness of the power law combined with its narrow dynamic range implies that relativistic reconnection is capable of producing the hard narrow-band flares observed in the Crab nebula but has difficulty producing the softer broad-band prompt gamma-ray burst emission.

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.

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.

Effects of biasing on the galaxy power spectrum at large scales

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

Beltran Jimenez, Jose; Departamento de Fisica Teorica, Universidad Complutense de Madrid, 28040, Madrid; Durrer, Ruth

2011-05-15

In this paper we study the effect of biasing on the power spectrum at large scales. We show that even though nonlinear biasing does introduce a white noise contribution on large scales, the P(k){proportional_to}k{sup n} behavior of the matter power spectrum on large scales may still be visible and above the white noise for about one decade. We show, that the Kaiser biasing scheme which leads to linear bias of the correlation function on large scales, also generates a linear bias of the power spectrum on rather small scales. This is a consequence of the divergence on small scales ofmore » the pure Harrison-Zeldovich spectrum. However, biasing becomes k dependent if we damp the underlying power spectrum on small scales. We also discuss the effect of biasing on the baryon acoustic oscillations.« less

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

NASA Astrophysics Data System (ADS)

Gaume, Johan; Löwe, Henning; Tan, Shurun; Tsang, Leung

2017-09-01

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number zc of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of zc and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density νc=zcϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Constraining the particle spectrum in blazar jets: importance of the hard X-ray spectrum

NASA Astrophysics Data System (ADS)

Sinha, Atreyee; Sahayanathan, Sunder; Chitnis, Varsha

2016-07-01

Measurement of the spectral curvature in blazar jets can throw light on the underlying particle spectral distribution, and hence, the acceleration and diffusion processes at play. With the advent of NuSTAR and ASTROSAT, and the upcoming ASTRO-H, this curvature can now be measured accurately across the broadband X-ray energies. We will discuss results from our recent works on two HBLs, Mkn421 (Sinha et al, A&A 2015) and 1ES1011+496 (Sinha et al, ApJ submitted), and show how simultaneous measurement at hard and soft X-ray energies can be crucial in understanding the underlying particle spectrum. Detection of lognormality in blazars is beginning to hint at strong disk-jet connections. India's recently launched multiwavelength satellite, the ASTROSAT will provide simultaneous time resolved data between 0.2-80keV, along with measurements at Optical-UV energies. We will discuss prospects from ASTROSAT for studying jet triggering mechanisms in blazars.

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

Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf

NASA Astrophysics Data System (ADS)

Solomon, S.; Richmond, P.

2002-05-01

In recent years we have found that logistic systems of the Generalized Lotka-Volterra type (GLV) describing statistical systems of auto-catalytic elements posses power law distributions of the Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in market returns. These power laws and their exponent α are invariant to arbitrary variations in the total wealth of the system and to other endogenously and exogenously induced variations.

Resurrecting the Power-law, Intermediate, and Logamediate Inflations in the DBI Scenario with Constant Sound Speed

NASA Astrophysics Data System (ADS)

Amani, Roonak; Rezazadeh, Kazem; Abdolmaleki, Asrin; Karami, Kayoomars

2018-02-01

We investigate the power-law, intermediate, and logamediate inflationary models in the framework of DBI non-canonical scalar field with constant sound speed. In the DBI setting, we first represent the power spectrum of both scalar density and tensor gravitational perturbations. Then, we derive different inflationary observables including the scalar spectral index n s , the running of the scalar spectral index {{dn}}s/d{ln}k, and the tensor-to-scalar ratio r. We show that the 95% CL constraint of the Planck 2015 T + E data on the non-Gaussianity parameter {f}{NL}{DBI} leads to the sound speed bound {c}s≥slant 0.087 in the DBI inflation. Moreover, our results imply that, although the predictions of the power-law, intermediate, and logamediate inflations in the standard canonical framework (c s = 1) are not consistent with the Planck 2015 data, in the DBI scenario with constant sound speed {c}s< 1, the result of the r-{n}s diagram for these models can lie inside the 68% CL region favored by Planck 2015 TT,TE,EE+lowP data. We also specify the parameter space of the power-law, intermediate, and logamediate inflations for which our models are compatible with the 68% or 95% CL regions of the Planck 2015 TT,TE,EE+lowP data. Using the allowed ranges of the parameter space of the intermediate and logamediate inflationary models, we estimate the running of the scalar spectral index and find that it is compatible with the 95% CL constraint from the Planck 2015 TT,TE,EE+lowP data.

The power law for the perception of rotation by airline pilots.

NASA Technical Reports Server (NTRS)

Clark, B.; Stewart, J. D.

1972-01-01

The purpose of this study was to determine the power laws for the perception of rotation about the three major body axes. Eighteen airline pilots made magnitude estimates of 5-sec pulses of nine angular accelerations having a range of acceleration x time of 10-150 deg/sec. The results showed that (1) the power law with an exponent of 1.4 describes the subjective motion of these pilots for all three major body axes, (2) the power law also describes the perception of motion for individual pilots with a substantial range of exponents, (3) there were significant correlations among the exponents for the three body axes, and (4) the data suggest that the power law over the wide range used may be more complex than implied by a formula with a single exponent.

Discovery of Diffuse Hard X-ray Emission associated with Jupiter

NASA Astrophysics Data System (ADS)

Ezoe, Y.; Miyoshi, Y.; Ishikawa, K.; Ohashi, T.; Terada, N.; Uchiyama, Y.; Negoro, H.

2009-12-01

Our discovery of diffuse hard (1-5 keV) X-ray emission around Jupiter is reported. Recent Chandra and XMM-Newton observations revealed several types of X-rays in the vicinity of Jupiter such as auroral and disk emission from Jupiter and faint diffuse X-rays from the Io Plasma Torus (see Bhardwaj et al. 2007 for review). To investigate possible diffuse hard X-ray emission around Jupiter with the highest sensitivity, we conducted data analysis of Suzaku XIS observations of Jupiter on Feb 2006. After removing satellite and planetary orbital motions, we detected a significant diffuse X-ray emission extending to ~6 x 3 arcmin with the 1-5 keV X-ray luminosity of ~3e15 erg/s. The emitting region very well coincided with the Jupiter's radiation belts. The 1-5 keV X-ray spectrum was represented by a simple power law model with a photon index of 1.4. Such a flat continuum strongly suggests non-thermal origin. Although such an emission can be originated from multiple background point sources, its possibility is quite low. We hence examined three mechanisms, assuming that the emission is truly diffuse: bremsstrahlung by keV electrons, synchrotron emission by TeV electrons, and inverse Compton scattering of solar photons by MeV electrons. The former two can be rejected because of the X-ray spectral shape and implausible existence of TeV electrons around Jupiter, respectively. The last possibility was found to be possible because tens MeV electrons, which have been confirmed in inner radiation belts (Bolton et al. 2002), can kick solar photons to the keV energy range and provide a simple power-law continuum. We estimated an average electron density from the X-ray luminosity assuming the oblate spheroid shaped emitting region with 8 x 8 x 4 Jovian radii. The necessary density was 0.02 1/cm3 for 50 MeV electrons. Hence, our results may suggest a new particle acceleration phenomenon around Jupiter.

Estimation of primordial spectrum with post-WMAP 3-year data

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

Shafieloo, Arman; Souradeep, Tarun

2008-07-15

In this paper we implement an improved (error-sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the Wilkinson Microwave Anisotropy Probe (WMAP) 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat {lambda}CDM cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a 'bestmore » fit' power law spectrum up to {delta}{chi}{sub eff}{sup 2}{approx_equal}-30. We use discrete wavelet transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, for a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat cold dark matter model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.« less

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.

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.

A soft-hard combination-based cooperative spectrum sensing scheme for cognitive radio networks.

PubMed

Do, Nhu Tri; An, Beongku

2015-02-13

In this paper we propose a soft-hard combination scheme, called SHC scheme, for cooperative spectrum sensing in cognitive radio networks. The SHC scheme deploys a cluster based network in which Likelihood Ratio Test (LRT)-based soft combination is applied at each cluster, and weighted decision fusion rule-based hard combination is utilized at the fusion center. The novelties of the SHC scheme are as follows: the structure of the SHC scheme reduces the complexity of cooperative detection which is an inherent limitation of soft combination schemes. By using the LRT, we can detect primary signals in a low signal-to-noise ratio regime (around an average of -15 dB). In addition, the computational complexity of the LRT is reduced since we derive the closed-form expression of the probability density function of LRT value. The SHC scheme also takes into account the different effects of large scale fading on different users in the wide area network. The simulation results show that the SHC scheme not only provides the better sensing performance compared to the conventional hard combination schemes, but also reduces sensing overhead in terms of reporting time compared to the conventional soft combination scheme using the LRT.

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.

Comparative power law analysis of structured breast phantom and patient images in digital mammography and breast tomosynthesis.

PubMed

Cockmartin, L; Bosmans, H; Marshall, N W

2013-08-01

This work characterizes three candidate mammography phantoms with structured background in terms of power law analysis in the low frequency region of the power spectrum for 2D (planar) mammography and digital breast tomosynthesis (DBT). The study was performed using three phantoms (spheres in water, Voxmam, and BR3D CIRS phantoms) on two DBT systems from two different vendors (Siemens Inspiration and Hologic Selenia Dimensions). Power spectra (PS) were calculated for planar projection, DBT projection, and reconstructed images and curve fitted in the low frequency region from 0.2 to 0.7 mm(-1) with a power law function characterized by an exponent β and magnitude κ. The influence of acquisition dose and tube voltage on the power law parameters was first explored. Then power law parameters were calculated from images acquired with the same anode∕filter combination and tube voltage for the three test objects, and compared with each other. Finally, PS curves for automatic exposure controlled acquisitions (anode∕filter combination and tube voltages selected by the systems based on the breast equivalent thickness of the test objects) were compared against PS analysis performed on patient data (for Siemens 80 and for Hologic 48 mammograms and DBT series). Dosimetric aspects of the three test objects were also examined. The power law exponent (β) was found to be independent of acquisition dose for planar mammography but varied more for DBT projections of the sphere-phantom. Systematic increase of tube voltage did not affect β but decreased κ, both in planar and DBT projection phantom images. Power spectra of the BR3D phantom were closer to those of the patients than these of the Voxmam phantom; the Voxmam phantom gave high values of κ compared to the other phantoms and the patient series. The magnitude of the PS curves of the BR3D phantom was within the patient range but β was lower than the average patient value. Finally, PS magnitude for the sphere

Power Laws in Stochastic Processes for Social Phenomena: An Introductory Review

NASA Astrophysics Data System (ADS)

Kumamoto, Shin-Ichiro; Kamihigashi, Takashi

2018-03-01

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon process as well as some recent models. The main purpose of this paper is to explain the mathematical details of their mechanisms in a self-contained manner.

Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State

NASA Astrophysics Data System (ADS)

Stoop, Ruedi; Gomez, Florian

2016-07-01

The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.

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.

Between disorder and order: A case study of power law

NASA Astrophysics Data System (ADS)

Cao, Yong; Zhao, Youjie; Yue, Xiaoguang; Xiong, Fei; Sun, Yongke; He, Xin; Wang, Lichao

2016-08-01

Power law is an important feature of phenomena in long memory behaviors. Zipf ever found power law in the distribution of the word frequencies. In physics, the terms order and disorder are Thermodynamic or statistical physics concepts originally and a lot of research work has focused on self-organization of the disorder ingredients of simple physical systems. It is interesting what make disorder-order transition. We devise an experiment-based method about random symbolic sequences to research regular pattern between disorder and order. The experiment results reveal power law is indeed an important regularity in transition from disorder to order. About these results the preliminary study and analysis has been done to explain the reasons.

Fractal power law in literary English

NASA Astrophysics Data System (ADS)

Gonçalves, L. L.; Gonçalves, L. B.

2006-02-01

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.

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

Power-law tail probabilities of drainage areas in river basins

USGS Publications Warehouse

Veitzer, S.A.; Troutman, B.M.; Gupta, V.K.

2003-01-01

The significance of power-law tail probabilities of drainage areas in river basins was discussed. The convergence to a power law was not observed for all underlying distributions, but for a large class of statistical distributions with specific limiting properties. The article also discussed about the scaling properties of topologic and geometric network properties in river basins.

NuSTAR observations of the powerful radio-galaxy Cygnus A

DOE PAGES

Reynolds, Christopher S.; Lohfink, Anne M.; Ogle, Patrick M.; ...

2015-07-29

Here, we present NuSTAR observations of the powerful radio galaxy Cygnus A, focusing on the central absorbed active galactic nucleus (AGN). Cygnus A is embedded in a cool-core galaxy cluster, and hence we also examine archival XMM-Newton data to facilitate the decomposition of the spectrum into the AGN and intracluster medium components. NuSTAR gives a source-dominated spectrum of the AGN out tomore » $$\\gt 70$$ keV. In gross terms, the NuSTAR spectrum of the AGN has the form of a power law ($${\\rm{\\Gamma }}\\sim 1.6-1.7$$) absorbed by a neutral column density of $${N}_{{\\rm{H}}}\\sim 1.6\\times {10}^{23}\\;\\;{\\mathrm{cm}}^{-2}$$. However, we also detect curvature in the hard ($$\\gt 10$$ keV) spectrum resulting from reflection by Compton-thick matter out of our line of sight to the X-ray source. Compton reflection, possibly from the outer accretion disk or obscuring torus, is required even permitting a high-energy cut off in the continuum source; the limit on the cut-off energy is $${E}_{\\mathrm{cut}}\\gt 111$$ keV(90% confidence). Interestingly, the absorbed power law plus reflection model leaves residuals suggesting the absorption/emission from a fast ($$15,000-26,000\\;\\;\\mathrm{km}\\;\\;{{\\rm{s}}}^{-1}\\;$$), high column-density ($${N}_{W}\\gt 3\\times {10}^{23}\\;\\;{\\mathrm{cm}}^{-2}$$), highly ionized ($$\\xi \\sim 2500\\;\\mathrm{erg}\\;\\mathrm{cm}\\;{{\\rm{s}}}^{-1}$$) wind. A second, even faster ionized wind component is also suggested by these data. We show that the ionized wind likely carries a significant mass and momentum flux, and may carry sufficient kinetic energy to exercise feedback on the host galaxy. If confirmed, the simultaneous presence of a strong wind and powerful jets in Cygnus A demonstrates that feedback from radio-jets and sub-relativistic winds are not mutually exclusive phases of AGN activity but can occur simultaneously.« less

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.

On the Nature of the Variability Power Decay toward Soft Spectral States in X-Ray Binaries: Case Study in Cygnus X-1

NASA Astrophysics Data System (ADS)

Titarchuk, Lev; Shaposhnikov, Nikolai

2008-05-01

A characteristic feature of the Fourier power density spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broadband-limited noise characterized by a constant below some frequency (a "break" frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time t0 is related to the phenomenological break frequency, while the PDS power-law slope above the "break" is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black holes and neutron stars) during an evolution of these sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-Ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power Px decreases approximately as the square root of the characteristic frequency of the driving oscillations νdr. The RXTE observations of Cyg X-1 allow us to infer Pdr and t0 as a function of νdr. Using the inferred dependences of the integrated power of the driving oscillations Pdr and t0 on νdr we demonstrate that the power predicted by the model also decays as Px,diff propto ν-0.5dr, which is similar to the observed Px behavior. We also apply the basic parameters of observed PDSs, power-law indices, and low-frequency quasi-periodic oscillations to infer the Reynolds number (Re) from the observations using the method developed in our previous paper. Our analysis shows that Re increases from values of about 10 in low/hard state to about 70 during the high/soft state.

On the nature of the variability power decay towards soft spectral states in X-ray binaries. Case study in Cyg X-1

NASA Astrophysics Data System (ADS)

Titarchuk, Lev; Shaposhnikov, Nikolai

2008-01-01

A characteristic feature of the Fourier Power Density Spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broad band-limited noise, characterized by a constant below some frequency (a ``break'' frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time t0 is related to the phenomenological break frequency, while the PDS power-law slope above the ``break'' is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black hole and neutron star) during an evolution of theses sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power Px decreases approximately as a square root of the characteristic frequency of the driving oscillations νdr. The RXTE observations of Cyg X-1 allow us to infer Pdr and t0 as a function of νdr. Using the inferred dependences of the integrated power of the driving oscillations Pdr and t0 on νdr we demonstrate that the power predicted by the model also decays as Px,diff~νdr-0.5 that is similar to the observed Px behavior. We also apply the basic parameters of observed PDSs, power-law index and low frequency quasiperiodic oscillations, to infer Reynolds (Re) number from the observations using the method developed in our previous paper. Our analysis shows that Re-number increases from values about 10 in low/hard state to that about 70 during the high/soft state.

General relativistic corrections to the weak lensing convergence power spectrum

NASA Astrophysics Data System (ADS)

Giblin, John T.; Mertens, James B.; Starkman, Glenn D.; Zentner, Andrew R.

2017-11-01

We compute the weak lensing convergence power spectrum, Cℓκκ, in a dust-filled universe using fully nonlinear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and partially utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, ℓ˜2 - 3 , and percent-level corrections at intermediate angular scales of ℓ˜20 - 30 .

22 CFR 1423.19 - Duties and powers of the Administrative Law Judge.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 22 Foreign Relations 2 2010-04-01 2010-04-01 true Duties and powers of the Administrative Law... RELATIONS AUTHORITY UNFAIR LABOR PRACTICE PROCEEDINGS § 1423.19 Duties and powers of the Administrative Law Judge. It shall be the duty of the Administrative Law Judge to inquire fully into the facts as they...

Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy

NASA Astrophysics Data System (ADS)

Komatsu, Nobuyoshi

2017-11-01

A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the α th power of the Hubble parameter, where α is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constantlike when α is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.

The non-linear power spectrum of the Lyman alpha forest

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

Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo

2015-12-01

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate themore » comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.« less

Anisotropic power spectrum of refractive-index fluctuation in hypersonic turbulence.

PubMed

Li, Jiangting; Yang, Shaofei; Guo, Lixin; Cheng, Mingjian

2016-11-10

An anisotropic power spectrum of the refractive-index fluctuation in hypersonic turbulence was obtained by processing the experimental image of the hypersonic plasma sheath and transforming the generalized anisotropic von Kármán spectrum. The power spectrum suggested here can provide as good a fit to measured spectrum data for hypersonic turbulence as that recorded from the nano-planar laser scattering image. Based on the newfound anisotropic hypersonic turbulence power spectrum, Rytov approximation was employed to establish the wave structure function and the spatial coherence radius model of electromagnetic beam propagation in hypersonic turbulence. Enhancing the anisotropy characteristics of the hypersonic turbulence led to a significant improvement in the propagation performance of electromagnetic beams in hypersonic plasma sheath. The influence of hypersonic turbulence on electromagnetic beams increases with the increase of variance of the refractive-index fluctuation and the decrease of turbulence outer scale and anisotropy parameters. The spatial coherence radius was much smaller than that in atmospheric turbulence. These results are fundamental to understanding electromagnetic wave propagation in hypersonic turbulence.

Exploring the effect of power law social popularity on language evolution.

PubMed

Gong, Tao; Shuai, Lan

2014-01-01

We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.

Power spectrum for the small-scale Universe

NASA Astrophysics Data System (ADS)

Widrow, Lawrence M.; Elahi, Pascal J.; Thacker, Robert J.; Richardson, Mark; Scannapieco, Evan

2009-08-01

The first objects to arise in a cold dark matter (CDM) universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N = 7203-15843) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) ~ kn, with -2.5 <= n <= - 1. Self-similar scaling is established for n = -1 and -2 more convincingly than in previous, lower resolution simulations and for the first time, self-similar scaling is established for an n = -2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n = -2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasi-linear regime. In the non-linear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis versus halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.

Non-Thermal Hard X-Ray Emission in Galaxy Clusters Observed with the BeppoSAX PDS

NASA Technical Reports Server (NTRS)

Nevalainen, Jukka H.; Oosterbroeck, T.; Bonamente, Max; Six, N. Frank (Technical Monitor)

2002-01-01

We studied the X-ray emission in a sample of clusters using the BeppoSAX PDS instrument in the 20 -- 80 keV energy band. We estimated the non-thermal cluster emission (HXR) by modeling the thermal contribution from the cluster gas and the non-thermal contamination from the AGN in the field, and propagating the corresponding uncertainties. We also evaluated and propagated the systematic uncertainties due to the background fluctuations. The resulting non-thermal component is detected at a sigma level in approx. 50 % of the non-significantly AGN-contaminated clusters, i.e. in clusters A2142, A2256, A3376, Coma, Ophiuchus and Virgo. Furthermore, Virgo is detected at a 4 sigma level. All the clusters detected at a 2 sigma level exhibit some degree of merger signatures, i.e. deviations from the azimuthally symmetric brightness and temperature distributions, while the relaxed clusters are detected at a lower confidence. The data are consistent with a scenario whereby relaxed clusters have no non-thermal hard X-ray component, whereas merger clusters do, with a 20 -- 80 keV luminosity of approx. 10(exp 42-44)((h(sub 50))(exp -2))(erg/s). Consistent with merger boosting of cluster temperatures, the non-thermal luminosity increases by 2-3 orders of magnitude between the average cluster temperatures 2 and 10 keV, as L(sub NTE) is proportional to T(sup j) with j = 2.4+/-0.3. These results corroborate the assumption which is the essential element in most non-thermal hard X-ray emission models. The co-added spectrum of all non-significantly AGN-contaminated clusters indicates a power-law spectrum for the non-thermal component with a photon index of 1.5+/-0.25 at 1 sigma confidence level. Unless there is a high energy cut-off in the electron velocity distribution, the total spectrum implies that Inverse Compton scatter of Cosmic Microwave Background photons from electron population dominates over the non-thermal bremsstrahlung in producing hard X-rays in clusters on the merger

The double power law in human collaboration behavior: The case of Wikipedia

NASA Astrophysics Data System (ADS)

Kwon, Okyu; Son, Woo-Sik; Jung, Woo-Sung

2016-11-01

We study human behavior in terms of the inter-event time distribution of revision behavior on Wikipedia, an online collaborative encyclopedia. We observe a double power law distribution for the inter-editing behavior at the population level and a single power law distribution at the individual level. Although interactions between users are indirect or moderate on Wikipedia, we determine that the synchronized editing behavior among users plays a key role in determining the slope of the tail of the double power law distribution.

