Ackermann, M.; Asano, K.; Atwood, W. B.; ...
2010-05-27
We present detailed observations of the bright short-hard gamma-ray burst GRB 090510 made with the Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) on board the Fermi observatory. GRB 090510 is the first burst detected by the LAT that shows strong evidence for a deviation from a Band spectral fitting function during the prompt emission phase. The time-integrated spectrum is fit by the sum of a Band function with E peak = 3.9 ± 0.3 MeV, which is the highest yet measured, and a hard power-law component with photon index –1.62 ± 0.03 that dominates the emission below ≈20more » keV and above ≈100 MeV. The onset of the high-energy spectral component appears to be delayed by ~0.1 s with respect to the onset of a component well fit with a single Band function. A faint GBM pulse and a LAT photon are detected 0.5 s before the main pulse. During the prompt phase, the LAT detected a photon with energy 30.5 +5.8 –2.6 GeV, the highest ever measured from a short GRB. Observation of this photon sets a minimum bulk outflow Lorentz factor, Γ≳ 1200, using simple γγ opacity arguments for this GRB at redshift z = 0.903 and a variability timescale on the order of tens of ms for the ≈100 keV-few MeV flux. Stricter high confidence estimates imply Γ ≳ 1000 and still require that the outflows powering short GRBs are at least as highly relativistic as those of long-duration GRBs. Finally, implications of the temporal behavior and power-law shape of the additional component on synchrotron/synchrotron self-Compton, external-shock synchrotron, and hadronic models are considered.« less
A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4
Chakrabarty, Deepto; Nowak, Michael A.; Tomsick, John A.
2014-12-20
The low-mass X-ray binary (LMXB) Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1×10{sup 33} D{sub kpc}{sup 2} erg s{sup –1}, with ≅60% in the thermalmore » component. We clearly detect a cutoff of the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. We show that thermal Comptonization and synchrotron shock origins for the hard X-ray emission are ruled out on physical grounds. However, the hard X-ray spectrum is well fit by a thermal bremsstrahlung model with kT{sub e} = 18 keV, which can be understood as arising either in a hot layer above the neutron star atmosphere or in a radiatively inefficient accretion flow. The power-law cutoff energy may be set by the degree of Compton cooling of the bremsstrahlung electrons by thermal seed photons from the neutron star surface. Lower thermal luminosities should lead to higher (possibly undetectable) cutoff energies. We compare Cen X-4's behavior with PSR J1023+0038, IGR J18245–2452, and XSS J12270–4859, which have shown transitions between LMXB and radio pulsar modes at a similar X-ray luminosity.« less
NASA Astrophysics Data System (ADS)
Lan, Hongzhi; Venkatesh, T. A.
2014-01-01
A comprehensive understanding of the relationship between the hardness and the elastic and plastic properties for a wide range of materials is obtained by analysing the hardness characteristics (that are predicted by experimentally verified indentation analyses) of over 9000 distinct combinations of material properties that represent isotropic, homogeneous, power-law hardening metallic materials. Finite element analysis has been used to develop the indentation algorithms that provide the relationships between the elastic and plastic properties of the indented material and its indentation hardness. Based on computational analysis and virtual testing, the following observations are made. The hardness (H) of a material tends to increase with an increase in the elastic modulus (E), yield strength (σy) and the strain-hardening exponent (n). Several materials with different combinations of elastic and plastic properties can exhibit identical true hardness (for a particular indenter geometry/apex angle). In general, combinations of materials that exhibit relatively low elastic modulus and high yield strength or strain-hardening exponents and those that exhibit relatively high elastic modulus and low yield strength or strain-hardening exponents exhibit similar hardness properties. Depending on the strain-hardening characteristics of the indented material, (i.e. n = 0 or ?), the ratio H/σy ranges, respectively, from 2.2 to 2.6 or 2 to 20 (for indentations with a cone angle of 70.3°). The materials that have lower σy/E and higher n exhibit higher H/σy ratios. The commonly invoked relationship between hardness and the yield strength, i.e. H ≈ 3σy, is not generally valid or applicable for all power-law hardening materials. The indentation hardness of a power law hardening material can be taken as following the relationship H ≈ (2.1-2.8)σr where σr is the representative stress based on Tabor's representative strain for a wide range of materials.
The Causal Connection Between Disc and Power-Law Variability in Hard State Black Hole X-Ray Binaries
NASA Technical Reports Server (NTRS)
Uttley, P.; Wilkinson, T.; Cassatella, P.; Wilms, J