Singularity problems of the power law for modeling creep compliance

NASA Technical Reports Server (NTRS)

Dillard, D. A.; Hiel, C.

1985-01-01

An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.

Power-law scaling of plasma pressure on laser-ablated tin microdroplets

NASA Astrophysics Data System (ADS)

Kurilovich, Dmitry; Basko, Mikhail M.; Kim, Dmitrii A.; Torretti, Francesco; Schupp, Ruben; Visschers, Jim C.; Scheers, Joris; Hoekstra, Ronnie; Ubachs, Wim; Versolato, Oscar O.

2018-01-01

The measurement of the propulsion of metallic microdroplets exposed to nanosecond laser pulses provides an elegant method for probing the ablation pressure in a dense laser-produced plasma. We present the measurements of the propulsion velocity over three decades in the driving Nd:YAG laser pulse energy and observe a near-perfect power law dependence. Simulations performed with the RALEF-2D radiation-hydrodynamic code are shown to be in good agreement with the power law above a specific threshold energy. The simulations highlight the importance of radiative losses which significantly modify the power of the pressure scaling. Having found a good agreement between the experiment and the simulations, we investigate the analytic origins of the obtained power law and conclude that none of the available analytic theories is directly applicable for explaining our power exponent.

Features in the primordial spectrum from WMAP: A wavelet analysis

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

Shafieloo, Arman; Souradeep, Tarun; Manimaran, P.

2007-06-15

Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper [A. Shafieloo and T. Souradeep, Phys. Rev. D 70, 043523 (2004).], we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, 'best fit' scale free spectra ({delta}lnL{approx_equal}25 withmore » respect to the Harrison-Zeldovich spectrum, and, {delta}lnL{approx_equal}11 with respect to the power law spectrum with n{sub s}=0.95). In this paper we use the discrete wavelet transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infrared cutoff at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localized at the horizon scale.« less

30 CFR 44.22 - Administrative law judges; powers and duties.

Code of Federal Regulations, 2013 CFR

2013-07-01

... hearing, may file with the Chief Administrative Law Judge of the Department of Labor a motion to be... motion of any party, and shall be granted in the discretion of the presiding administrative law judge... 30 Mineral Resources 1 2013-07-01 2013-07-01 false Administrative law judges; powers and duties...

30 CFR 44.22 - Administrative law judges; powers and duties.

Code of Federal Regulations, 2011 CFR

2011-07-01

... hearing, may file with the Chief Administrative Law Judge of the Department of Labor a motion to be... motion of any party, and shall be granted in the discretion of the presiding administrative law judge... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Administrative law judges; powers and duties...

Overlap Spectrum Fiber Bragg Grating Sensor Based on Light Power Demodulation

PubMed Central

Zhang, Hao; Jiang, Junzhen; Liu, Shuang; Chen, Huaixi; Zheng, Xiaoqian; Qiu, Yishen

2018-01-01

Demodulation is a bottleneck for applications involving fiber Bragg gratings (FBGs). An overlap spectrum FBG sensor based on a light power demodulation method is presented in this paper. The demodulation method uses two chirp FBGs (cFBGs) of which the reflection spectra partially overlap each other. The light power variation of the overlap spectrum can be linked to changes in the measurand, and the sensor function can be realized via this relationship. A temperature experiment showed that the relationship between the overlap power spectrum of the FBG sensor and temperature had good linearity and agreed with the theoretical analysis. PMID:29772793

Nonlinear evolution of f(R) cosmologies. II. Power spectrum

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

Oyaizu, Hiroaki; Hu, Wayne; Department of Astronomy and Astrophysics, University of Chicago, Chicago Illinois 60637

2008-12-15

We carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the inverse mass or Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular, the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the nonlinear regime if themore » background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level for models even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. Simple scaling relations that take the linear power spectrum into a nonlinear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications.« less

Universal Power Law Governing Pedestrian Interactions

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

Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.

2014-12-01

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory inmore » nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.« less

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.

Predicting the long tail of book sales: Unearthing the power-law exponent

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Levene, Mark; Loizou, George

2010-06-01

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.

On the power law of passive scalars in turbulence

NASA Astrophysics Data System (ADS)

Gotoh, Toshiyuki; Watanabe, Takeshi

2015-11-01

It has long been considered that the moments of the scalar increment with separation distance r obey power law with scaling exponents in the inertial convective range and the exponents are insensitive to variation of pumping of scalar fluctuations at large scales, thus the scaling exponents are universal. We examine the scaling behavior of the moments of increments of passive scalars 1 and 2 by using DNS up to the grid points of 40963. They are simultaneously convected by the same isotropic steady turbulence atRλ = 805 , but excited by two different methods. Scalar 1 is excited by the random scalar injection which is isotropic, Gaussian and white in time at law wavenumber band, while Scalar 2 is excited by the uniform mean scalar gradient. It is found that the local scaling exponents of the scalar 1 has a logarithmic correction, meaning that the moments of the scalar 1 do not obey simple power law. On the other hand, the moments of the scalar 2 is found to obey the well developed power law with exponents consistent with those in the literature. Physical reasons for the difference are explored. Grants-in-Aid for Scientific Research 15H02218 and 26420106, NIFS14KNSS050, HPCI project hp150088 and hp140024, JHPCN project jh150012.

The angular power spectrum measurement of the Galactic synchrotron emission using the TGSS survey

NASA Astrophysics Data System (ADS)

Choudhuri, Samir; Bharadwaj, Somnath; Ali, Sk. Saiyad; Roy, Nirupam; Intema, H. T.; Ghosh, Abhik

2018-05-01

Characterizing the diffuse Galactic synchrotron emission (DGSE) at arcminute angular scales is needed to remove this foregrounds in cosmological 21-cm measurements. Here, we present the angular power spectrum (Cl) measurement of the diffuse Galactic synchrotron emission using two fields observed by the TIFR GMRT Sky Survey (TGSS). We apply 2D Tapered Gridded Estimator (TGE) to estimate the Cl from the visibilities. We find that the residual data after subtracting the point sources is likely dominated by the diffuse Galactic synchrotron radiation across the angular multipole range 240 <= l <~ 500. We fit a power law to the measured Cl over this l range. We find that the slopes in both fields are consistent with earlier measurements. For the second field, however, we interpret the measured Cl as an upper limit for the DGSE as there is an indication of a significant residual point source contribution.

On the Nature of the Variability Power Decay towards Soft Spectral States in X-Ray Binaries. Case Study in Cyg X-1

NASA Technical Reports Server (NTRS)

Titarchuk, Lev; Shaposhinikov, Nikolai

2007-01-01

A characteristic feature of the Fourier Power Density Spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broad band-limited noise, characterized by a constant below some frequency (a "break" frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time to is related to the phenomenological break frequency, while the PDS power-law slope above the "break" is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black hole and neutron star) during an evolution of theses sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power P(sub x), decreases approximately as a square root of the characteristic frequency of the driving oscillations v(sub dr). The RXTE observations of Cyg X-1 allow us to infer P(sub dr), and t(sub o) as a function of v(sub dr). We also apply the basic parameters of observed PDSs, power-law index and low frequency quasiperiodic oscillations. to infer Reynolds (Re) number from the observations using the method developed in our previous paper. Our analysis shows that Re-number increases from values about 10 in low/hard state to that about 70 during the high/soft state. Subject headings: accretion, accretion disks-black hole physics-stars:individual (Cyg X-1) :radiation mechanisms: nonthermal-physical data and processes

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and Principal Component Analysis

NASA Astrophysics Data System (ADS)

Silberman, L.; Dekel, A.; Eldar, A.; Zehavi, I.

2001-08-01

We allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities and obtain ~35% lower values for the cosmological density parameter Ωm and for the amplitude of mass density fluctuations σ8Ω0.6m. This result is obtained under the assumption that the power spectrum in the linear regime is of the flat ΛCDM model (h=0.65, n=1, COBE normalized) with only Ωm as a free parameter. Since the likelihood is driven by the nonlinear regime, we ``break'' the power spectrum at kb~0.2 (h-1 Mpc)-1 and fit a power law at k>kb. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors and a linear relation between velocity and density. Tests using mock catalogs that properly simulate nonlinear effects demonstrate that this procedure results in a reduced bias and a better fit. We find for the Mark III and SFI data Ωm=0.32+/-0.06 and 0.37+/-0.09, respectively, with σ8Ω0.6m=0.49+/-0.06 and 0.63+/-0.08, in agreement with constraints from other data. The quoted 90% errors include distance errors and cosmic variance, for fixed values of the other parameters. The improvement in the likelihood due to the nonlinear correction is very significant for Mark III and moderately significant for SFI. When allowing deviations from ΛCDM, we find an indication for a wiggle in the power spectrum: an excess near k~0.05 (h-1 Mpc)-1 and a deficiency at k~0.1 (h-1 Mpc)-1, or a ``cold flow.'' This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the cosmic microwave background (CMB) anisotropy. A χ2 test applied to modes of a principal component analysis (PCA) shows that the nonlinear procedure improves the goodness of fit and reduces a spatial gradient that was of concern in the purely linear analysis. The PCA allows us to address spatial features of the data and to evaluate and fine-tune the theoretical and error models

Ionic fluids with r-6 pair interactions have power-law electrostatic screening

NASA Astrophysics Data System (ADS)

Kjellander, Roland; Forsberg, Björn

2005-06-01

The decay behaviour of radial distribution functions for large distances r is investigated for classical Coulomb fluids where the ions interact with an r-6 potential (e.g. a dispersion interaction) in addition to the Coulombic and the short-range repulsive potentials (e.g. a hard core). The pair distributions and the density-density (NN), charge-density (QN) and charge-charge (QQ) correlation functions are investigated analytically and by Monte Carlo simulations. It is found that the NN correlation function ultimately decays like r-6 for large r, just as it does for fluids of electroneutral particles interacting with an r-6 potential. The prefactor is proportional to the squared compressibility in both cases. The QN correlations decay in general like r-8 and the QQ correlations like r-10 in the ionic fluid. The average charge density around an ion decays generally like r-8 and the average electrostatic potential like r-6. This behaviour is in stark contrast to the decay behaviour for classical Coulomb fluids in the absence of the r-6 potential, where all these functions decay exponentially for large r. The power-law decays are, however, the same as for quantum Coulomb fluids. This indicates that the inclusion of the dispersion interaction as an effective r-6 interaction potential in classical systems yields the same decay behaviour for the pair correlations as in quantum ionic systems. An exceptional case is the completely symmetric binary electrolyte for which only the NN correlation has a power-law decay but not the QQ correlations. These features are shown by an analysis of the bridge function.

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.

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) .

Generating Discrete Power-Law Distributions from a Death- Multiple Immigration Population Process

NASA Astrophysics Data System (ADS)

Matthews, J. O.; Jakeman, E.; Hopcraft, K. I.

2003-04-01

We consider the evolution of a simple population process governed by deaths and multiple immigrations that arrive with rates particular to their order. For a particular choice of rates, the equilibrium solution has a discrete power-law form. The model is a generalization of a process investigated previously where immigrants arrived in pairs [1]. The general properties of this model are discussed in a companion paper. The population is initiated with precisely M individuals present and evolves to an equilibrium distribution with a power-law tail. However the power-law tails of the equilibrium distribution are established immediately, so that moments and correlation properties of the population are undefined for any non-zero time. The technique we develop to characterize this process utilizes external monitoring that counts the emigrants leaving the population in specified time intervals. This counting distribution also possesses a power-law tail for all sampling times and the resulting time series exhibits two features worthy of note, a large variation in the strength of the signal, reflecting the power-law PDF; and secondly, intermittency of the emissions. We show that counting with a detector of finite dynamic range regularizes naturally the fluctuations, in effect `clipping' the events. All previously undefined characteristics such as the mean, autocorrelation and probabilities to the first event and time between events are well defined and derived. These properties, although obtained by discarding much data, nevertheless possess embedded power-law regimes that characterize the population in a way that is analogous to box averaging determination of fractal-dimension.

Using Functional Assessment to Treat Behavior Problems of Deaf and Hard of Hearing Children Diagnosed with Autism Spectrum Disorder

ERIC Educational Resources Information Center

Zane, Thomas; Carlson, Mark; Estep, David; Quinn, Mike

2013-01-01

A defining feature of autism spectrum disorders is atypical behaviors, e.g., stereotypy, noncompliance, rituals, and aggression. Deaf and hard of hearing individuals with autism present a greater challenge because of additional issues related to their hearing status. One conceptualization of problem behavior is that it serves a communication…

Modeling Flare Hard X-ray Emission from Electrons in Contracting Magnetic Islands

NASA Astrophysics Data System (ADS)

Guidoni, Silvina E.; Allred, Joel C.; Alaoui, Meriem; Holman, Gordon D.; DeVore, C. Richard; Karpen, Judith T.

2016-05-01

The mechanism that accelerates particles to the energies required to produce the observed impulsive hard X-ray emission in solar flares is not well understood. It is generally accepted that this emission is produced by a non-thermal beam of electrons that collides with the ambient ions as the beam propagates from the top of a flare loop to its footpoints. Most current models that investigate this transport assume an injected beam with an initial energy spectrum inferred from observed hard X-ray spectra, usually a power law with a low-energy cutoff. In our previous work (Guidoni et al. 2016), we proposed an analytical method to estimate particle energy gain in contracting, large-scale, 2.5-dimensional magnetic islands, based on a kinetic model by Drake et al. (2010). We applied this method to sunward-moving islands formed high in the corona during fast reconnection in a simulated eruptive flare. The overarching purpose of the present work is to test this proposed acceleration model by estimating the hard X-ray flux resulting from its predicted accelerated-particle distribution functions. To do so, we have coupled our model to a unified computational framework that simulates the propagation of an injected beam as it deposits energy and momentum along its way (Allred et al. 2015). This framework includes the effects of radiative transfer and return currents, necessary to estimate flare emission that can be compared directly to observations. We will present preliminary results of the coupling between these models.

NuSTAR Hard X-Ray Survey of the Galactic Center Region I: Hard X-Ray Morphology and Spectroscopy of the Diffuse Emission

NASA Astrophysics Data System (ADS)

Mori, Kaya; Hailey, Charles J.; Krivonos, Roman; Hong, Jaesub; Ponti, Gabriele; Bauer, Franz; Perez, Kerstin; Nynka, Melania; Zhang, Shuo; Tomsick, John A.; Alexander, David M.; Baganoff, Frederick K.; Barret, Didier; Barrière, Nicolas; Boggs, Steven E.; Canipe, Alicia M.; Christensen, Finn E.; Craig, William W.; Forster, Karl; Giommi, Paolo; Grefenstette, Brian W.; Grindlay, Jonathan E.; Harrison, Fiona A.; Hornstrup, Allan; Kitaguchi, Takao; Koglin, Jason E.; Luu, Vy; Madsen, Kristen K.; Mao, Peter H.; Miyasaka, Hiromasa; Perri, Matteo; Pivovaroff, Michael J.; Puccetti, Simonetta; Rana, Vikram; Stern, Daniel; Westergaard, Niels J.; Zhang, William W.; Zoglauer, Andreas

2015-12-01

We present the first sub-arcminute images of the Galactic Center above 10 keV, obtained with NuSTAR. NuSTAR resolves the hard X-ray source IGR J17456-2901 into non-thermal X-ray filaments, molecular clouds, point sources, and a previously unknown central component of hard X-ray emission (CHXE). NuSTAR detects four non-thermal X-ray filaments, extending the detection of their power-law spectra with Γ ˜ 1.3-2.3 up to ˜50 keV. A morphological and spectral study of the filaments suggests that their origin may be heterogeneous, where previous studies suggested a common origin in young pulsar wind nebulae (PWNe). NuSTAR detects non-thermal X-ray continuum emission spatially correlated with the 6.4 keV Fe Kα fluorescence line emission associated with two Sgr A molecular clouds: MC1 and the Bridge. Broadband X-ray spectral analysis with a Monte-Carlo based X-ray reflection model self-consistently determined their intrinsic column density (˜1023 cm-2), primary X-ray spectra (power-laws with Γ ˜ 2) and set a lower limit of the X-ray luminosity of Sgr A* flare illuminating the Sgr A clouds to LX ≳ 1038 erg s-1. Above ˜20 keV, hard X-ray emission in the central 10 pc region around Sgr A* consists of the candidate PWN G359.95-0.04 and the CHXE, possibly resulting from an unresolved population of massive CVs with white dwarf masses MWD ˜ 0.9 M⊙. Spectral energy distribution analysis suggests that G359.95-0.04 is likely the hard X-ray counterpart of the ultra-high gamma-ray source HESS J1745-290, strongly favoring a leptonic origin of the GC TeV emission.

Second law analysis of a conventional steam power plant

NASA Technical Reports Server (NTRS)

Liu, Geng; Turner, Robert H.; Cengel, Yunus A.

1993-01-01

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.

Can the cosmic x ray and gamma ray background be due to reflection of a steep power law spectrum and Compton scattering by relativistic electrons?

NASA Technical Reports Server (NTRS)

Zycki, Piotr T.; Zdziarski, Andrzej A.; Svensson, Roland

1991-01-01

We reconsider the recent model for the origin in the cosmic X-ray and gamma-ray background by Rogers and Field. The background in the model is due to an unresolved population of AGNs. An individual AGN spectrum contains three components: a power law with the energy index of alpha = 1.1, an enhanced reflection component, and a component from Compton scattering by relativistic electrons with a low energy cutoff at some minimum Lorentz factor, gamma(sub min) much greater than 1. The MeV bump seen in the gamma-ray background is then explained by inverse Compton emission by the electrons. We show that the model does not reproduce the shape of the observed X-ray and gamma-ray background below 10 MeV and that it overproduces the background at larger energies. Furthermore, we find the assumptions made for the Compton component to be physically inconsistent. Relaxing the inconsistent assumptions leads to model spectra even more different from that of the observed cosmic background. Thus, we can reject the hypothesis that the high-energy cosmic background is due to the described model.

A NuSTAR Observation of the Reflection Spectrum of the Low-Mass X-Ray Binary 4U 1728-34

NASA Technical Reports Server (NTRS)

Sleator, Clio C.; Tomsick, John A.; King, Ashley L.; Miller, Jon M.; Boggs, Steven E.; Bachetti, Matteo; Barret, Didier; Chenevez, Jerome; Christensen, Finn E.; Craig, William W.;

Calculation of power spectrums from digital time series with missing data points

NASA Technical Reports Server (NTRS)

Murray, C. W., Jr.

1980-01-01

Two algorithms are developed for calculating power spectrums from the autocorrelation function when there are missing data points in the time series. Both methods use an average sampling interval to compute lagged products. One method, the correlation function power spectrum, takes the discrete Fourier transform of the lagged products directly to obtain the spectrum, while the other, the modified Blackman-Tukey power spectrum, takes the Fourier transform of the mean lagged products. Both techniques require fewer calculations than other procedures since only 50% to 80% of the maximum lags need be calculated. The algorithms are compared with the Fourier transform power spectrum and two least squares procedures (all for an arbitrary data spacing). Examples are given showing recovery of frequency components from simulated periodic data where portions of the time series are missing and random noise has been added to both the time points and to values of the function. In addition the methods are compared using real data. All procedures performed equally well in detecting periodicities in the data.

Spectrum and power allocation in cognitive multi-beam satellite communications with flexible satellite payloads

NASA Astrophysics Data System (ADS)

Liu, Zhihui; Wang, Haitao; Dong, Tao; Yin, Jie; Zhang, Tingting; Guo, Hui; Li, Dequan

2018-02-01

In this paper, the cognitive multi-beam satellite system, i.e., two satellite networks coexist through underlay spectrum sharing, is studied, and the power and spectrum allocation method is employed for interference control and throughput maximization. Specifically, the multi-beam satellite with flexible payload reuses the authorized spectrum of the primary satellite, adjusting its transmission band as well as power for each beam to limit its interference on the primary satellite below the prescribed threshold and maximize its own achievable rate. This power and spectrum allocation problem is formulated as a mixed nonconvex programming. For effective solving, we first introduce the concept of signal to leakage plus noise ratio (SLNR) to decouple multiple transmit power variables in the both objective and constraint, and then propose a heuristic algorithm to assign spectrum sub-bands. After that, a stepwise plus slice-wise algorithm is proposed to implement the discrete power allocation. Finally, simulation results show that adopting cognitive technology can improve spectrum efficiency of the satellite communication.

Hidden power law patterns in the top European football leagues

NASA Astrophysics Data System (ADS)

Da Silva, Sergio; Matsushita, Raul; Silveira, Eliza

2013-11-01

Because sports are stylized combat, sports may follow power laws similar to those found for wars, individual clashes, and acts of terrorism. We show this fact for football (soccer) by adjusting power laws that show a close relationship between rank and points won by the clubs participating in the latest seasons of the top fifteen European football leagues. In addition, we use Shannon entropy for gauging league competitive balance. As a result, we are able to rank the leagues according to competitiveness.

Two-Season Atacama Cosmology Telescope Polarimeter Lensing Power Spectrum

NASA Technical Reports Server (NTRS)

Shewin, Blake D.; van Engelen, Alexander; Sehgal, Neelima; Madhavacheril, Mathew; Addison, Graeme E.; Aiola, Simone; Allison, Rupert; Battaglia, Nicholas; Becker, Daniel T.; Beall, James A.;

Poissonian renormalizations, exponentials, and power laws.

PubMed

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Hard diffraction and deep inelastic scattering

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

Bjorken, J.D.

1994-04-01

Since the advent of hard-collision physics, the study of diffractive processes - shadow physics - has been less prominent than before. However, there is now a renewed interest in the subject, especially in that aspect which synthesizes the short-distance, hard-collision phenomena with the classical physics of large rapidity-gaps. This is especially stimulated by the recent data on deep-inelastic scattering from HERA, as well as the theoretical work which relates to it. The word diffraction is sometimes used by high-energy physicists in a loose way. The author defines this term to mean: A diffractive process occurs if and only if theremore » is a large rapidity gap in the produced-particle phase space which is not exponentially suppressed. Here a rapidity gap means essentially no hadrons produced into the rapidity gap (which operates in the {open_quotes}lego{close_quotes} phase-space of pseudo-rapidity and azimuthal angle). And non-exponential suppression implies that the cross-section for creating a gap with width {Delta}{eta} does not have a power-law decrease with increasing subenergy s=e{sup {Delta}{eta}}, but behaves at most like some power of pseudorapidity {Delta}{eta}{approx}log(s). The term hard diffraction shall simply refer to those diffractive process which have jets in the final-state phase-space.« less

Broad distribution spectrum from Gaussian to power law appears in stochastic variations in RNA-seq data.

PubMed

Awazu, Akinori; Tanabe, Takahiro; Kamitani, Mari; Tezuka, Ayumi; Nagano, Atsushi J

2018-05-29

Gene expression levels exhibit stochastic variations among genetically identical organisms under the same environmental conditions. In many recent transcriptome analyses based on RNA sequencing (RNA-seq), variations in gene expression levels among replicates were assumed to follow a negative binomial distribution, although the physiological basis of this assumption remains unclear. In this study, RNA-seq data were obtained from Arabidopsis thaliana under eight conditions (21-27 replicates), and the characteristics of gene-dependent empirical probability density function (ePDF) profiles of gene expression levels were analyzed. For A. thaliana and Saccharomyces cerevisiae, various types of ePDF of gene expression levels were obtained that were classified as Gaussian, power law-like containing a long tail, or intermediate. These ePDF profiles were well fitted with a Gauss-power mixing distribution function derived from a simple model of a stochastic transcriptional network containing a feedback loop. The fitting function suggested that gene expression levels with long-tailed ePDFs would be strongly influenced by feedback regulation. Furthermore, the features of gene expression levels are correlated with their functions, with the levels of essential genes tending to follow a Gaussian-like ePDF while those of genes encoding nucleic acid-binding proteins and transcription factors exhibit long-tailed ePDF.

COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS

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

Mota, David F.; Winther, Hans A.

2011-05-20

In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to {Lambda}CDM, but can in some special cases enhance the growth of the linear perturbationsmore » at low redshifts. For the models we consider, it is found that this region of the parameter space is ruled out by local gravity constraints. Imposing a coupling to dark matter only, the local constraints are avoided, and it is possible to have observable signatures on the linear matter perturbations.« less

Power laws governing epidemics in isolated populations

NASA Astrophysics Data System (ADS)

Rhodes, C. J.; Anderson, R. M.

1996-06-01

TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1-11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12-14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16-19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.

Fitting power-laws in empirical data with estimators that work for all exponents

PubMed Central

Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan

2017-01-01

Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes. PMID:28245249

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.

Application of power spectrum, cepstrum, higher order spectrum and neural network analyses for induction motor fault diagnosis

NASA Astrophysics Data System (ADS)

Liang, B.; Iwnicki, S. D.; Zhao, Y.

2013-08-01

The power spectrum is defined as the square of the magnitude of the Fourier transform (FT) of a signal. The advantage of FT analysis is that it allows the decomposition of a signal into individual periodic frequency components and establishes the relative intensity of each component. It is the most commonly used signal processing technique today. If the same principle is applied for the detection of periodicity components in a Fourier spectrum, the process is called the cepstrum analysis. Cepstrum analysis is a very useful tool for detection families of harmonics with uniform spacing or the families of sidebands commonly found in gearbox, bearing and engine vibration fault spectra. Higher order spectra (HOS) (also known as polyspectra) consist of higher order moment of spectra which are able to detect non-linear interactions between frequency components. For HOS, the most commonly used is the bispectrum. The bispectrum is the third-order frequency domain measure, which contains information that standard power spectral analysis techniques cannot provide. It is well known that neural networks can represent complex non-linear relationships, and therefore they are extremely useful for fault identification and classification. This paper presents an application of power spectrum, cepstrum, bispectrum and neural network for fault pattern extraction of induction motors. The potential for using the power spectrum, cepstrum, bispectrum and neural network as a means for differentiating between healthy and faulty induction motor operation is examined. A series of experiments is done and the advantages and disadvantages between them are discussed. It has been found that a combination of power spectrum, cepstrum and bispectrum plus neural network analyses could be a very useful tool for condition monitoring and fault diagnosis of induction motors.

The Synchrotron Spectrum of Fast Cooling Electrons Revisited.

PubMed

Granot; Piran; Sari

2000-05-10

We discuss the spectrum arising from synchrotron emission by fast cooling (FC) electrons, when fresh electrons are continually accelerated by a strong blast wave, into a power-law distribution of energies. The FC spectrum has so far been described by four power-law segments divided by three break frequencies nusaspectrum, introducing a new break frequency, nuacspectrum for GRBs and their afterglows in the context of the internal-external shock model. Observations of Fnu~nu11&solm0;8 would enable us to probe scales much smaller than the typical size of the system and to constrain the amount of turbulent mixing behind the shock.

The Spectrum and Morphology of the Fermi Bubbles

NASA Technical Reports Server (NTRS)

Ackermann, M.; Albert, A.; Atwood, W. B.; Baldini, L.; Ballet, J.; Barbiellini, G.; Bastieri, D.; Bellazini, R.; Bissaldi, E.; Brandt, T. J.;

A common mode of origin of power laws in models of market and earthquake

NASA Astrophysics Data System (ADS)

Bhattacharyya, Pratip; Chatterjee, Arnab; Chakrabarti, Bikas K.

2007-07-01

We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random-saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap model for earthquakes. We find that the power laws appear as the asymptotic forms of ever-widening log-normal distributions for the agents’ money and the overlap magnitude, respectively. The identification of the generic origin of the power laws helps in better understanding and in developing generalized views of phenomena in such diverse areas as economics and geophysics.

29 CFR 458.76 - Duties and powers of the Administrative Law Judge.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 29 Labor 2 2010-07-01 2010-07-01 false Duties and powers of the Administrative Law Judge. 458.76... of the Administrative Law Judge. It shall be the duty of the Administrative Law Judge to inquire... the Assistant Secretary, the Administrative Law Judge shall have the authority to: (a) Grant requests...

Broadband X-Ray Spectra of GX 339-4 and the Geometry of Accreting Black Holes in the Hard State

NASA Technical Reports Server (NTRS)

Tomsick; Kalemci; Kaaret; Markoff; Corbel; Migliari; Fender; Bailyn; Buxton

2008-01-01

A major question in the study of black hole binaries involves our understanding of the accretion geometry when the sources are in the "hard" state. In this state, the X-ray energy spectrum is dominated by a hard power-law component and radio observations indicate the presence of a steady and powerful "compact" jet. Although the common hard state picture is that the accretion disk is truncated, perhaps at hundreds of gravitational radii (R(sub g)) from the black hole, recent results for the recurrent transient GX 339-4 by Miller and co-workers show evidence for optically thick material very close to the black hole's innermost stable circular orbit. That work focused on an observation of GX 339-4 at a luminosity of about 5% of the Eddington limit (L(sub Edd)) and used parameters from a relativistic reflection model and the presence of a soft, thermal component as diagnostics. In this work, we use similar diagnostics, but extend the study to lower luminosities (2.3% and 0.8% L(sub Edd)) using Swift and RXTE observations of GX 339-4. We detect a thermal component with an inner disk temperature of approx.0.2 keV at 2.3% L(sub Edd). At 0.8% L(sub Edd), the spectrum is consistent with the presence of such a component, but the component is not required with high confidence. At both luminosities, we detect broad features due to iron Ka that are likely related to reflection of hard X-rays off the optically thick material. If these features are broadened by relativistic effects, they indicate that optically thick material resides within 10 R(sub g) down to 0.8% L(sub Edd), and the measurements are consistent with the inner radius of the disk remaining at approx.4 R(sub g) down to this level. However, we also discuss an alternative model for the broadening, and we note that the evolution of the thermal component is not entirely consistent with the constant inner radius interpretation. Finally, we discuss the results in terms of recent theoretical work by Liu and co-workers on

Letting students discover the power, and the limits, of simple models: Coulomb's law

NASA Astrophysics Data System (ADS)

Bohacek, Peter; Vonk, Matthew; Dill, Joseph; Boehm, Emma

2017-09-01

The inverse-square law pops up all over. It's a simplified model of reality that describes light, sound, gravity, and static electricity. But when it's brought up in class, students are often just handed the equations. They rarely have an opportunity to discover Coulomb's law or Newton's law of gravitation for themselves. It's not hard to understand why. A quantitative demonstration of Coulomb's law can be difficult. The forces are smaller than many force sensors can measure and static electricity tends to be finicky. In addition, off-the-shelf units are expensive or difficult to use. As a result, many instructors skip this lab in favor of qualitative demonstrations or simulations. Adolf Cortel sought to remedy this by designing a straightforward experiment for measuring Coulomb's law using charged metalized-glass spheres (Christmas ornaments) and an electronic balance. Building on Cortel's design, we've made a series of video-based experiments that students can use to discover the relationships that underlie electric force.

Adiabatic regularization of the power spectrum in nonminimally coupled general single-field inflation

NASA Astrophysics Data System (ADS)

Alinea, Allan L.; Kubota, Takahiro

2018-03-01

We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruh's model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of e -folds. As in the result for the canonical inflation, the regularized power spectrum tends to the "bare" power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the "bare" power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving nonminimal coupling and varying speed of sound.

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.

Logarithmic and power law input-output relations in sensory systems with fold-change detection.

PubMed

Adler, Miri; Mayo, Avi; Alon, Uri

2014-08-01

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.

Cosmic-ray electron-positron spectrum from 7 GeV to 2 TeV with the Fermi Large Area Telescope

DOE PAGES

Abdollahi, S.; Ackermann, M.; Ajello, M.; ...

2017-04-15

Here, we present a measurement of the cosmic-ray electron+positron spectrum between 7 GeV and 2 TeV performed with almost seven years of data collected with the Fermi Large Area Telescope. We find that the spectrum is well fit by a broken power law with a break energy at about 50 GeV. Above 50 GeV, the spectrum is well described by a single power law with a spectral index of 3.07 ± 0.02(stat + syst) ± 0.04(energy measurement). An exponential cutoff lower than 1.8 TeV is excluded at 95% CL.

Cosmic-ray electron-positron spectrum from 7 GeV to 2 TeV with the Fermi Large Area Telescope

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

Abdollahi, S.; Ackermann, M.; Ajello, M.

Here, we present a measurement of the cosmic-ray electron+positron spectrum between 7 GeV and 2 TeV performed with almost seven years of data collected with the Fermi Large Area Telescope. We find that the spectrum is well fit by a broken power law with a break energy at about 50 GeV. Above 50 GeV, the spectrum is well described by a single power law with a spectral index of 3.07 ± 0.02(stat + syst) ± 0.04(energy measurement). An exponential cutoff lower than 1.8 TeV is excluded at 95% CL.

Poissonian renormalizations, exponentials, and power laws

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Two-season Atacama Cosmology Telescope polarimeter lensing power spectrum

NASA Astrophysics Data System (ADS)

Sherwin, Blake D.; van Engelen, Alexander; Sehgal, Neelima; Madhavacheril, Mathew; Addison, Graeme E.; Aiola, Simone; Allison, Rupert; Battaglia, Nicholas; Becker, Daniel T.; Beall, James A.; Bond, J. Richard; Calabrese, Erminia; Datta, Rahul; Devlin, Mark J.; Dünner, Rolando; Dunkley, Joanna; Fox, Anna E.; Gallardo, Patricio; Halpern, Mark; Hasselfield, Matthew; Henderson, Shawn; Hill, J. Colin; Hilton, Gene C.; Hubmayr, Johannes; Hughes, John P.; Hincks, Adam D.; Hlozek, Renée; Huffenberger, Kevin M.; Koopman, Brian; Kosowsky, Arthur; Louis, Thibaut; Maurin, Loïc; McMahon, Jeff; Moodley, Kavilan; Naess, Sigurd; Nati, Federico; Newburgh, Laura; Niemack, Michael D.; Page, Lyman A.; Sievers, Jonathan; Spergel, David N.; Staggs, Suzanne T.; Thornton, Robert J.; Van Lanen, Jeff; Vavagiakis, Eve; Wollack, Edward J.

2017-06-01

We report a measurement of the power spectrum of cosmic microwave background (CMB) lensing from two seasons of Atacama Cosmology Telescope polarimeter (ACTPol) CMB data. The CMB lensing power spectrum is extracted from both temperature and polarization data using quadratic estimators. We obtain results that are consistent with the expectation from the best-fit Planck Λ CDM model over a range of multipoles L =80 - 2100 , with an amplitude of lensing Alens=1.06 ±0.15 (stat )±0.06 (sys ) relative to Planck. Our measurement of the CMB lensing power spectrum gives σ8Ωm0.25=0.643 ±0.054 ; including baryon acoustic oscillation scale data, we constrain the amplitude of density fluctuations to be σ8=0.831 ±0.053 . We also update constraints on the neutrino mass sum. We verify our lensing measurement with a number of null tests and systematic checks, finding no evidence of significant systematic errors. This measurement relies on a small fraction of the ACTPol data already taken; more precise lensing results can therefore be expected from the full ACTPol data set.

Energy spectrum of tearing mode turbulence in sheared background field

NASA Astrophysics Data System (ADS)

Hu, Di; Bhattacharjee, Amitava; Huang, Yi-Min

2018-06-01

The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause an effective damping during the energy cascade. The other is the scale-independent anisotropy induced by the large-scale modes tilting the sheared background field, as opposed to the scale-dependent anisotropy frequently encountered in traditional critically balanced turbulence theories. Due to these two differences, the energy spectrum deviates from a simple power law and takes the form of a power law multiplied by an exponential falloff. Numerical simulations are carried out using visco-resistive MHD equations to verify our theoretical predictions, and a reasonable agreement is found between the numerical results and our model.

Simulation of Quiet-Sun Hard X-rays Related to Solar Wind Superhalo Electrons

NASA Astrophysics Data System (ADS)

Wang, W.; Wang, L.; Krucker, S.; Hannah, I. G.

2016-12-01

Abstract. In this paper, we propose that the accelerated electrons in the quiet-Sun could collide with the solar atmosphere to emit Hard X-rays (HXRs) via non-thermal bremsstrahlung, while some of these electrons would move upwards and escape into the interplanetary medium, to form a superhalo electron population measured in the solar wind. After considering the electron energy loss due to Coulomb collisions and the ambipolar electrostatic potential, we find that the sources of superhalo could only occur high in the corona (at a heliocentric altitude ≥ 1.9 Rs), to remain a power-law shape of electron spectrum as observed by STEREO at 1 AU near solar minimum (Wang et al, 2012).The modeled quiet-Sun HXRs related to the superhalo electrons fit well to a power-law spectrum, f(ɛ) ∝ ɛ-γ, with an index γ ≈ 2.0-2.3 (3.3-3.7) at 10-100 keV, for the warm/cold thick-target (thin-target) emissions produced by the downward-traveling (upward-traveling) accelerated electrons. These simulated quiet-Sun spectra are significantly harder than the observed spectra of most solar HXR flares. Assuming that the quiet-Sun sources cover 5% of the solar surface, the modeled thin-target HXRs are more than six orders of magnitude weaker than the RHESSI upper limits of quiet-Sun HXRs (Hannah et al., 2010). Using the thick-target model for the downward-traveling electrons, the RHESSI upper limits restrict the number of downward-traveling electrons to maximal ≈ 3 times the number of escaping electrons. This ratio is fundamentally different from what is observed during solar flares associated with escaping electrons where the fraction of downward-traveling electrons dominates by a factor of 100 to 1000 over the escaping population. References: 1. Hannah et al., APJ, 724, 487(2010) 2. Wang et al., APJ Letters,753,L23(2012) 3. Yang et al., RAA,Vol.15,No.3,348-362(2015) 4. Brown J.C., Solar Physics,Vol.18,Issue 3,489,502­­­(1971)

Hard X-ray and high-frequency decimetric radio observations of the 4 April 2002 solar flare

NASA Astrophysics Data System (ADS)

Kane, S. R.; Sawant, H. S.; Cecatto, J. R.; Andrade, M. C.; Fernandes, F. C. R.; Karlicky, M.; Meszarosova, H.

Hard X-ray and high frequency decimetric type III radio bursts have been observed in association with the soft X-raysolar flare (GOES class M 6.1) on 4 April 2002 (˜1532 UT). The flare apparently occurred ˜ 6 degrees behind the east limb of the Sun in the active region NOAA 9898. Hard X-ray spectra and images were obtained by the X-ray imager on RHESSI during the impulsive phase of the flare. The Brazilian Solar Spectroscope and Ondrejov Radio Telescopes recorded type III bursts in 800-1400 MHz range in association with the flare. The images of the 3-6, 6-12, 12-25, and 25-50 keV X-ray sources, obtained simultaneously by RHESSI during the early impulsive phase of the flare, show that all the four X-ray sources were essentially at the same location well above the limb of the Sun. During the early impulsive phase, the X-ray spectrum over 8-30 keV range was consistent with a power law with a negative exponent of ˜ 6. The radio spectra show drifting radio structures with emission in a relatively narrow (Δf ≤ 200 MHz) frequency range indicating injection of energetic electrons into a plasmoid which is slowly drifting upwards in the corona.

[The Lambert-Beer's law characterization of formal analysis in Terahertz spectrum quantitative testing].

PubMed

Su, Hai-Xia; Zhang, Zhao-Hui; Zhao, Xiao-Yan; Li, Zhi; Yan, Fang; Zhang, Han

2013-12-01

The present paper discusses the Lambert-Beer' s law application in the terahertz spectrum, studies the single amino acid tablet sample (glutamine) and two kinds of amino acids mixture tablet (threonine and cystine) under the condition of different concentrations. Absorbance and absorption coefficient was analyzed in the description of the terahertz optical properties of matter. By comparing absorption coefficient and absorbance value of the single component in the vicinity of 1. 72 THz, we verified the material under two kinds of absorption characterization of quantity of THz wave absorption along with the change in the concentration. Using the index of goodness of fit R , it studied the stand or fall of linear relationship between the terahertz absorption quantity of material and concentration under two kinds of representation. This paper analyzes the two components mixture under two kinds of absorption characterization of quantity of terahertz absorption in 0. 3-2. 6 THz. Using the similarity co- efficient and the estimate concentration error as evaluation index, it has been clear that the absorbance of additivity instead of the absorption coefficient should be used during the terahertz spectrum quantitative test, and the Lambert-Beer's law application in the terahertz wave band was further clarified.

Timing of continuous motor imagery: the two-thirds power law originates in trajectory planning.

PubMed

Karklinsky, Matan; Flash, Tamar

2015-04-01

The two-thirds power law, v = γκ(-1/3), expresses a robust local relationship between the geometrical and temporal aspects of human movement, represented by curvature κ and speed v, with a piecewise constant γ. This law is equivalent to moving at a constant equi-affine speed and thus constitutes an important example of motor invariance. Whether this kinematic regularity reflects central planning or peripheral biomechanical effects has been strongly debated. Motor imagery, i.e., forming mental images of a motor action, allows unique access to the temporal structure of motor planning. Earlier studies have shown that imagined discrete movements obey Fitts's law and their durations are well correlated with those of actual movements. Hence, it is natural to examine whether the temporal properties of continuous imagined movements comply with the two-thirds power law. A novel experimental paradigm for recording sparse imagery data from a continuous cyclic tracing task was developed. Using the likelihood ratio test, we concluded that for most subjects the distributions of the marked positions describing the imagined trajectory were significantly better explained by the two-thirds power law than by a constant Euclidean speed or by two other power law models. With nonlinear regression, the β parameter values in a generalized power law, v = γκ(-β), were inferred from the marked position records. This resulted in highly variable yet mostly positive β values. Our results imply that imagined trajectories do follow the two-thirds power law. Our findings therefore support the conclusion that the coupling between velocity and curvature originates in centrally represented motion planning. Copyright © 2015 the American Physiological Society.

Power spectrum, correlation function, and tests for luminosity bias in the CfA redshift survey

NASA Astrophysics Data System (ADS)

Park, Changbom; Vogeley, Michael S.; Geller, Margaret J.; Huchra, John P.

1994-08-01

We describe and apply a method for directly computing the power spectrum for the galaxy distribution in the extension of the Center for Astrophysics Redshift Survey. Tests show that our technique accurately reproduces the true power spectrum for k greater than 0.03 h Mpc-1. The dense sampling and large spatial coverage of this survey allow accurate measurement of the redshift-space power spectrum on scales from 5 to approximately 200 h-1 Mpc. The power spectrum has slope n approximately equal -2.1 on small scales (lambda less than or equal 25 h-1 Mpc) and n approximately -1.1 on scales 30 less than lambda less than 120 h-1 Mpc. On larger scales the power spectrum flattens somewhat, but we do not detect a turnover. Comparison with N-body simulations of cosmological models shows that an unbiased, open universe CDM model (OMEGA h = 0.2) and a nonzero cosmological constant (CDM) model (OMEGA h = 0.24, lambdazero = 0.6, b = 1.3) match the CfA power spectrum over the wavelength range we explore. The standard biased CDM model (OMEGA h = 0.5, b = 1.5) fails (99% significance level) because it has insufficient power on scales lambda greater than 30 h-1 Mpc. Biased CDM with a normalization that matches the Cosmic Microwave Background (CMB) anisotropy (OMEGA h = 0.5, b = 1.4, sigma8 (mass) = 1) has too much power on small scales to match the observed galaxy power spectrum. This model with b = 1 matches both Cosmic Background Explorer Satellite (COBE) and the small-scale power spect rum but has insufficient power on scales lambda approximately 100 h-1 Mpc. We derive a formula for the effect of small-scale peculiar velocities on the power spectrum and combine this formula with the linear-regime amplification described by Kaiser to compute an estimate of the real-space power spectrum. Two tests reveal luminosity bias in the galaxy distribution: First, the amplitude of the power spectrum is approximately 40% larger for the brightest 50% of galaxies in volume-limited samples that

Theoretical Conversions of Different Hardness and Tensile Strength for Ductile Materials Based on Stress-Strain Curves

NASA Astrophysics Data System (ADS)

Chen, Hui; Cai, Li-Xun

2018-04-01

Based on the power-law stress-strain relation and equivalent energy principle, theoretical equations for converting between Brinell hardness (HB), Rockwell hardness (HR), and Vickers hardness (HV) were established. Combining the pre-existing relation between the tensile strength ( σ b ) and Hollomon parameters ( K, N), theoretical conversions between hardness (HB/HR/HV) and tensile strength ( σ b ) were obtained as well. In addition, to confirm the pre-existing σ b -( K, N) relation, a large number of uniaxial tensile tests were conducted in various ductile materials. Finally, to verify the theoretical conversions, plenty of statistical data listed in ASTM and ISO standards were adopted to test the robustness of the converting equations with various hardness and tensile strength. The results show that both hardness conversions and hardness-strength conversions calculated from the theoretical equations accord well with the standard data.

Musical rhythm spectra from Bach to Joplin obey a 1/f power law.

PubMed

Levitin, Daniel J; Chordia, Parag; Menon, Vinod

2012-03-06

Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/f(β) power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.

Spectrum-based estimators of the bivariate Hurst exponent

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav

2014-12-01

We discuss two alternate spectrum-based estimators of the bivariate Hurst exponent in the power-law cross-correlations setting, the cross-periodogram and local X -Whittle estimators, as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration during estimation, a simulation study showing performance of the estimators under varying bandwidth parameter as well as correlation between processes and their specification is provided as well. These estimators are less biased than the already existent averaged periodogram estimator, which, however, has slightly lower variance. The spectrum-based estimators can serve as a good complement to the popular time domain estimators.

Genetic noise mechanism for power-law switching in bacterial flagellar motors

NASA Astrophysics Data System (ADS)

Krivonosov, M. I.; Zaburdaev, V.; Denisov, S. V.; Ivanchenko, M. V.

2018-06-01

Switching of the direction of flagella rotations is the key control mechanism governing the chemotactic activity of E. coli and many other bacteria. Power-law distributions of switching times are most peculiar because their emergence cannot be deduced from simple thermodynamic arguments. Recently, it was suggested that by adding finite-time correlations into Gaussian fluctuations regulating the energy height of the barrier between the two rotation states, it is possible to generate switching statistics with an intermediate power-law asymptotics. By using a simple model of a regulatory pathway, we demonstrate that the required amount of correlated ‘noise’ can be produced by finite number fluctuations of reacting protein molecules, a condition common to the intracellular chemistry. The corresponding power-law exponent appears as a tunable characteristic controlled by parameters of the regulatory pathway network such as the equilibrium number of molecules, sensitivities, and the characteristic relaxation time.

NuSTAR Search for Hard X-ray Emission from the Star Formation Regions in Sh2-104

NASA Astrophysics Data System (ADS)

Gotthelf, Eric V.

2016-04-01

We present NuSTAR hard X-ray observations of Sh2-104, a compact Hii region containing several young massive stellar clusters (YMSCs). We have detected distinct hard X-ray sources coincident with localized VERITAS TeV emission recently resolved from the giant gamma-ray complex MGRO J2019+37 in the Cygnus region. Faint, diffuse X-ray emission coincident with the eastern YMSC in Sh2-104 is likely the result of colliding winds of component stars. Just outside the radio shell of Sh2-104 lies 3XMM J201744.7+365045 and nearby nebula NuSTAR J201744.3+364812, whose properties are most consistent with extragalactic objects. The combined XMM-Newton and NuSTAR spectrum of 3XMM J201744.7+365045 is well-fit to an absorbed power-law model with NH = (3.1+/-1.0)E22 1/cm^2 and photon index Gamma = 2.1+/-0.1. Based on possible long-term flux variation and lack of detected pulsations (<43% modulation), this object is likely a background AGN rather than a Galactic pulsar. The spectrum of the NuSTAR nebula shows evidence of an emission line at E = 5.6 keV suggesting an optically obscured galaxy cluster at z = 0.19+/-0.02 (d = 800 Mpc) and Lx = 1.2E44 erg/s. Follow-up Chandra observations of Sh2-104 will help identify the nature of the X-ray sources and their relation to MGRO J2019+37.

Machining Specific Fourier Power Spectrum Profiles into Plastics for High Energy Density Physics Experiments [Machining Specific Fourier Power Spectrum Profiles into Plastics for HEDP Experiments

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

Schmidt, Derek William; Cardenas, Tana; Doss, Forrest W.

In this paper, the High Energy Density Physics program at Los Alamos National Laboratory (LANL) has had a multiyear campaign to verify the predictive capability of the interface evolution of shock propagation through different profiles machined into the face of a plastic package with an iodine-doped plastic center region. These experiments varied the machined surface from a simple sine wave to a double sine wave and finally to a multitude of different profiles with power spectrum ranges and shapes to verify LANL’s simulation capability. The MultiMode-A profiles had a band-pass flat region of the power spectrum, while the MultiMode-B profilemore » had two band-pass flat regions. Another profile of interest was the 1-Peak profile, a band-pass concept with a spike to one side of the power spectrum. All these profiles were machined in flat and tilted orientations of 30 and 60 deg. Tailor-made machining profiles, supplied by experimental physicists, were compared to actual machined surfaces, and Fourier power spectra were compared to see the reproducibility of the machining process over the frequency ranges that physicists require.« less

Machining Specific Fourier Power Spectrum Profiles into Plastics for High Energy Density Physics Experiments [Machining Specific Fourier Power Spectrum Profiles into Plastics for HEDP Experiments

DOE PAGES

Schmidt, Derek William; Cardenas, Tana; Doss, Forrest W.; ...

2018-01-15

In this paper, the High Energy Density Physics program at Los Alamos National Laboratory (LANL) has had a multiyear campaign to verify the predictive capability of the interface evolution of shock propagation through different profiles machined into the face of a plastic package with an iodine-doped plastic center region. These experiments varied the machined surface from a simple sine wave to a double sine wave and finally to a multitude of different profiles with power spectrum ranges and shapes to verify LANL’s simulation capability. The MultiMode-A profiles had a band-pass flat region of the power spectrum, while the MultiMode-B profilemore » had two band-pass flat regions. Another profile of interest was the 1-Peak profile, a band-pass concept with a spike to one side of the power spectrum. All these profiles were machined in flat and tilted orientations of 30 and 60 deg. Tailor-made machining profiles, supplied by experimental physicists, were compared to actual machined surfaces, and Fourier power spectra were compared to see the reproducibility of the machining process over the frequency ranges that physicists require.« less

Power spectrum, correlation function, and tests for luminosity bias in the CfA redshift survey

NASA Technical Reports Server (NTRS)

Park, Changbom; Vogeley, Michael S.; Geller, Margaret J.; Huchra, John P.

1994-01-01

We describe and apply a method for directly computing the power spectrum for the galaxy distribution in the extension of the Center for Astrophysics Redshift Survey. Tests show that our technique accurately reproduces the true power spectrum for k greater than 0.03 h Mpc(exp -1). The dense sampling and large spatial coverage of this survey allow accurate measurement of the redshift-space power spectrum on scales from 5 to approximately 200 h(exp -1) Mpc. The power spectrum has slope n approximately equal -2.1 on small scales (lambda less than or equal 25 h(exp -1) Mpc) and n approximately -1.1 on scales 30 less than lambda less than 120 h(exp -1) Mpc. On larger scales the power spectrum flattens somewhat, but we do not detect a turnover. Comparison with N-body simulations of cosmological models shows that an unbiased, open universe CDM model (OMEGA h = 0.2) and a nonzero cosmological constant (CDM) model (OMEGA h = 0.24, lambda(sub zero) = 0.6, b = 1.3) match the CfA power spectrum over the wavelength range we explore. The standard biased CDM model (OMEGA h = 0.5, b = 1.5) fails (99% significance level) because it has insufficient power on scales lambda greater than 30 h(exp -1) Mpc. Biased CDM with a normalization that matches the Cosmic Microwave Background (CMB) anisotropy (OMEGA h = 0.5, b = 1.4, sigma(sub 8) (mass) = 1) has too much power on small scales to match the observed galaxy power spectrum. This model with b = 1 matches both Cosmic Background Explorer Satellite (COBE) and the small-scale power spect rum but has insufficient power on scales lambda approximately 100 h(exp -1) Mpc. We derive a formula for the effect of small-scale peculiar velocities on the power spectrum and combine this formula with the linear-regime amplification described by Kaiser to compute an estimate of the real-space power spectrum. Two tests reveal luminosity bias in the galaxy distribution: First, the amplitude of the pwer spectrum is approximately 40% larger for the brightest

State intervention in pregnancy: Should the law respond thus to the problem of Foetal Alcohol Spectrum Disorder?

PubMed

Gordon, Emily

2015-09-01

Maternal consumption of alcohol during pregnancy poses a serious threat to the life and health of unborn children. A submission to the Queensland Child Protection Commission of Inquiry proposed that the State's Child Protection Act be extended to allow intervention to protect unborn children, with a court empowered to order that the mother be taken into care pending birth, or otherwise impose conditions upon conduct. This article considers whether or not the law in Australia should respond to the problem of Foetal Alcohol Spectrum Disorder by allowing the involuntary treatment and detention of pregnant women. The focus, is upon intervention in response to existing pregnancies. Using a utilitarian critical framework, this article evaluates the merits of creating powers to compel treatment and detain in light of current legal principles relating to maternal autonomy and the legal position of the foetus. The common law position is considered, as well as current legislation allowing intervention in autonomous decision-making and whether or not these statutes may be enlivened to prevent foetal harm. This article suggests that permitting involuntary treatment and detention would be a significant policy change. It weighs up benefits and potential harms in considering whether or not such action would result in the most "good".

Scaling range of power laws that originate from fluctuation analysis

NASA Astrophysics Data System (ADS)

Grech, Dariusz; Mazur, Zygmunt

2013-05-01

We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.

Hard X-ray Emission and Efficient Particle Acceleration by Supernova Remnants

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

Vink, Jacco

I discuss the non-thermal X-ray emission from young supernova remnants. Over the last decade it has become clear from both X-ray and {gamma}-ray observations that young supernovae accelerate particles up to 100 TeV. In soft X-rays the accelerated >10 TeV electrons produce synchrotron radiation, coming from narrow filaments located at the shock fronts. The width of these filaments shows that the magnetic fields are relatively high, thus providing evidence for magnetic field amplification.The synchrotron radiation of several remnants is known to extend into the hard X-ray regime. In particular Cas A, has a spectrum that appears as a power lawmore » up to almost 100 TeV. This is very surprising, as a steepening is expected going from the soft to the hard X-ray band. The spectrum is likely a result of many superimposed individual spectra, each steepening at different energies. This implies considerable spatial variation in hard X-rays, an obvious target for Simbol-X. The variations will be important to infer local shock acceleration properties, but also magnetic field fluctuations may cause spatial and temporal variations.Finally, I draw the attention to super bubbles and supernovae as sources of cosmic rays. As such they may be sources of hard X-ray emission. In particular, supernovae exploding inside the dense red supergiants winds of their progenitors ares promising candidates for hard X-ray emission.« less

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

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

Mukherjee, Suvodip; Das, Santanu; 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 m{sub eff} 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 independentmore » parameters, namely spectral index for tensor perturbation ν{sub t} and change in spectral index for scalar perturbation ν{sub st} 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 n{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.« less

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.

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.

The Spectrum And Morphology Of The Fermi Bubbles

DOE PAGES

Ackermann, M.

2014-09-05

The Fermi bubbles are two large structures in the gamma-ray sky extending to 55° above and below the Galactic center. We analyze 50 months of Fermi Large Area Telescope data between 100 MeV and 500 GeV above 10° in Galactic latitude to derive the spectrum and morphology of the Fermi bubbles. We thoroughly explore the systematic uncertainties that arise when modeling the Galactic diffuse emission through two separate approaches. The gamma-ray spectrum is well described by either a log parabola or a power law with an exponential cutoff. We exclude a simple power law with more than 7σ signi cance.more » The power law with an exponential cutoff has an index of 1:9±0:2 and a cutoff energy of 110 ± 50 GeV. We nd that the gamma-ray luminosity of the bubbles is 4:4+2:4 -0:9 X 1037 erg s -1. We confirm a signi cant enhancement of gamma-ray emission in the south-eastern part of the bubbles, but we do not nd signi cant evidence for a jet. No signi cant variation of the spectrum across the bubbles is detected. The width of the boundary of the bubbles is estimated to be 3:4+3:7 -2:6 deg. Both inverse Compton (IC) models and hadronic models including IC emission from secondary leptons t the gamma-ray data well. In the IC scenario, the synchrotron emission from the same population of electrons can also explain the WMAP and Planck microwave haze with a magnetic eld between 5 and 20 μG.« less

Reconstruction of the primordial power spectrum using temperature and polarisation data from multiple experiments

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

Nicholson, Gavin; Contaldi, Carlo R., E-mail: gavin.nicholson05@imperial.ac.uk, E-mail: c.contaldi@imperial.ac.uk

2009-07-01

We develop a method to reconstruct the primordial power spectrum, P(k), using both temperature and polarisation data from the joint analysis of a number of Cosmic Microwave Background (CMB) observations. The method is an extension of the Richardson-Lucy algorithm, first applied in this context by Shafieloo and Souradeep [1]. We show how the inclusion of polarisation measurements can decrease the uncertainty in the reconstructed power spectrum. In particular, the polarisation data can constrain oscillations in the spectrum more effectively than total intensity only measurements. We apply the estimator to a compilation of current CMB results. The reconstructed spectrum is consistentmore » with the best-fit power spectrum although we find evidence for a 'dip' in the power on scales k ≈ 0.002 Mpc{sup −1}. This feature appears to be associated with the WMAP power in the region 18 ≤ l ≤ 26 which is consistently below best-fit models. We also forecast the reconstruction for a simulated, Planck-like [2] survey including sample variance limited polarisation data.« less

Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

NASA Astrophysics Data System (ADS)

Sibatov, R. T.

2011-08-01

A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.

Chandra X-ray Spectroscopy of the Focused Wind In the Cygnus X-1 System I. The Non-Dip Spectrum in the Low/Hard State

NASA Technical Reports Server (NTRS)

Hanke, Manfred; Wilms, Jorn; Nowak, Michael A.; Pottschmidt, Katja; Schultz, Norbert S.; Lee, Julia C.

2008-01-01

We present analyses of a 50 ks observation of the supergiant X-ray binary system CygnusX-1/HDE226868 taken with the Chandra High Energy Transmission Grating Spectrometer (HETGS). CygX-1 was in its spectrally hard state and the observation was performed during superior conjunction of the black hole, allowing for the spectroscopic analysis of the accreted stellar wind along the line of sight. A significant part of the observation covers X-ray dips as commonly observed for CygX-1 at this orbital phase, however, here we only analyze the high count rate non-dip spectrum. The full 0.5-10 keV continuum can be described by a single model consisting of a disk, a narrow and a relativistically broadened Fe K line, and a power law component, which is consistent with simultaneous RXTE broad band data. We detect absorption edges from overabundant neutral O, Ne and Fe, and absorption line series from highly ionized ions and infer column densities and Doppler shifts. With emission lines of He-like Mg XI, we detect two plasma components with velocities and densities consistent with the base of the spherical wind and a focused wind. A simple simulation of the photoionization zone suggests that large parts of the spherical wind outside of the focused stream are completely ionized, which is consistent with the low velocities (<200 km/s) observed in the absorption lines, as the position of absorbers in a spherical wind at low projected velocity is well constrained. Our observations provide input for models that couple the wind activity of HDE 226868 to the properties of the accretion flow onto the black hole.

Blinking in quantum dots: The origin of the grey state and power law statistics

NASA Astrophysics Data System (ADS)

Ye, Mao; Searson, Peter C.

2011-09-01

Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.

The speed–curvature power law in Drosophila larval locomotion

PubMed Central

2016-01-01

We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species. PMID:28120807

The speed-curvature power law in Drosophila larval locomotion.

PubMed

Zago, Myrka; Lacquaniti, Francesco; Gomez-Marin, Alex

2016-10-01

We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species. © 2016 The Authors.

Supernovae anisotropy power spectrum

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

Ghodsi, Hoda; Baghram, Shant; Habibi, Farhang, E-mail: h.ghodsi@mehr.sharif.ir, E-mail: baghram@sharif.edu, E-mail: habibi@lal.in2p3.fr

2017-10-01

We contribute another anisotropy study to this field of research using Type Ia supernovae (SNe Ia). In this work, we utilise the power spectrum calculation method and apply it to both the current SNe Ia data and simulation. Using the Union2.1 data set at all redshifts, we compare the spectrum of the residuals of the observed distance moduli to that expected from an isotropic universe affected by the Union2.1 observational uncertainties at low multipoles. Through this comparison we find a dipolar anisotropy with tension of less that 2σ towards l = 171° ± 21° and b = −26° ± 28°more » which is mainly induced by anisotropic spatial distribution of the SNe with z > 0.2 rather than being a cosmic effect. Furthermore, we find a tension of ∼ 4σ at ℓ = 4 between the two spectra. Our simulations are constructed with the characteristics of the upcoming surveys like the Large Synoptic Survey Telescope (LSST), which shall bring us the largest SNe Ia collection to date. We make predictions for the amplitude of a possible dipolar anisotropy that would be detectable by future SNe Ia surveys.« less

Dark Energy Constraints from the Thermal Sunyaev Zeldovich Power Spectrum

NASA Astrophysics Data System (ADS)

Bolliet, Boris; Comis, Barbara; Komatsu, Eiichiro; Macías-Pérez, Juan Francisco

2018-03-01

We constrain the dark energy equation of state parameter, w, using the power spectrum of the thermal Sunyaev-Zeldovich (tSZ) effect. We improve upon previous analyses by taking into account the trispectrum in the covariance matrix and marginalising over the foreground parameters, the correlated noise, the mass bias B in the Planck universal pressure profile, and all the relevant cosmological parameters (i.e., not just Ωm and σ8). We find that the amplitude of the tSZ power spectrum at ℓ ≲ 103 depends primarily on F ≡ σ8(Ωm/B)0.40h-0.21, where B is related to more commonly used variable b by B = (1 - b)-1. We measure this parameter with 2.6% precision, F = 0.460 ± 0.012 (68% CL). By fixing the bias to B = 1.25 and adding the local determination of the Hubble constant H0 and the amplitude of the primordial power spectrum constrained by the Planck Cosmic Microwave Background (CMB) data, we find w = -1.10 ± 0.12, σ8 = 0.802 ± 0.037, and Ωm = 0.265 ± 0.022 (68% CL). Our limit on w is consistent with and is as tight as that from the distance-alone constraint from the CMB and H0. Finally, by combining the tSZ power spectrum and the CMB data we find, in the Λ Cold Dark Matter (CDM) model, the mass bias of B = 1.71 ± 0.17, i.e., 1 - b = 0.58 ± 0.06 (68% CL).

NuSTAR HARD X-RAY SURVEY OF THE GALACTIC CENTER REGION. I. HARD X-RAY MORPHOLOGY AND SPECTROSCOPY OF THE DIFFUSE EMISSION

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

Mori, Kaya; Hailey, Charles J.; Perez, Kerstin

2015-12-01

We present the first sub-arcminute images of the Galactic Center above 10 keV, obtained with NuSTAR. NuSTAR resolves the hard X-ray source IGR J17456–2901 into non-thermal X-ray filaments, molecular clouds, point sources, and a previously unknown central component of hard X-ray emission (CHXE). NuSTAR detects four non-thermal X-ray filaments, extending the detection of their power-law spectra with Γ ∼ 1.3–2.3 up to ∼50 keV. A morphological and spectral study of the filaments suggests that their origin may be heterogeneous, where previous studies suggested a common origin in young pulsar wind nebulae (PWNe). NuSTAR detects non-thermal X-ray continuum emission spatially correlated with the 6.4more » keV Fe Kα fluorescence line emission associated with two Sgr A molecular clouds: MC1 and the Bridge. Broadband X-ray spectral analysis with a Monte-Carlo based X-ray reflection model self-consistently determined their intrinsic column density (∼10{sup 23} cm{sup −2}), primary X-ray spectra (power-laws with Γ ∼ 2) and set a lower limit of the X-ray luminosity of Sgr A* flare illuminating the Sgr A clouds to L{sub X} ≳ 10{sup 38} erg s{sup −1}. Above ∼20 keV, hard X-ray emission in the central 10 pc region around Sgr A* consists of the candidate PWN G359.95–0.04 and the CHXE, possibly resulting from an unresolved population of massive CVs with white dwarf masses M{sub WD} ∼ 0.9 M{sub ⊙}. Spectral energy distribution analysis suggests that G359.95–0.04 is likely the hard X-ray counterpart of the ultra-high gamma-ray source HESS J1745–290, strongly favoring a leptonic origin of the GC TeV emission.« less

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

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.

Relativistic jet feedback - II. Relationship to gigahertz peak spectrum and compact steep spectrum radio galaxies

NASA Astrophysics Data System (ADS)

Bicknell, Geoffrey V.; Mukherjee, Dipanjan; Wagner, Alexander Y.; Sutherland, Ralph S.; Nesvadba, Nicole P. H.

2018-04-01

We propose that Gigahertz Peak Spectrum (GPS) and Compact Steep Spectrum (CSS) radio sources are the signposts of relativistic jet feedback in evolving galaxies. Our simulations of relativistic jets interacting with a warm, inhomogeneous medium, utilizing cloud densities and velocity dispersions in the range derived from optical observations, show that free-free absorption can account for the ˜ GHz peak frequencies and low-frequency power laws inferred from the radio observations. These new computational models replace a power-law model for the free-free optical depth a more fundamental model involving disrupted log-normal distributions of warm gas. One feature of our new models is that at early stages, the low-frequency spectrum is steep but progressively flattens as a result of a broader distribution of optical depths, suggesting that the steep low-frequency spectra discovered by Callingham et al. may possibly be attributed to young sources. We also investigate the inverse correlation between peak frequency and size and find that the initial location on this correlation is determined by the average density of the warm ISM. The simulated sources track this correlation initially but eventually fall below it, indicating the need for a more extended ISM than presently modelled. GPS and CSS sources can potentially provide new insights into the phenomenon of AGN feedback since their peak frequencies and spectra are indicative of the density, turbulent structure, and distribution of gas in the host galaxy.

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.

The Trial Software version for DEMETER power spectrum files visualization and mapping

NASA Astrophysics Data System (ADS)

Lozbin, Anatoliy; Inchin, Alexander; Shpadi, Maxim

2010-05-01

In the frame of Kazakhstan's Scientific Space System creation for earthquakes precursors research, the hardware and software of DEMETER satellite was investigated. The data processing Software of DEMETER is based on package SWAN under IDL Virtual machine and realizes many features, but we can't find an important tool for the spectrograms analysis - space-time visualization of power spectrum files from electromagnetic devices as ICE and IMSC. For elimination of this problem we have developed Software which is offered to use. The DeSS (DEMETER Spectrogram Software) - it is Software for visualization, analysis and a mapping of power spectrum data from electromagnetic devices ICE and IMSC. The Software primary goal is to give the researcher friendly tool for the analysis of electromagnetic data from DEMETER Satellite for earthquake precursors and other ionosphere events researches. The Input data for DeSS Software is a power spectrum files: - Power spectrum of 1 component of the electric field in the VLF range (APID 1132); - Power spectrum of 1 component of the electric field in the HF range (APID 1134); - Power spectrum of 1 component of the magnetic field in the VLF range (APID 1137). The main features and operations of the software is possible: - various time and frequency filtration; - visualization of time dependence of signal intensity on fixed frequency; - spectral density visualization for fixed frequency range; - spectrogram autosize and smooth spectrogram; - the information in each point of the spectrogram: time, frequency and intensity; - the spectrum information in the separate window, consisting of 4 blocks; - data mapping with 6 range scale. On the map we can browse next information: - satellite orbit; - conjugate point at the satellite altitude; - north conjugate point at the altitude 110 km; - south conjugate point at the altitude 110 km. This is only trial software version to help the researchers and we always ready collaborate with scientists for

The spectrum of the geoid from altimeter data

NASA Technical Reports Server (NTRS)

Wagner, C. A.

1977-01-01

A variety of sources of detailed information has been analyzed to arrive at a geoid power spectrum from global altimeter data. Using the equivalent of only two revolutions of data (mostly from GEOS-3) from all the major oceans, the high frequency geoid power (rms) is estimated (most simply) to be 80.7 n to the minus 1.47th power meters, where n is in cycles/global revolutions. This law is valid for all frequencies above 19 cycles but includes sea state. The (simple) law has more power than predicted by Kaula's rule for the geopotential. However, the data shows significantly less power for frequencies below 100 cycles. A closer approximation to the altimetry accumulates 2.18m (rss) for all frequencies higher than 19 cycles/rev. (including sea state), somewhat less power than predicted by the rule. The data permits up to 1.25 (rms) non-gravitational departures from the high frequency marine geoid.

Strategies for Radiation Hardness Testing of Power Semiconductor Devices

NASA Technical Reports Server (NTRS)

Soltis, James V. (Technical Monitor); Patton, Martin O.; Harris, Richard D.; Rohal, Robert G.; Blue, Thomas E.; Kauffman, Andrew C.; Frasca, Albert J.

2005-01-01

Plans on the drawing board for future space missions call for much larger power systems than have been flown in the past. These systems would employ much higher voltages and currents to enable more powerful electric propulsion engines and other improvements on what will also be much larger spacecraft. Long term human outposts on the moon and planets would also require high voltage, high current and long life power sources. Only hundreds of watts are produced and controlled on a typical robotic exploration spacecraft today. Megawatt systems are required for tomorrow. Semiconductor devices used to control and convert electrical energy in large space power systems will be exposed to electromagnetic and particle radiation of many types, depending on the trajectory and duration of the mission and on the power source. It is necessary to understand the often very different effects of the radiations on the control and conversion systems. Power semiconductor test strategies that we have developed and employed will be presented, along with selected results. The early results that we have obtained in testing large power semiconductor devices give a good indication of the degradation in electrical performance that can be expected in response to a given dose. We are also able to highlight differences in radiation hardness that may be device or material specific.

TRACING THE REVERBERATION LAG IN THE HARD STATE OF BLACK HOLE X-RAY BINARIES

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

De Marco, B.; Ponti, G.; Nandra, K.

2015-11-20

We report results obtained from a systematic analysis of X-ray lags in a sample of black hole X-ray binaries, with the aim of assessing the presence of reverberation lags and studying their evolution during outburst. We used XMM-Newton and simultaneous Rossi X-ray Timing Explorer (RXTE) observations to obtain broadband energy coverage of both the disk and the hard X-ray Comptonization components. In most cases the detection of reverberation lags is hampered by low levels of variability-power signal-to-noise ratio (typically when the source is in a soft state) and/or short exposure times. The most detailed study was possible for GX 339-4more » in the hard state, which allowed us to characterize the evolution of X-ray lags as a function of luminosity in a single source. Over all the sampled frequencies (∼0.05–9 Hz), we observe the hard lags intrinsic to the power-law component, already well known from previous RXTE studies. The XMM-Newton soft X-ray response allows us to detail the disk variability. At low frequencies (long timescales) the disk component always leads the power-law component. On the other hand, a soft reverberation lag (ascribable to thermal reprocessing) is always detected at high frequencies (short timescales). The intrinsic amplitude of the reverberation lag decreases as the source luminosity and the disk fraction increase. This suggests that the distance between the X-ray source and the region of the optically thick disk where reprocessing occurs gradually decreases as GX 339-4 rises in luminosity through the hard state, possibly as a consequence of reduced disk truncation.« less

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

Joint Estimation of the Epoch of Reionization Power Spectrum and Foregrounds

NASA Astrophysics Data System (ADS)

Sims, Peter; Pober, Jonathan

2018-01-01

Bright astrophysical foregrounds present a significant impediment to the detection of redshifted 21-cm emission from the Epoch of Reionization on large spatial scales. In this talk I present a framework for the joint modeling of the power spectral contamination by astrophysical foregrounds and the power spectrum of the Epoch of Reionization. I show how informative priors on the power spectral contamination by astrophysical foregrounds at high redshifts, where emission from both the Epoch of Reionization and its foregrounds is present in the data, can be obtained through analysis of foreground-only emission at lower redshifts. Finally, I demonstrate how, by using such informative foreground priors, joint modeling can be employed to mitigate bias in estimates of the power spectrum of the Epoch of Reionization signal and, in particular, to enable recovery of more robust power spectral estimates on large spatial scales.

Power-law rheology controls aftershock triggering and decay

PubMed Central

Zhang, Xiaoming; Shcherbakov, Robert

2016-01-01

The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established. PMID:27819355

Spreading law of non-Newtonian power-law liquids on a spherical substrate by an energy-balance approach.

PubMed

Iwamatsu, Masao

2017-07-01

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation that governs the evolution of the contact line. The time evolution of the dynamic contact angle θ of a droplet obeys a power law θ∼t^{-α} with the spreading exponent α, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

NuSTAR Hard X-Ray Observation of the Gamma-Ray Binary Candidate HESS J1832-093

NASA Astrophysics Data System (ADS)

Mori, Kaya; Gotthelf, E. V.; Hailey, Charles J.; Hord, Ben J.; de Oña Wilhelmi, Emma; Rahoui, Farid; Tomsick, John A.; Zhang, Shuo; Hong, Jaesub; Garvin, Amani M.; Boggs, Steven E.; Christensen, Finn E.; Craig, William W.; Harrison, Fiona A.; Stern, Daniel; Zhang, William W.

2017-10-01

We present a hard X-ray observation of the TeV gamma-ray binary candidate HESS J1832-093, which is coincident with the supernova remnant G22.7-0.2, using the Nuclear Spectroscopic Telescope Array. Non-thermal X-ray emission from XMMU J183245-0921539, the X-ray source associated with HESS J1832-093, is detected up to ˜30 keV and is well-described by an absorbed power-law model with a best-fit photon index {{Γ }}=1.5+/- 0.1. A re-analysis of archival Chandra and XMM-Newton data finds that the long-term X-ray flux increase of XMMU J183245-0921539 is {50}-20+40 % (90% C.L.), much less than previously reported. A search for a pulsar spin period or binary orbit modulation yields no significant signal to a pulse fraction limit of {f}p< 19 % in the range 4 ms < P< 40 ks. No red noise is detected in the FFT power spectrum to suggest active accretion from a binary system. While further evidence is required, we argue that the X-ray and gamma-ray properties of XMMU J183245-0921539 are most consistent with a non-accreting binary generating synchrotron X-rays from particle acceleration in the shock formed as a result of the pulsar and stellar wind collision. We also report on three nearby hard X-ray sources, one of which may be associated with diffuse emission from a fast-moving supernova fragment interacting with a dense molecular cloud.

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

The high energy X-ray spectrum of 4U 1700-37 observed from OSO 8

NASA Technical Reports Server (NTRS)

Dolan, J. F.; Coe, M. J.; Crannell, C. J.; Dennis, B. R.; Frost, K. J.; Orwig, L. E.; Maurer, G. S.

1980-01-01

The most intense hard X-ray source in the confused region in Scorpius has been identified as 4U 1700-37 (=HD 153919). Observations extending over three binary periods in 1978 September were carried out with the high-energy X-ray spectrometer on OSO 8. The 3.4 day modulation is seen above 20 keV with the intensity during eclipse being consistent with zero flux. The photonumber spectrum from 20 to 150 keV is well represented by a single power law with a photonumber spectral index of -2.77 + or - 0.35 or by a thermal bremsstrahlung spectrum with kT = 27 (+15, -7)keV. The counting rate above 20 keV outside of eclipse shows no evidence for the 96.8 minute X-ray modulation previously reported at lower energies. Despite the difficulties that exist in reconciling both the lack of periodic modulation in the emitted X-radiation and the orbital dynamics of the system with our currently accepted theories of the evolution and physical properties of neutron stars, the observed properties of 4U 1700-37 are all consistent with the source being a spherically accreting neutron star rather than a black hole.

A new method to cluster genomes based on cumulative Fourier power spectrum.

PubMed

Dong, Rui; Zhu, Ziyue; Yin, Changchuan; He, Rong L; Yau, Stephen S-T

2018-06-20

Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum). Copyright © 2018. Published by Elsevier B.V.

The Accreting Black Hole Swift J1753.5-0127 from Radio to Hard X-Ray

NASA Astrophysics Data System (ADS)

Tomsick, John A.; Rahoui, Farid; Kolehmainen, Mari; Miller-Jones, James; Fürst, Felix; Yamaoka, Kazutaka; Akitaya, Hiroshi; Corbel, Stéphane; Coriat, Mickael; Done, Chris; Gandhi, Poshak; Harrison, Fiona A.; Huang, Kuiyun; Kaaret, Philip; Kalemci, Emrah; Kanda, Yuka; Migliari, Simone; Miller, Jon M.; Moritani, Yuki; Stern, Daniel; Uemura, Makoto; Urata, Yuji

2015-07-01

We report on multiwavelength measurements of the accreting black hole Swift J1753.5-0127 in the hard state at low luminosity (L ˜ 2.7 × 1036 erg s-1 assuming a distance of d = 3 kpc) in 2014 April. The radio emission is optically thick synchrotron, presumably from a compact jet. We take advantage of the low extinction (E(B-V)=0.45 from earlier work) and model the near-IR to UV emission with a multitemperature disk model. Assuming a black hole mass of MBH = 5 M⊙ and a system inclination of i = 40°, the fits imply an inner radius for the disk of Rin/Rg > 212d3(MBH/5 M⊙)-1, where Rg is the gravitational radius of the black hole and d3 is the distance to the source in units of 3 kpc. The outer radius is Rout/Rg=90,000 d3(MBH/5 M⊙)-1, which corresponds to 6.6 × 1010 d3 cm, consistent with the expected size of the disk given previous measurements of the size of the companion's Roche lobe. The 0.5-240 keV energy spectrum measured by Swift/X-ray Telescope (XRT), Suzaku (XIS, PIN, and GSO), and Nuclear Spectroscopic Telescope Array is relatively well characterized by an absorbed power law with a photon index of Γ = 1.722 ± 0.003 (90% confidence error), but a significant improvement is seen when a second continuum component is added. Reflection is a possibility, but no iron line is detected, implying a low iron abundance. We are able to fit the entire (radio to 240 keV) spectral energy distribution (SED) with a multitemperature disk component, a Comptonization component, and a broken power law, representing the emission from the compact jet. The broken power law cannot significantly contribute to the soft X-ray emission, and this may be related to why Swift J1753.5-0127 is an outlier in the radio/X-ray correlation. The broken power law (i.e., the jet) might dominate above 20 keV, which would constrain the break frequency to be between 2.4 × 1010 and 3.6 × 1012 Hz. Although the fits to the full SED do not include significant thermal emission in the X-ray band

Identification of the Hard X-Ray Source Dominating the E > 25 keV Emission of the Nearby Galaxy M31

NASA Technical Reports Server (NTRS)

Yukita, M.; Ptak, A.; Hornschemeier, A. E.; Wik, D.; Maccarone, T.J.; Pottschmidt, Katja; Zezas, A.; Antoniou, V.; Ballhausen, R.; Lehmer, B.D.;

Identification of the Hard X-Ray Source Dominating the E > 25 keV Emission of the Nearby Galaxy M31

NASA Technical Reports Server (NTRS)

Yukita, M.; Ptak, A.; Hornschemeier, A. E.; Wik, D.; Maccarone, T. J.; Pottschmidt, K.; Zezas, A.; Antoniou, V.; Ballhausen, R.; Lehmer, B. D.;

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.

Charting the Parameter Space of the 21-cm Power Spectrum

NASA Astrophysics Data System (ADS)

Cohen, Aviad; Fialkov, Anastasia; Barkana, Rennan

2018-05-01

The high-redshift 21-cm signal of neutral hydrogen is expected to be observed within the next decade and will reveal epochs of cosmic evolution that have been previously inaccessible. Due to the lack of observations, many of the astrophysical processes that took place at early times are poorly constrained. In recent work we explored the astrophysical parameter space and the resulting large variety of possible global (sky-averaged) 21-cm signals. Here we extend our analysis to the fluctuations in the 21-cm signal, accounting for those introduced by density and velocity, Lyα radiation, X-ray heating, and ionization. While the radiation sources are usually highlighted, we find that in many cases the density fluctuations play a significant role at intermediate redshifts. Using both the power spectrum and its slope, we show that properties of high-redshift sources can be extracted from the observable features of the fluctuation pattern. For instance, the peak amplitude of ionization fluctuations can be used to estimate whether heating occurred early or late and, in the early case, to also deduce the cosmic mean ionized fraction at that time. The slope of the power spectrum has a more universal redshift evolution than the power spectrum itself and can thus be used more easily as a tracer of high-redshift astrophysics. Its peaks can be used, for example, to estimate the redshift of the Lyα coupling transition and the redshift of the heating transition (and the mean gas temperature at that time). We also show that a tight correlation is predicted between features of the power spectrum and of the global signal, potentially yielding important consistency checks.

Dark energy constraints from the thermal Sunyaev-Zeldovich power spectrum

NASA Astrophysics Data System (ADS)

Bolliet, Boris; Comis, Barbara; Komatsu, Eiichiro; Macías-Pérez, Juan Francisco

2018-07-01

We constrain the dark energy equation of state parameter, {w}, using the power spectrum of the thermal Sunyaev-Zeldovich (tSZ) effect. We improve upon previous analyses by taking into account the trispectrum in the covariance matrix and marginalizing over the foreground parameters, the correlated noise, the mass bias B in the Planck universal pressure profile, and all the relevant cosmological parameters (i.e. not just Ωm and σ8). We find that the amplitude of the tSZ power spectrum at ℓ ≲ 103 depends primarily on F ≡ σ8(Ωm/B)0.40h-0.21, where B is related to more commonly used variable b by B = (1 - b)-1. We measure this parameter with 2.6 per cent precision, F = 0.460 ± 0.012 (68 per cent CL). By fixing the bias to B = 1.25 and adding the local determination of the Hubble constant H0 and the amplitude of the primordial power spectrum constrained by the Planck cosmic microwave background (CMB) data, we find {w} = -1.10 ± 0.12, σ8 = 0.802 ± 0.037, and Ωm = 0.265 ± 0.022 (68 per cent CL). Our limit on {w} is consistent with and is as tight as that from the distance-alone constraint from the CMB and H0. Finally, by combining the tSZ power spectrum and the CMB data we find, in the Λ cold dark matter model, the mass bias of B = 1.71 ± 0.17, i.e. 1 - b = 0.58 ± 0.06 (68 per cent CL).

X-RAY VARIABILITY AND HARDNESS OF ESO 243-49 HLX-1: CLEAR EVIDENCE FOR SPECTRAL STATE TRANSITIONS

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

Servillat, Mathieu; Farrell, Sean A.; Lin Dacheng

2011-12-10

The ultraluminous X-ray (ULX) source ESO 243-49 HLX-1, which reaches a maximum luminosity of 10{sup 42} erg s{sup -1} (0.2-10 keV), currently provides the strongest evidence for the existence of intermediate-mass black holes (IMBHs). To study the spectral variability of the source, we conduct an ongoing monitoring campaign with the Swift X-ray Telescope (XRT), which now spans more than two years. We found that HLX-1 showed two fast rise and exponential decay type outbursts in the Swift XRT light curve with increases in the count rate of a factor {approx}40 separated by 375 {+-} 13 days. We obtained new XMM-Newtonmore » and Chandra dedicated pointings that were triggered at the lowest and highest luminosities, respectively. From spectral fitting, the unabsorbed luminosities ranged from 1.9 Multiplication-Sign 10{sup 40} to 1.25 Multiplication-Sign 10{sup 42} erg s{sup -1}. We confirm here the detection of spectral state transitions from HLX-1 reminiscent of Galactic black hole binaries (GBHBs): at high luminosities, the X-ray spectrum showed a thermal state dominated by a disk component with temperatures of 0.26 keV at most, and at low luminosities the spectrum is dominated by a hard power law with a photon index in the range 1.4-2.1, consistent with a hard state. The source was also observed in a state consistent with the steep power-law state, with a photon index of {approx}3.5. In the thermal state, the luminosity of the disk component appears to scale with the fourth power of the inner disk temperature, which supports the presence of an optically thick, geometrically thin accretion disk. The low fractional variability (rms of 9% {+-} 9%) in this state also suggests the presence of a dominant disk. The spectral changes and long-term variability of the source cannot be explained by variations of the beaming angle and are not consistent with the source being in a super-Eddington accretion state as is proposed for most ULX sources with lower luminosities. All this

Characterising rock fracture aperture-spacing relationships using power-law relationships: some considerations

NASA Astrophysics Data System (ADS)

Brook, Martin; Hebblewhite, Bruce; Mitra, Rudrajit

2016-04-01

The size-scaling of rock fractures is a well-studied problem in geology, especially for permeability quantification. The intensity of fractures may control the economic exploitation of fractured reservoirs because fracture intensity describes the abundance of fractures potentially available for fluid flow. Moreover, in geotechnical engineering, fractures are important for parameterisation of stress models and excavation design. As fracture data is often collected from widely-spaced boreholes where core recovery is often incomplete, accurate interpretation and representation of fracture aperture-frequency relationships from sparse datasets is important. Fracture intensity is the number of fractures encountered per unit length along a sample scanline oriented perpendicular to the fractures in a set. Cumulative frequency of fractures (F) is commonly related to fracture aperture (A) in the form of a power-law (F = aA-b), with variations in the size of the a coefficient between sites interpreted to equate to fracture frequency for a given aperture (A). However, a common flaw in this approach is that even a small change in b can have a large effect on the response of the fracture frequency (F) parameter. We compare fracture data from the Late Permian Rangal Coal Measures from Australia's Bowen Basin, with fracture data from Jurassic carbonates from the Sierra Madre Oriental, northeastern Mexico. Both power-law coefficient a and exponent b control the fracture aperture-frequency relationship in conjunction with each other; that is, power-laws with relatively low a coefficients have relatively high b exponents and vice versa. Hence, any comparison of different power-laws must take both a and b into consideration. The corollary is that different sedimentary beds in the Sierra Madre carbonates do not show ˜8× the fracture frequency for a given fracture aperture, as based solely on the comparison of coefficient a. Rather, power-law "sensitivity factors" developed from both

Using Statistical Mechanics and Entropy Principles to Interpret Variability in Power Law Models of the Streamflow Recession

NASA Astrophysics Data System (ADS)

Dralle, D.; Karst, N.; Thompson, S. E.

2015-12-01

Multiple competing theories suggest that power law behavior governs the observed first-order dynamics of streamflow recessions - the important process by which catchments dry-out via the stream network, altering the availability of surface water resources and in-stream habitat. Frequently modeled as: dq/dt = -aqb, recessions typically exhibit a high degree of variability, even within a single catchment, as revealed by significant shifts in the values of "a" and "b" across recession events. One potential source of this variability lies in underlying, hard-to-observe fluctuations in how catchment water storage is partitioned amongst distinct storage elements, each having different discharge behaviors. Testing this and competing hypotheses with widely available streamflow timeseries, however, has been hindered by a power law scaling artifact that obscures meaningful covariation between the recession parameters, "a" and "b". Here we briefly outline a technique that removes this artifact, revealing intriguing new patterns in the joint distribution of recession parameters. Using long-term flow data from catchments in Northern California, we explore temporal variations, and find that the "a" parameter varies strongly with catchment wetness. Then we explore how the "b" parameter changes with "a", and find that measures of its variation are maximized at intermediate "a" values. We propose an interpretation of this pattern based on statistical mechanics, meaning "b" can be viewed as an indicator of the catchment "microstate" - i.e. the partitioning of storage - and "a" as a measure of the catchment macrostate (i.e. the total storage). In statistical mechanics, entropy (i.e. microstate variance, that is the variance of "b") is maximized for intermediate values of extensive variables (i.e. wetness, "a"), as observed in the recession data. This interpretation of "a" and "b" was supported by model runs using a multiple-reservoir catchment toy model, and lends support to the

Model for the broadband Crab nebula spectrum with injection of a log-parabola electron distribution at the wind termination shock

NASA Astrophysics Data System (ADS)

Fraschetti, F.; Pohl, M.

2017-10-01

We develop a model of the steady-state spectrum of the Crab nebula encompassing both the radio/soft X-ray and the GeV/multi-TeV observations. By solving the transport equation for TeV electrons injected at the wind termination shock as a log-parabola momentum distribution and evolved via energy losses, we determine analytically the resulting photon differential energy spectrum. We find an impressive agreement with the observations in the synchrotron region. The predicted synchrotron self-Compton accommodates the previously unsolved origin of the broad 200 GeV peak that matches the Fermi/LAT data beyond 1 GeV with the MAGIC data. A natural interpretation of the deviation from power-law of the photon spectrum customarily fit with empirical broken power-laws is provided. This model can be applied to the radio-to- multi-TeV spectra of a variety of astrophysical outflows, including pulsar wind nebulae and supernova remnants. We also show that MeV-range energetic particle distribution at interplanetary shocks typically fit with broken-power laws or Band function can be accurately reproduced by log-parabolas.

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

Anisotropic power-law inflation for a conformal-violating Maxwell model

NASA Astrophysics Data System (ADS)

Do, Tuan Q.; Kao, W. F.

2018-05-01

A set of power-law solutions of a conformal-violating Maxwell model with a non-standard scalar-vector coupling will be shown in this paper. In particular, we are interested in a coupling term of the form X^{2n} F^{μ ν }F_{μ ν } with X denoting the kinetic term of the scalar field. Stability analysis indicates that the new set of anisotropic power-law solutions is unstable during the inflationary phase. The result is consistent with the cosmic no-hair conjecture. We show, however, that a set of stable slowly expanding solutions does exist for a small range of parameters λ and n. Hence a small anisotropy can survive during the slowly expanding phase.

Diffuse Hard X-Ray Emission in Starburst Galaxies as Synchrotron from Very High Energy Electrons

NASA Astrophysics Data System (ADS)

Lacki, Brian C.; Thompson, Todd A.

2013-01-01

The origin of the diffuse hard X-ray (2-10 keV) emission from starburst galaxies is a long-standing problem. We suggest that synchrotron emission of 10-100 TeV electrons and positrons (e ±) can contribute to this emission, because starbursts have strong magnetic fields. We consider three sources of e ± at these energies: (1) primary electrons directly accelerated by supernova remnants, (2) pionic secondary e ± created by inelastic collisions between cosmic ray (CR) protons and gas nuclei in the dense interstellar medium of starbursts, and (3) pair e ± produced between the interactions between 10 and 100 TeV γ-rays and the intense far-infrared (FIR) radiation fields of starbursts. We create one-zone steady-state models of the CR population in the Galactic center (R <= 112 pc), NGC 253, M82, and Arp 220's nuclei, assuming a power-law injection spectrum for electrons and protons. We consider different injection spectral slopes, magnetic field strengths, CR acceleration efficiencies, and diffusive escape times, and include advective escape, radiative cooling processes, and secondary and pair e ±. We compare these models to extant radio and GeV and TeV γ-ray data for these starbursts, and calculate the diffuse synchrotron X-ray and inverse Compton (IC) luminosities of these starbursts in the models which satisfy multiwavelength constraints. If the primary electron spectrum extends to ~PeV energies and has a proton/electron injection ratio similar to the Galactic value, we find that synchrotron emission contributes 2%-20% of their unresolved, diffuse hard X-ray emission. However, there is great uncertainty in this conclusion because of the limited information on the CR electron spectrum at these high energies. IC emission is likewise a minority of the unresolved X-ray emission in these starbursts, from 0.1% in the Galactic center to 10% in Arp 220's nuclei, with the main uncertainty being the starbursts' magnetic field. We also model generic starbursts, including

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.

Measuring the power spectrum of dark matter substructure using strong gravitational lensing

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

Hezaveh, Yashar; Dalal, Neal; Holder, Gilbert

2016-11-01

In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies. Typically, only the most massive subhalos in the strong lensing region may be detected this way. In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually. In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing. We develop the mathematical framework of power spectrum estimation, andmore » test our method on mock observations. We use our results to determine the types of observations required to measure the substructure power spectrum with high significance. We predict that deep observations (∼10 hours on a single target) with current facilities can measure this power spectrum at the 3σ level, with no apparent degeneracy with unknown clumpiness in the background source structure or fluctuations from detector noise. Upcoming ALMA measurements of strong lenses are capable of placing strong constraints on the abundance of dark matter subhalos and the underlying particle nature of dark matter.« less

Power law for the duration of recession and prosperity in Latin American countries

NASA Astrophysics Data System (ADS)

Redelico, Francisco O.; Proto, Araceli N.; Ausloos, Marcel

2008-11-01

Ormerod and Mounfield [P. Ormerod, C. Mounfield, Power law distribution of duration and magnitude of recessions in capitalist economies: Breakdown of scaling, Physica A 293 (2001) 573] and Ausloos et al. [M. Ausloos, J. Mikiewicz, M. Sanglier, The durations of recession and prosperity: Does their distribution follow a power or an exponential law? Physica A 339 (2004) 548] have independently analyzed the duration of recessions for developed countries through the evolution of the GDP in different time windows. It was found that there is a power law governing the duration distribution. We have analyzed data collected from 19 Latin American countries in order to observe whether such results are valid or not for developing countries. The case of prosperity years is also discussed. We observe that the power law of recession time intervals, see Ref. [1], is valid for Latin American countries as well. Thus an interesting point is discovered: the same scaling time is found in the case of recessions for the three data sets (ca. 1 year), and this could represent a universal feature. Other time scale parameters differ significantly from each other.

SHJAR Jet Noise Data and Power Spectral Laws

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. The measured spectral data are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of 0.0 to 10.0. The measured data are reported as lossless (i.e., atmospheric attenuation is added to measurements), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter (200-in.) arc. Following the work of Viswanathan, velocity power factors are evaluated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit and the confidence margins for the two regression parameters are studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. As an immediate application of the velocity power laws, spectral density in shockcontaining jets are decomposed into components attributed to jet mixing noise and shock noise. From this analysis, jet noise prediction tools can be developed with different spectral components derived from different physics.

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

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

Understanding the impact of Light cone effect on the EoR/CD 21-cm power spectrum

NASA Astrophysics Data System (ADS)

Datta, Kanan K.; Mondal, Rajesh; Ghara, Raghunath; Bharadwaj, Somnath; Choudhury, T. Roy

2018-05-01

Redshifted HI 21-cm signal from the cosmic dawn and epoch of reionization evolve considerably along the LoS. We study the impact of this evolution (so called the light cone effect) on the HI 21-cm power spectrum. It is found that the LC effect has a significant impact on the 3D power spectrum and the change could be up to a factor of few. The LC effect is particularly strong during the cosmic dawn near the `peaks' and `dips' in the power spectrum when plotted with redshift. We also show that the 3D power spectrum, which could fully describe ergodic and periodic signal, losses out some information regarding the second order statistics of the signal as the EoR/CD 21-cm signal is non-ergodic and non-periodic along the line of sight. We show that the multi-frequency angular power spectrum (MAPS) \\ell (\

A Simple Power Law Governs Many Sensory Amplifications and Multisensory Enhancements.

PubMed

Billock, Vincent A; Havig, Paul R

2018-05-16

When one sensory response occurs in the presence of a different sensory stimulation, the sensory response is often amplified. The variety of sensory enhancement data tends to obscure the underlying rules, but it has long been clear that weak signals are usually amplified more than strong ones (the Principle of Inverse Effectiveness). Here we show that for many kinds of sensory amplification, the underlying law is simple and elegant: the amplified response is a power law of the unamplified response, with a compressive exponent that amplifies weak signals more than strong. For both psychophysics and cortical electrophysiology, for both humans and animals, and for both sensory integration and enhancement within a sense, gated power law amplification (amplification of one sense triggered by the presence of a different sensory signal) is often sufficient to explain sensory enhancement.

Inferred Cosmic-Ray Spectrum from Fermi-LAT Gamma-Ray Observations of the Earths Limb

NASA Technical Reports Server (NTRS)

Ackermann, M.; Ajello, M.; Albert, A.; Allafort, A.; Baldini, L.; Barbiellini, G.; Bastieri, D.; Bechtol, K.; Bellazzini, R.; Blandford, R. D.;

High-energy properties of the high-redshift flat spectrum radio quasar PKS 2149-306

DOE PAGES

D'Ammando, F.; Orienti, M.

2015-11-19

We investigate the γ-ray and X-ray properties of the flat spectrum radio quasar PKS 2149-306 at redshift z = 2.345. A strong γ-ray flare from this source was detected by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope satellite in 2013 January, reaching on January 20 a daily peak flux of (301 ± 36)×10 -8 ph cm -2 s -1 in the 0.1–100 GeV energy range. This flux corresponds to an apparent isotropic luminosity of (1.5±0.2)×1050 erg s -1, comparable to the highest values observed by a blazar so far. During the flare the increase of fluxmore » was accompanied by a significant change of the spectral properties. Moreover significant flux variations on a 6-h time- scale were observed, compatible with the light crossing time of the event horizon of the central black hole. The broad band X-ray spectra of PKS 2149-306 observed by Swift-XRT and NuSTAR are well described by a broken power-law model, with a very hard spectrum (Γ 1 ~1) below the break energy, at Ebreak = 2.5–3.0 keV, and Γ 2 ~ 1.4–1.5 above the break energy. The steepening of the spectrum below ~3 keV may indicate that the soft X- ray emission is produced by the low-energy relativistic electrons. This is in agreement with the small variability amplitude and the lack of spectral changes in that part of the X-ray spectrum observed between the two NuSTAR and Swift joint observations. As for the other high-redshift FSRQ detected by both Fermi-LAT and Swift-BAT, the photon index of PKS 2149-306 in hard X-ray is 1.6 or lower and the average γ-ray luminosity higher than 2×1048 erg s -1.« less

High-energy properties of the high-redshift flat spectrum radio quasar PKS 2149-306

NASA Astrophysics Data System (ADS)

D'Ammando, F.; Orienti, M.

2016-01-01

We investigate the γ-ray and X-ray properties of the flat spectrum radio quasar PKS 2149-306 at redshift z = 2.345. A strong γ-ray flare from this source was detected by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope satellite in 2013 January, reaching on January 20 a daily peak flux of (301 ± 36) × 10-8 ph cm-2 s-1 in the 0.1-100 GeV energy range. This flux corresponds to an apparent isotropic luminosity of (1.5 ± 0.2) × 1050 erg s-1, comparable to the highest values observed by a blazar so far. During the flare the increase of flux was accompanied by a significant change of the spectral properties. Moreover significant flux variations on a 6-h time-scale were observed, compatible with the light crossing time of the event horizon of the central black hole. The broad-band X-ray spectra of PKS 2149-306 observed by Swift-XRT and NuSTAR are well described by a broken power-law model, with a very hard spectrum (Γ1 ˜ 1) below the break energy, at E break = 2.5-3.0 keV, and Γ2 ˜ 1.4-1.5 above the break energy. The steepening of the spectrum below ˜3 keV may indicate that the soft X-ray emission is produced by the low-energy relativistic electrons. This is in agreement with the small variability amplitude and the lack of spectral changes in that part of the X-ray spectrum observed between the two NuSTAR and Swift joint observations. As for the other high-redshift FSRQ detected by both Fermi-LAT and Swift-BAT, the photon index of PKS 2149-306 in hard X-ray is 1.6 or lower and the average γ-ray luminosity higher than 2 × 1048 erg s-1.

Coexistence of a well-determined kinetic law and a scale-invariant power law during the same physical process

NASA Astrophysics Data System (ADS)

Zreihan, Noam; Faran, Eilon; Vives, Eduard; Planes, Antoni; Shilo, Doron

2018-01-01

It is generally claimed that physical processes which display scale-invariant power-law distributions are subjected to a dynamic criticality that prohibits a well-defined kinetic law. In this paper, we demonstrate the coexistence of these two apparently contradicting behaviors during the same physical process—the motion of type-II twin boundaries in martensite Ni-Mn-Ga. The process is investigated by combined measurements of the temporal twin-boundary velocity and the acoustic emitted energy. Velocity values are extracted from high-resolution force measurements taken during displacement-driven mechanical tests, as well as from force-driven magnetic tests, and cover an overall range of six orders of magnitude. Acoustic emission (AE) is measured during mechanical tests. Velocity values follow a normal distribution whose characteristic value is determined by the material's kinetic relation, and its width scales with the average velocity. In addition, it is observed that velocity distributions are characterized by a heavy tail at the right (i.e., faster) end that exhibits a power law over more than one and a half orders of magnitude. At the same time, the AE signals follow a scale-invariant power-law distribution, which is not sensitive to the average twin-boundary velocity. The coexistence of these two different statistical behaviors reflects the complex nature of twin-boundary motion and suggests the possibility that the transformation proceeds through physical subprocesses that are close to criticality alongside other processes that are not.

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.

Explaining the power-law distribution of human mobility through transportation modality decomposition

PubMed Central

Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu

2015-01-01

Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns. PMID:25779306

Explaining the power-law distribution of human mobility through transportation modality decomposition.

PubMed

Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu

2015-03-16

Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.

Explaining the power-law distribution of human mobility through transportation modality decomposition

NASA Astrophysics Data System (ADS)

Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu

2015-03-01

Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.

On the predictability of individual events in power-law systems

NASA Astrophysics Data System (ADS)

de, Rumi

2006-11-01

We consider a modified Burridge-Knopoff model with a view to understand results of acoustic emission (AE) relevant to earthquakes by adding a dissipative term which mimics bursts of acous- tic signals. Interestingly, we find a precursor effect in the cumulative energy dissipated which allows identification of a large slip event. Further, the AE activity for several large slip events follows a universal stretched exponential behavior with corrections in terms of time-to-failure. We find that many features of the statistics of AE signals such as their amplitudes, durations and the intervals between successive AE bursts obey power laws consistent with recent experimental results. Large magnitude events have different power law from that of the small ones, the latter being sensitive to the pulling speed.

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.

Observation of pulsed hard X-rays/gamma-rays from PSR 1509-58

NASA Astrophysics Data System (ADS)

Gunji, S.; Hirayama, M.; Kamae, T.; Miyazaki, S.; Sekimoto, Y.; Takahashi, T.; Tamura, T.; Tanaka, M.; Yamasaki, N.; Yamagami, T.; Nomachi, M.; Murakami, H.; Braga, J.; Neri, J. A.

1994-06-01

We observed a young rotation-powered pulsar, PSR 1509-58, in the hard X-ray/gamma-ray or the soft gamma-ray band with a balloon-borne detector in Brazil on 1991 November 19 (UT). With a timing analysis we detected pulsations in the energy band 94-240 keV at the 150.687 ms period determined from radio observations. The pulsating flux is (7.1 +/- 1.7) x 10-4 per sq cm per sec in this band, and the energy spectrum follows a power law with photon index alpha = 1.64 +/- 0.4. The averaged pulse profile shows a broad single peak with a sharp rise and has a duty cycle around 50% or higher: these features are similar to what have been observed in the X-ray band by the Ginga satellite. Based on the data available now, the fraction of energy transformed from rotational energy loss to pulsed/nonpulsed soft gamma-ray radiation is estimated. If the solid angle swept by the pulsed beam is about the same as for the Crab pulsar (PSR 0531+21) and the Vela pulsar (PSR 0833-45), PSR 1509-58 turn out to be an extremely efficient pulsar, converting a large fraction of its rotational energy loss to radiation, as the outer gap model predicts. The observed pulsed spectrum, however, is strong in the soft gamma-ray band, in a sharp contrast to what has been observed in the Vela pulsar, a pulsar expected to be similar PSR 1509-58 in the outer gap model. The fact that the pulse profile remains broad and single-peaked in the soft gamma-ray band is also new for Crab-like pulsars. In these regards, PSR 1509-58 may require some alteration to the standard outer gap model or even a new model for gamma-ray emission in pulsars.

Observational constraints on the primordial curvature power spectrum

NASA Astrophysics Data System (ADS)

Emami, Razieh; Smoot, George F.

2018-01-01

CMB temperature fluctuation observations provide a precise measurement of the primordial power spectrum on large scales, corresponding to wavenumbers 10‑3 Mpc‑1 lesssim k lesssim 0.1 Mpc‑1, [1-7, 11]. Luminous red galaxies and galaxy clusters probe the matter power spectrum on overlapping scales (0.02 Mpc‑1 lesssim k lesssim 0.7 Mpc‑1 [10, 12-20]), while the Lyman-alpha forest reaches slightly smaller scales (0.3 Mpc‑1 lesssim k lesssim 3 Mpc‑1 [22]). These observations indicate that the primordial power spectrum is nearly scale-invariant with an amplitude close to 2 × 10‑9, [5, 23-28]. These observations strongly support Inflation and motivate us to obtain observations and constraints reaching to smaller scales on the primordial curvature power spectrum and by implication on Inflation. We are able to obtain limits to much higher values of k lesssim 105 Mpc‑1 and with less sensitivity even higher k lesssim 1019‑ 1023 Mpc‑1 using limits from CMB spectral distortions and other limits on ultracompact minihalo objects (UCMHs) and Primordial Black Holes (PBHs). PBHs are one of the known candidates for the Dark Matter (DM). Due to their very early formation, they could give us valuable information about the primordial curvature perturbations. These are complementary to other cosmological bounds on the amplitude of the primordial fluctuations. In this paper, we revisit and collect all the published constraints on both PBHs and UCMHs. We show that unless one uses the CMB spectral distortion, PBHs give us a very relaxed bounds on the primordial curvature perturbations. UCMHs, on the other hand, are very informative over a reasonable k range (3 lesssim k lesssim 106 Mpc‑1) and lead to significant upper-bounds on the curvature spectrum. We review the conditions under which the tighter constraints on the UCMHs could imply extremely strong bounds on the fraction of DM that could be PBHs in reasonable models. Failure to satisfy these conditions would

2MTF - VI. Measuring the velocity power spectrum

NASA Astrophysics Data System (ADS)

Howlett, Cullan; Staveley-Smith, Lister; Elahi, Pascal J.; Hong, Tao; Jarrett, Tom H.; Jones, D. Heath; Koribalski, Bärbel S.; Macri, Lucas M.; Masters, Karen L.; Springob, Christopher M.

2017-11-01

We present measurements of the velocity power spectrum and constraints on the growth rate of structure fσ8, at redshift zero, using the peculiar motions of 2062 galaxies in the completed 2MASS Tully-Fisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of non-linear redshift space distortions (RSD), allowing us to recover unbiased fits down to scales k = 0.2 h Mpc-1 without the need to smooth or grid the data. Our fitting methods are validated using a set of simulated 2MTF surveys. Using these simulations we also identify that the Gaussian distributed estimator for peculiar velocities of Watkins & Feldman is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations δm, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalize over this. We obtain scale-dependent constraints on the growth rate of structure in two bins, finding fσ 8 = [0.55^{+0.16}_{-0.13},0.40^{+0.16}_{-0.17}] in the ranges k = [0.007-0.055, 0.55-0.150] h Mpc-1. We also find consistent results using four bins. Assuming scale-independence we find a value fσ 8 = 0.51^{+0.09}_{-0.08}, a ˜16 per cent measurement of the growth rate. Performing a consistency check of general relativity (GR) and combining our results with cosmic microwave background data only we find γ = 0.45^{+0.10}_{-0.11}, a remarkable constraint considering the small number of galaxies. All of our results are completely independent of the effects of galaxy bias, and fully consistent with the predictions of GR (scale-independent fσ8 and γ ≈ 0.55).

The power laws of violence against women: rescaling research and policies.

PubMed

Kappler, Karolin E; Kaltenbrunner, Andreas

2012-01-01

Violence against Women -despite its perpetuation over centuries and its omnipresence at all social levels- entered into social consciousness and the general agenda of Social Sciences only recently, mainly thanks to feminist research, campaigns, and general social awareness. The present article analyzes in a secondary analysis of German prevalence data on Violence against Women, whether the frequency and severity of Violence against Women can be described with power laws. Although the investigated distributions all resemble power-law distributions, a rigorous statistical analysis accepts this hypothesis at a significance level of 0.1 only for 1 of 5 cases of the tested frequency distributions and with some restrictions for the severity of physical violence. Lowering the significance level to 0.01 leads to the acceptance of the power-law hypothesis in 2 of the 5 tested frequency distributions and as well for the severity of domestic violence. The rejections might be mainly due to the noise in the data, with biases caused by self-reporting, errors through rounding, desirability response bias, and selection bias. Future victimological surveys should be designed explicitly to avoid these deficiencies in the data to be able to clearly answer the question whether Violence against Women follows a power-law pattern. This finding would not only have statistical implications for the processing and presentation of the data, but also groundbreaking consequences on the general understanding of Violence against Women and policy modeling, as the skewed nature of the underlying distributions makes evident that Violence against Women is a highly disparate and unequal social problem. This opens new questions for interdisciplinary research, regarding the interplay between environmental, experimental, and social factors on victimization.

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.

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.

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.

Anomalous metallic state with strong charge fluctuations in BaxTi8O16 +δ revealed by hard x-ray photoemission spectroscopy

NASA Astrophysics Data System (ADS)

Dash, S.; Kajita, T.; Okawa, M.; Saitoh, T.; Ikenaga, E.; Saini, N. L.; Katsufuji, T.; Mizokawa, T.

2018-04-01

We have studied a charge-orbital driven metal-insulator transition (MIT) in hollandite-type BaxTi8O16 +δ by means of hard x-ray photoemission spectroscopy (HAXPES). The Ti 2 p HAXPES indicates strong Ti3 +/Ti4 + charge fluctuation in the metallic phase above the MIT temperature. The metallic phase is characterized by a power-law spectral function near the Fermi level which would be a signature of bad metal with non-Drude polaronic behavior. The power-law spectral shape is associated with the large Seebeck coefficient of the metallic phase in BaxTi8O16 +δ .

An XMM-Newton Observation of the Seyfert Galaxy 1H0419-577 in an Extreme Low State

NASA Technical Reports Server (NTRS)

Pounds, K. A.; Reeves, J. N.; Page, K. L.; O'Brien, P. T.

2003-01-01

Previous observations of the luminous Seyfert galaxy 1H 0419-577 have found its X-ray spectrum to range from that of a typical Seyfert 1 with 2-10 keV power law index Gamma approx. 1.9 to a much flatter power law of Gamma approx. 1.5 or less. We report here a new XMM-Newton observation which allows the low state spectrum to be studied in much greater detail than hitherto. We find a very hard spectrum (Gamma approx. 1.0) which exhibits broad features that can be modelled with the addition of an extreme relativistic Fe K emission line or with partial covering of the underlying continuum by a substantial column density of near-neutral gas. Both the EPIC and RGS data show evidence for strong line emission of OVII and OVIII requiring an extended region of low density photoionised gas in 1H 0419- 577. Comparison with an earlier XMM-Newton observation when 1H 0419-577 was X-ray bright indicates the dominant spectral variability occurs via a steep power law component.

An XMM-Newton Observation of the Seyfert 1 Galaxy 1H 0419-577 in an Extreme Low State

NASA Technical Reports Server (NTRS)

Pounds, K. A.; Reeves, J. N.; Page, K. L.; OBrien, P. T.

2004-01-01

Previous observations of the luminous Seyfert 1 galaxy 1H 0419-577 have found its X-ray spectrum to range from that of a typical Seyfert 1 with 2-10 keV power law index Gamma approx. 1.9 to a much flatter power law of Gamma approx. 1.5 or less. We report here a new XMM-Newton observation which allows the low state spectrum to be studied in much greater detail than hitherto. We find a very hard spectrum (Gamma approx. 1.0), which exhibits broad features that can be modelled myth the addition of an extreme relativistic Fe K emission line or with partial covering of the underlying continuum by a substantial column density of near-neutral gas. Both the EPIC and RGS data show evidence for strong line emission of OVII and OVIII requiring an extended region of low density photoionised gas in 1H 0419-577. Comparison with an earlier XMM-Newton observation when 1H 0419-577 was 'X-ray bright' indicates the dominant spectral variability occurs via a steep power law component.

Interrelation of soft and hard X-ray emissions during solar flares. II - Simulation model

NASA Technical Reports Server (NTRS)

Winglee, R. M.; Dulk, G. A.; Bornmann, P. L.; Brown, J. C.

1991-01-01

Two-dimensional electrostatic particle simulations are presented which incorporate the effect of quasi-static electric fields on particle dynamics as well as effects associated with wave-particle interactions induced by the accelerated particles. The properties of the soft and hard X-ray and microwave emissions from such systems are examined. In particular, it is shown that acceleration by quasi-static electric fields and heating via wave-particle interactions produces electron distributions with a broken-power law, similar to those inferred from hard X-ray spectra. Also, heating of the ambient plasma gives rise to a region of hot plasma propagating down to the chromosphere at about the ion sound speed.

Multiwavelength Observations of the Powerful Gamma-ray Quasar PKS 1510-089: Clues on the Jet Composition

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

Kataoka, J.; Madejski, G.; Sikora, M.

2007-09-28

We present the results from a multiwavelength campaign conducted in August 2006 of the powerful {gamma}-ray quasar PKS 1510--089 (z = 0.361). This campaign commenced with a deep Suzaku observation lasting three days for a total exposure time of 120 ks, and continued with Swift monitoring over 18 days. Besides Swift observations, which sampled the optical/UV flux in all 6 UVOT filters as well as the X-ray spectrum in the 0.3--10 keV energy range, the campaign included ground-based optical and radio data, and yielded a quasi-simultaneous broad-band spectral energy distribution from 109 Hz to 1019 Hz. Thanks to its lowmore » instrumental background, the Suzaku observation provided a high S/N X-ray spectrum, which is well represented by an extremely hard power-law with photon index {Gamma}{approx_equal}1.2, augmented by a soft component apparent below 1 keV, which is well described by a black-body model with temperature kT {approx_equal}0.2 keV. Monitoring by Suzaku revealed temporal variability which is different between the low and high energy bands, again suggesting the presence of a second, variable component in addition to the primary power-law emission. We model the broadband spectrum of PKS 1510--089 assuming that the high energy spectral component results from Comptonization of infrared radiation produced by hot dust located in the surrounding molecular torus. In the adopted internal shock scenario, the derived model parameters imply that the power of the jet is dominated by protons but with a number of electrons/positrons exceeding a number of protons by a factor {approx} 10. We also find that inhomogeneities responsible for the shock formation, prior to the collision may produce bulk-Compton radiation which can explain the observed soft X-ray excess and possible excess at {approx} 18 keV. We note, however, that the bulk-Compton interpretation is not unique, and the observed soft excess could arise as well via some other processes discussed briefly in the

The very low frequency power spectrum of Centaurus X-3

NASA Technical Reports Server (NTRS)

Gruber, D. E.

1988-01-01

The long-term variability of Cen X-3 on time scales ranging from days to years has been examined by combining data obtained by the HEAO 1 A-4 instrument with data from Vela 5B. A simple interpretation of the data is made in terms of the standard alpha-disk model of accretion disk structure and dynamics. Assuming that the low-frequency variance represents the inherent variability of the mass transfer from the companion, the decline in power at higher frequencies results from the leveling of radial structure in the accretion disk through viscous mixing. The shape of the observed power spectrum is shown to be in excellent agreement with a calculation based on a simplified form of this model. The observed low-frequency power spectrum of Cen X-3 is consistent with a disk in which viscous mixing occurs about as rapidly as possible and on the largest scale possible.

Saturn systems holddown acoustic efficiency and normalized acoustic power spectrum.

NASA Technical Reports Server (NTRS)

Gilbert, D. W.

1972-01-01

Saturn systems field acoustic data are used to derive mid- and far-field prediction parameters for rocket engine noise. The data were obtained during Saturn vehicle launches at the Kennedy Space Center. The data base is a sorted set of acoustic data measured during the period 1961 through 1971 for Saturn system launches SA-1 through AS-509. The model assumes hemispherical radiation from a simple source located at the intersection of the longitudinal axis of each booster and the engine exit plane. The model parameters are evaluated only during vehicle holddown. The acoustic normalized power spectrum and efficiency for each system are isolated as a composite from the data using linear numerical methods. The specific definitions of each allows separation. The resulting power spectra are nondimensionalized as a function of rocket engine parameters. The nondimensional Saturn system acoustic spectrum and efficiencies are compared as a function of Strouhal number with power spectra from other systems.

Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated

NASA Astrophysics Data System (ADS)

Langlois, Dominic; Cousineau, Denis; Thivierge, J. P.

2014-01-01

The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.

Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated.

PubMed

Langlois, Dominic; Cousineau, Denis; Thivierge, J P

2014-01-01

The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.

Hard X-Ray Emission from SH 2-104: A NuSTAR Search for Gamma-Ray Counterparts

NASA Technical Reports Server (NTRS)

Gotthelf, E. V.; Mori, K.; Aliu, E.; Paredes, J. M.; Tomsick, J. A.; Boggs, S. E.; Christensen, F. E.; Craig, W. W.; Hailey, C. J.; Harrison, F. A.;

Hard X-Ray Emission from Sh 2-104: A NuSTAR Search for Gamma-Ray Counterparts

NASA Astrophysics Data System (ADS)

Gotthelf, E. V.; Mori, K.; Aliu, E.; Paredes, J. M.; Tomsick, J. A.; Boggs, S. E.; Christensen, F. E.; Craig, W. W.; Hailey, C. J.; Harrison, F. A.; Hong, J. S.; Rahoui, F.; Stern, D.; Zhang, W. W.

2016-07-01

We present NuSTAR hard X-ray observations of Sh 2-104, a compact H II region containing several young massive stellar clusters (YMSCs). We have detected distinct hard X-ray sources coincident with localized VERITAS TeV emission recently resolved from the giant gamma-ray complex MGRO J2019+37 in the Cygnus region. Fainter, diffuse X-rays coincident with the eastern YMSC in Sh2-104 likely result from the colliding winds of a component star. Just outside the radio shell of Sh 2-104 lies 3XMM J201744.7+365045 and a nearby nebula, NuSTAR J201744.3+364812, whose properties are most consistent with extragalactic objects. The combined XMM-Newton and NuSTAR spectrum of 3XMM J201744.7+365045 is well-fit to an absorbed power-law model with {N}{{H}}=(3.1+/- 1.0)× {10}22 cm-2 and a photon index {{Γ }}=2.1+/- 0.1. Based on possible long-term flux variation and the lack of detected pulsations (≤43% modulation), this object is likely a background active galactic nucleus rather than a Galactic pulsar. The spectrum of the NuSTAR nebula shows evidence of an emission line at E = 5.6 keV, suggesting an optically obscured galaxy cluster at z = 0.19 ± 0.02 (d = 800 Mpc) and L X = 1.2 × 1044 erg s-1. Follow-up Chandra observations of Sh 2-104 will help identify the nature of the X-ray sources and their relation to MGRO J2019+37. We also show that the putative VERITAS excess south of Sh 2-104, is most likely associated with the newly discovered Fermi pulsar PSR J2017+3625 and not the H II region.

A Bayesian analysis of inflationary primordial spectrum models using Planck data

NASA Astrophysics Data System (ADS)

Santos da Costa, Simony; Benetti, Micol; Alcaniz, Jailson

2018-03-01

The current available Cosmic Microwave Background (CMB) data show an anomalously low value of the CMB temperature fluctuations at large angular scales (l < 40). This lack of power is not explained by the minimal ΛCDM model, and one of the possible mechanisms explored in the literature to address this problem is the presence of features in the primordial power spectrum (PPS) motivated by the early universe physics. In this paper, we analyse a set of cutoff inflationary PPS models using a Bayesian model comparison approach in light of the latest CMB data from the Planck Collaboration. Our results show that the standard power-law parameterisation is preferred over all models considered in the analysis, which motivates the search for alternative explanations for the observed lack of power in the CMB anisotropy spectrum.

Disrupted Stimulus Control but Not Reward Sensitivity in Individuals with Autism Spectrum Disorders: A Matching Law Analysis

ERIC Educational Resources Information Center

Reed, Phil; Hawthorn, Rose; Bolger, Sam; Meredith, Katie; Bishop, Ruth

2012-01-01

The matching law suggests that behavior is emitted in proportion to the level of reinforcement available. The current study investigated this effect in individuals with autism spectrum disorders (ASD), and focused on the effects of magnitude of reinforcement (Study 1), and rate of reinforcement (Studies 2 and 3), on matching performance. Studies 1…

Measuring the Power Spectrum with Peculiar Velocities

NASA Astrophysics Data System (ADS)

Macaulay, Edward; Feldman, H. A.; Ferreira, P. G.; Jaffe, A. H.; Agarwal, S.; Hudson, M. J.; Watkins, R.

2012-01-01

The peculiar velocities of galaxies are an inherently valuable cosmological probe, providing an unbiased estimate of the distribution of matter on scales much larger than the depth of the survey. Much research interest has been motivated by the high dipole moment of our local peculiar velocity field, which suggests a large scale excess in the matter power spectrum, and can appear to be in some tension with the LCDM model. We use a composite catalogue of 4,537 peculiar velocity measurements with a characteristic depth of 33 h-1 Mpc to estimate the matter power spectrum. We compare the constraints with this method, directly studying the full peculiar velocity catalogue, to results from Macaulay et al. (2011), studying minimum variance moments of the velocity field, as calculated by Watkins, Feldman & Hudson (2009) and Feldman, Watkins & Hudson (2010). We find good agreement with the LCDM model on scales of k > 0.01 h Mpc-1. We find an excess of power on scales of k < 0.01 h Mpc-1, although with a 1 sigma uncertainty which includes the LCDM model. We find that the uncertainty in the excess at these scales is larger than an alternative result studying only moments of the velocity field, which is due to the minimum variance weights used to calculate the moments. At small scales, we are able to clearly discriminate between linear and nonlinear clustering in simulated peculiar velocity catalogues, and find some evidence (although less clear) for linear clustering in the real peculiar velocity data.

Power spectrum estimation from peculiar velocity catalogues

NASA Astrophysics Data System (ADS)

Macaulay, E.; Feldman, H. A.; Ferreira, P. G.; Jaffe, A. H.; Agarwal, S.; Hudson, M. J.; Watkins, R.

2012-09-01

The peculiar velocities of galaxies are an inherently valuable cosmological probe, providing an unbiased estimate of the distribution of matter on scales much larger than the depth of the survey. Much research interest has been motivated by the high dipole moment of our local peculiar velocity field, which suggests a large-scale excess in the matter power spectrum and can appear to be in some tension with the Λ cold dark matter (ΛCDM) model. We use a composite catalogue of 4537 peculiar velocity measurements with a characteristic depth of 33 h-1 Mpc to estimate the matter power spectrum. We compare the constraints with this method, directly studying the full peculiar velocity catalogue, to results by Macaulay et al., studying minimum variance moments of the velocity field, as calculated by Feldman, Watkins & Hudson. We find good agreement with the ΛCDM model on scales of k > 0.01 h Mpc-1. We find an excess of power on scales of k < 0.01 h Mpc-1 with a 1σ uncertainty which includes the ΛCDM model. We find that the uncertainty in excess at these scales is larger than an alternative result studying only moments of the velocity field, which is due to the minimum variance weights used to calculate the moments. At small scales, we are able to clearly discriminate between linear and non-linear clustering in simulated peculiar velocity catalogues and find some evidence (although less clear) for linear clustering in the real peculiar velocity data.

How to estimate the 3D power spectrum of the Lyman-α forest

NASA Astrophysics Data System (ADS)

Font-Ribera, Andreu; McDonald, Patrick; Slosar, Anže

2018-01-01

We derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.

How to estimate the 3D power spectrum of the Lyman-α forest

DOE PAGES

Font-Ribera, Andreu; McDonald, Patrick; Slosar, Anže

2018-01-02

Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fouriermore » transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.« less

How to estimate the 3D power spectrum of the Lyman-α forest

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

Font-Ribera, Andreu; McDonald, Patrick; Slosar, Anže

Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fouriermore » transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.« less

Discovery and Monitoring of a New Black Hole Candidate XTE J1752-223 with RXTE: RMS Spectrum Evolution, BH Mass and the Source Distance

NASA Technical Reports Server (NTRS)

Shaposhinikov, Nikolai; Markwardt, Craig; Swank, Jean; Krimm, Hans

2010-01-01

We report on the discovery and monitoring observations of a new galactic black hole candidate XTE J1752-223 by Rossi X-ray Timing Explorer (RXTE). The new source appeared on the X-ray sky on October 21 2009 and was active for almost 8 months. Phenomenologically, the source exhibited the low-hard/highsoft spectral state bi-modality and the variability evolution during the state transition that matches standard behavior expected from a stellar mass black hole binary. We model the energy spectrum throughout the outburst using a generic Comptonization model assuming that part of the input soft radiation in the form of a black body spectrum gets reprocessed in the Comptonizing medium. We follow the evolution of fractional root-mean-square (RMS) variability in the RXTE/PCA energy band with the source spectral state and conclude that broad band variability is strongly correlated with the source hardness (or Comptonized fraction). We follow changes in the energy distribution of rms variability during the low-hard state and the state transition and find further evidence that variable emission is strongly concentrated in the power-law spectral component. We discuss the implication of our results to the Comptonization regimes during different spectral states. Correlations of spectral and variability properties provide measurements of the BH mass and distance to the source. The spectral-timing correlation scaling technique applied to the RXTE observations during the hardto- soft state transition indicates a mass of the BH in XTE J1752-223 between 8 and 11 solar masses and a distance to the source about 3.5 kiloparsec.

The Power Laws of Violence against Women: Rescaling Research and Policies

PubMed Central

Kappler, Karolin E.; Kaltenbrunner, Andreas

2012-01-01

Background Violence against Women –despite its perpetuation over centuries and its omnipresence at all social levels– entered into social consciousness and the general agenda of Social Sciences only recently, mainly thanks to feminist research, campaigns, and general social awareness. The present article analyzes in a secondary analysis of German prevalence data on Violence against Women, whether the frequency and severity of Violence against Women can be described with power laws. Principal Findings Although the investigated distributions all resemble power-law distributions, a rigorous statistical analysis accepts this hypothesis at a significance level of 0.1 only for 1 of 5 cases of the tested frequency distributions and with some restrictions for the severity of physical violence. Lowering the significance level to 0.01 leads to the acceptance of the power-law hypothesis in 2 of the 5 tested frequency distributions and as well for the severity of domestic violence. The rejections might be mainly due to the noise in the data, with biases caused by self-reporting, errors through rounding, desirability response bias, and selection bias. Conclusion Future victimological surveys should be designed explicitly to avoid these deficiencies in the data to be able to clearly answer the question whether Violence against Women follows a power-law pattern. This finding would not only have statistical implications for the processing and presentation of the data, but also groundbreaking consequences on the general understanding of Violence against Women and policy modeling, as the skewed nature of the underlying distributions makes evident that Violence against Women is a highly disparate and unequal social problem. This opens new questions for interdisciplinary research, regarding the interplay between environmental, experimental, and social factors on victimization. PMID:22768348

A Power-Law Growth and Decay Model with Autocorrelation for Posting Data to Social Networking Services.

PubMed

Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi

2016-01-01

We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria.

General relativistic description of the observed galaxy power spectrum: Do we understand what we measure?

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

Yoo, Jaiyul

2010-10-15

We extend the general relativistic description of galaxy clustering developed in Yoo, Fitzpatrick, and Zaldarriaga (2009). For the first time we provide a fully general relativistic description of the observed matter power spectrum and the observed galaxy power spectrum with the linear bias ansatz. It is significantly different from the standard Newtonian description on large scales and especially its measurements on large scales can be misinterpreted as the detection of the primordial non-Gaussianity even in the absence thereof. The key difference in the observed galaxy power spectrum arises from the real-space matter fluctuation defined as the matter fluctuation at themore » hypersurface of the observed redshift. As opposed to the standard description, the shape of the observed galaxy power spectrum evolves in redshift, providing additional cosmological information. While the systematic errors in the standard Newtonian description are negligible in the current galaxy surveys at low redshift, correct general relativistic description is essential for understanding the galaxy power spectrum measurements on large scales in future surveys with redshift depth z{>=}3. We discuss ways to improve the detection significance in the current galaxy surveys and comment on applications of our general relativistic formalism in future surveys.« less

Scaling laws in decaying helical hydromagnetic turbulence

NASA Astrophysics Data System (ADS)

Christensson, M.; Hindmarsh, M.; Brandenburg, A.

2005-07-01

We study the evolution of growth and decay laws for the magnetic field coherence length ξ, energy E_M and magnetic helicity H in freely decaying 3D MHD turbulence. We show that with certain assumptions, self-similarity of the magnetic power spectrum alone implies that ξ σm t1/2. This in turn implies that magnetic helicity decays as Hσm t-2s, where s=(ξ_diff/ξH)2, in terms of ξ_diff, the diffusion length scale, and ξ_H, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as E_M σm t-1/2-2s. The parameter s is inversely proportional to the magnetic Reynolds number Re_M, which is constant in the self-similar regime.

Disentangling Hadronic and Leptonic Cascade Scenarios from the Very-High-Energy Gamma-Ray Emission of Distant Hard-Spectrum Blazars

DOE PAGES

Takami, Hajime; Murase, Kohta; Dermer, Charles D.

2013-06-26

We show that recent data from the Fermi Large Area Telescope have revealed about a dozen distant hard-spectrum blazars that have very-high-energy (VHE; ≳ 100 eV) photons associated with them, but most of them have not yet been detected by imaging atmospheric Cherenkov Telescopes. Most of these high-energy gamma-ray spectra, like those of other extreme high-frequency peaked BL Lac objects, can be well explained either by gamma rays emitted at the source or by cascades induced by ultra-high-energy cosmic rays, as we show specifically for KUV 00311–1938. We consider the prospects for detection of the VHE sources by the plannedmore » Cherenkov Telescope Array (CTA) and show how it can distinguish the two scenarios by measuring the integrated flux above ~500 GeV (depending on source redshift) for several luminous sources with z ≲ 1 in the sample. Strong evidence for the origin of ultra-high-energy cosmic rays could be obtained from VHE observations with CTA. Depending on redshift, if the often quoted redshift of KUV 00311–1938 (z = 0.61) is believed, then preliminary H.E.S.S. data favor cascades induced by ultra-high-energy cosmic rays. Lastly, accurate redshift measurements of hard-spectrum blazars are essential for this study.« less

Dense power-law networks and simplicial complexes

NASA Astrophysics Data System (ADS)

Courtney, Owen T.; Bianconi, Ginestra

2018-05-01

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e., their degree distributions follow P (k ) ∝k-γ with γ ∈(1 ,2 ] . Models of growing networks have been successfully employed to produce scale-free networks using preferential attachment, however these models can only produce sparse networks as the numbers of links and nodes being added at each time step is constant. Here we present a modeling framework which produces networks that are both dense and scale-free. The mechanism by which the networks grow in this model is based on the Pitman-Yor process. Variations on the model are able to produce undirected scale-free networks with exponent γ =2 or directed networks with power-law out-degree distribution with tunable exponent γ ∈(1 ,2 ) . We also extend the model to that of directed two-dimensional simplicial complexes. Simplicial complexes are generalization of networks that can encode the many body interactions between the parts of a complex system and as such are becoming increasingly popular to characterize different data sets ranging from social interacting systems to the brain. Our model produces dense directed simplicial complexes with power-law distribution of the generalized out-degrees of the nodes.

A NOVEL EMISSION SPECTRUM FROM A RELATIVISTIC ELECTRON MOVING IN A RANDOM MAGNETIC FIELD

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

Teraki, Yuto; Takahara, Fumio, E-mail: teraki@vega.ess.sci.osaka-u.ac.jp

2011-07-10

We numerically calculate the radiation spectrum from relativistic electrons moving in small-scale turbulent magnetic fields expected in high-energy astrophysical sources. Such a radiation spectrum is characterized by the strength parameter a = {lambda}{sub B} e|B|/mc {sup 2}, where {lambda}{sub B} is the length scale of the turbulent field. When a is much larger than the Lorentz factor of a radiating electron {gamma}, synchrotron radiation is realized, while a << 1 corresponds to the so-called jitter radiation regime. Because for 1 < a < {gamma} we cannot use either approximations, we should have recourse to the Lienard-Wiechert potential to evaluate themore » radiation spectrum, which is performed in this Letter. We generate random magnetic fields assuming Kolmogorov turbulence, inject monoenergetic electrons, solve the equation of motion, and calculate the radiation spectrum. We perform numerical calculations for several values of a with {gamma} = 10. We obtain various types of spectra ranging between jitter radiation and synchrotron radiation. For a {approx} 7, the spectrum takes a novel shape which had not been noticed up to now. It is like a synchrotron spectrum in the middle energy region, but in the low frequency region it is a broken power law and in the high frequency region an extra power-law component appears beyond the synchrotron cutoff. We give a physical explanation of these features.« less

UCSD OSO-7 observations of the hard X-ray spectrum and variability of Centaurus A

NASA Technical Reports Server (NTRS)

Mushotzky, R. F.; Baity, W. A.; Wheaton, W. A.; Peterson, L. E.

1976-01-01

Results are reported for four X-ray scans of the region containing Cen A. It is found that the X-ray source had a hard number spectrum (spectral index of -1.2) during these observations and that the intensity in the range from 10 to 100 keV apparently increased by 230% with no detectable change in spectral shape between two observations 210 days apart. Either a Compton-synchrotron mechanism or thermal bremsstrahlung at any temperature greater than 200 keV is suggested as the source of the X-rays. It is noted that the present observations, together with a similar detection of another galaxy, may establish a distinct class of extragalactic X-ray objects with flat and highly absorbed spectra.

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.

Emergence of power-law in a market with mixed models

NASA Astrophysics Data System (ADS)

Ali Saif, M.; Gade, Prashant M.

2007-10-01

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.

Halo Substructure and the Power Spectrum

NASA Astrophysics Data System (ADS)

Zentner, Andrew R.; Bullock, James S.

2003-11-01

We present a semianalytic model to investigate the merger history, destruction rate, and survival probability of substructure in hierarchically formed dark matter halos and use it to study the substructure content of halos as a function of input primordial power spectrum. For a standard cold dark matter ``concordance'' cosmology (ΛCDM n=1, σ8=0.95) we successfully reproduce the subhalo velocity function and radial distribution profile seen in N-body simulations and determine that the rate of merging and disruption peaks ~10-12 Gyr in the past for Milky Way-like halos, while surviving substructures are typically accreted within the last ~0-8 Gyr. We explore power spectra with normalizations and spectral ``tilts'' spanning the ranges σ8~=1-0.65 and n~=1-0.8, and include a ``running-index'' model with dn/dlnk=-0.03 similar to the best-fit model discussed in the first-year Wilkinson Microwave Anisotropy Probe (WMAP) report. We investigate spectra with truncated small-scale power, including a broken-scale inflation model and three warm dark matter cases with mW=0.75-3.0 keV. We find that the mass fraction in substructure is relatively insensitive to the tilt and overall normalization of the primordial power spectrum. All of the CDM-type models yield projected substructure mass fractions that are consistent with, but on the low side, of published estimates from strong lens systems: f9=0.4%-1.5% (64th percentile) for subhalos smaller than 109 Msolar within projected cylinders of radius r<10 kpc. Truncated models produce significantly smaller fractions, f9=0.02%-0.2% for mW~=1 keV, and are disfavored by lensing estimates. This suggests that lensing and similar probes can provide a robust test of the CDM paradigm and a powerful constraint on broken-scale inflation/warm particle masses, including masses larger than the ~1 keV upper limits of previous studies. We compare our predicted subhalo velocity functions with the dwarf satellite population of the Milky Way. Assuming

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.

Inferred Cosmic-Ray Spectrum from Fermi Large Area Telescope γ -Ray Observations of Earth’s Limb

DOE PAGES

Ackermann, M.; Ajello, M.; Albert, A.; ...

2014-04-17

Accurate measurements of cosmic-ray (CR) species by ATIC-2, CREAM, and PAMELA recently reveal an unexpected hardening in the proton and He spectra above a few hundred GeV, a gradual softening of the spectra just below a few hundred GeV, and a harder spectrum of He compared to that of protons. These newly discovered features may offer a clue to the origin of high-energy CRs. Here, we use the Fermi Large Area Telescope observations of the γ -ray emission from Earth’s limb for an indirect measurement of the local spectrum of CR protons in the energy range ~ 90 GeV –more » 6 TeV (derived from a photon energy range 15 GeV–1 TeV). Our analysis shows that single power law and broken power law spectra fit the data equally well and yield a proton spectrum with index 2.68 ± 0.04 and 2.61 ± 0.08 above ~ 200 GeV , respectively.« less

Effect of Body Perturbations on Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Mirels, Harold; Thornton, Philip R.

1959-01-01

Hypersonic-slender-body theory, in the limit as the free-stream Mach number becomes infinite, is used to find the effect of slightly perturbing the surface of slender two-dimensional and axisymmetric power law bodies, The body perturbations are assumed to have a power law variation (with streamwise distance downstream of the nose of the body). Numerical results are presented for (1) the effect of boundary-layer development on two dimensional and axisymmetric bodies, (2) the effect of very small angles of attack (on tow[dimensional bodies), and (3) the effect of blunting the nose of very slender wedges and cones.

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.

Power-law behavior in complex organizational communication networks during crisis

NASA Astrophysics Data System (ADS)

Uddin, Shahadat; Murshed, Shahriar Tanvir Hasan; Hossain, Liaquat

2011-08-01

Communication networks can be described as patterns of contacts which are created due to the flow of messages and information shared among participating actors. Contemporary organizations are now commonly viewed as dynamic systems of adaptation and evolution containing several parts, which interact with one another both in internal and in external environment. Although there is limited consensus among researchers on the precise definition of organizational crisis, there is evidence of shared meaning: crisis produces individual crisis, crisis can be associated with positive or negative conditions, crises can be situations having been precipitated quickly or suddenly or situations that have developed over time and are predictable etc. In this research, we study the power-law behavior of an organizational email communication network during crisis from complexity perspective. Power law simply describes that, the probability that a randomly selected node has k links (i.e. degree k) follows P(k)∼k, where γ is the degree exponent. We used social network analysis tools and techniques to analyze the email communication dataset. We tested two propositions: (1) as organization goes through crisis, a few actors, who are prominent or more active, will become central, and (2) the daily communication network as well as the actors in the communication network exhibit power-law behavior. Our preliminary results support these two propositions. The outcome of this study may provide significant advancement in exploring organizational communication network behavior during crisis.

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.

Spectro-Timing Study of GX 339-4 in a Hard Intermediate State

NASA Technical Reports Server (NTRS)

Furst, F.; Grinberg, V.; Tomsick, J. A.; Bachetti, M.; Boggs, S. E.; Brightman, M.; Christensen, F. E.; Craig, W. W.; Ghandi, P.; Zhang, William W.

2016-01-01

We present an analysis of Nuclear Spectroscopic Telescope Array observations of a hard intermediate state of the transient black hole GX 339-4 taken in 2015 January. With the source softening significantly over the course of the 1.3 day long observation we split the data into 21 sub-sets and find that the spectrum of all of them can be well described by a power-law continuum with an additional relativistically blurred reflection component. The photon index increases from approx. 1.69 to approx. 1.77 over the course of the observation. The accretion disk is truncated at around nine gravitational radii in all spectra. We also perform timing analysis on the same 21 individual data sets, and find a strong type-C quasi-periodic oscillation (QPO), which increases in frequency from approx. 0.68 to approx. 1.05 Hz with time. The frequency change is well correlated with the softening of the spectrum. We discuss possible scenarios for the production of the QPO and calculate predicted inner radii in the relativistic precession model as well as the global disk mode oscillations model. We find discrepancies with respect to the observed values in both models unless we allow for a black hole mass of approx. 100 Mass compared to the Sun, which is highly unlikely. We discuss possible systematic uncertainties, in particular with the measurement of the inner accretion disk radius in the relativistic reflection model. We conclude that the combination of observed QPO frequencies and inner accretion disk radii, as obtained from spectral fitting, is difficult to reconcile with current models.

Spectrum sensing and resource allocation for multicarrier cognitive radio systems under interference and power constraints

NASA Astrophysics Data System (ADS)

Dikmese, Sener; Srinivasan, Sudharsan; Shaat, Musbah; Bader, Faouzi; Renfors, Markku

2014-12-01

Multicarrier waveforms have been commonly recognized as strong candidates for cognitive radio. In this paper, we study the dynamics of spectrum sensing and spectrum allocation functions in cognitive radio context using very practical signal models for the primary users (PUs), including the effects of power amplifier nonlinearities. We start by sensing the spectrum with energy detection-based wideband multichannel spectrum sensing algorithm and continue by investigating optimal resource allocation methods. Along the way, we examine the effects of spectral regrowth due to the inevitable power amplifier nonlinearities of the PU transmitters. The signal model includes frequency selective block-fading channel models for both secondary and primary transmissions. Filter bank-based wideband spectrum sensing techniques are applied for detecting spectral holes and filter bank-based multicarrier (FBMC) modulation is selected for transmission as an alternative multicarrier waveform to avoid the disadvantage of limited spectral containment of orthogonal frequency-division multiplexing (OFDM)-based multicarrier systems. The optimization technique used for the resource allocation approach considered in this study utilizes the information obtained through spectrum sensing and knowledge of spectrum leakage effects of the underlying waveforms, including a practical power amplifier model for the PU transmitter. This study utilizes a computationally efficient algorithm to maximize the SU link capacity with power and interference constraints. It is seen that the SU transmission capacity depends critically on the spectral containment of the PU waveform, and these effects are quantified in a case study using an 802.11-g WLAN scenario.

Constraining the CO intensity mapping power spectrum at intermediate redshifts

NASA Astrophysics Data System (ADS)

Padmanabhan, Hamsa

2018-04-01

We compile available constraints on the carbon monoxide (CO) 1-0 luminosity functions and abundances at redshifts 0-3. This is used to develop a data driven halo model for the evolution of the CO galaxy abundances and clustering across intermediate redshifts. It is found that the recent constraints from the CO Power Spectrum Survey (z ˜ 3; Keating et al. 2016), when combined with existing observations of local galaxies (z ˜ 0; Keres, Yun & Young 2003), lead to predictions that are consistent with the results of smaller surveys at intermediate redshifts (z ˜ 1-2). We provide convenient fitting forms for the evolution of the CO luminosity-halo mass relation, and estimates of the mean and uncertainties in the CO power spectrum in the context of future intensity mapping experiments.

An Evolving Compact Jet in the Black Hole X-Ray Binary Maxi J1836-194

NASA Technical Reports Server (NTRS)

Russell, D. M.; Russell, T. D.; Miller-Jones, J. C. A.; O'Brien, K.; Soria, R.; Sivakoff, G. R.; Slaven-Blair, T.; Lewis, F.; Markoff, S.; Homan, J.;

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Soft Power and Hard Measures: Large-Scale Assessment, Citizenship and the European Union

ERIC Educational Resources Information Center

Rutkowski, David; Engel, Laura C.

2010-01-01

This article explores the International Civic and Citizenship Education Study (ICCS) with particular emphasis on the European Union's (EU's) involvement in the regional portion. Using the ICCS, the EU actively combines hard measures with soft power, allowing the EU to define and steer cross-national rankings of values of EU citizenship. The…

A Power-Law Growth and Decay Model with Autocorrelation for Posting Data to Social Networking Services

PubMed Central

Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi

2016-01-01

We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria. PMID:27505155

Halo Pressure Profile through the Skew Cross-power Spectrum of the Sunyaev-Zel’dovich Effect and CMB Lensing in Planck

NASA Astrophysics Data System (ADS)

Timmons, Nicholas; Cooray, Asantha; Feng, Chang; Keating, Brian

2017-11-01

We measure the cosmic microwave background (CMB) skewness power spectrum in Planck, using frequency maps of the HFI instrument and the Sunyaev-Zel’dovich (SZ) component map. The two-to-one skewness power spectrum measures the cross-correlation between CMB lensing and the thermal SZ effect. We also directly measure the same cross-correlation using the Planck CMB lensing map and the SZ map and compare it to the cross-correlation derived from the skewness power spectrum. We model fit the SZ power spectrum and CMB lensing-SZ cross-power spectrum via the skewness power spectrum to constrain the gas pressure profile of dark matter halos. The gas pressure profile is compared to existing measurements in the literature including a direct estimate based on the stacking of SZ clusters in Planck.

Power laws and fragility in flow networks.

PubMed

Shore, Jesse; Chu, Catherine J; Bianchi, Matt T

2013-01-01

What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence.

From the Cover: Musical rhythm spectra from Bach to Joplin obey a 1/f power law

NASA Astrophysics Data System (ADS)

Levitin, Daniel J.; Chordia, Parag; Menon, Vinod

2012-03-01

Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

NASA Astrophysics Data System (ADS)

Zhao, Hanqing; Wang, Wen-ge

2018-01-01

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

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.

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.

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.

Maximal compression of the redshift-space galaxy power spectrum and bispectrum

NASA Astrophysics Data System (ADS)

Gualdi, Davide; Manera, Marc; Joachimi, Benjamin; Lahav, Ofer

2018-05-01

We explore two methods of compressing the redshift-space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data vector (e.g. 1000 elements) to the number of cosmological parameters considered (e.g. seven ) using the Karhunen-Loève algorithm. In the first case, we run MCMC sampling on the compressed data vector in order to recover the 1D and 2D posterior distributions. The second option, approximately 2000 times faster, works by orthogonalizing the parameter space through diagonalization of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, Euclid, and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data vector, both compression methods on average recover the 68 {per cent} credible regions to within 0.7 {per cent} and 2 {per cent} of those resulting from standard MCMC sampling, respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by 81 per cent, 80 per cent, and 82 per cent respectively, for the bias parameter b1, the growth rate f, and the scalar amplitude parameter As.

Effect of strain and stress on the relative dimensions of the 'hard' and 'soft' regions in crept NaCl single crystals

NASA Technical Reports Server (NTRS)

Raj, S. V.; Freed, Alan D.

1992-01-01

It is shown that the L exp h and L exp s ratio, where these are respectively the average dimensions of the hard and soft regions as a function of stress and strain in crept NaCl single crystals, significantly influences the steady-state creep and power-law breakdown in these crystals. This is suggested to be due to a change in the internal stresses of the material. The present observations also indicate that steady-state creep is more likely to be influenced by the degree of refinement in the cell boundaries within the subgrains than by the formation of equiaxed subgrains under power-law conditions.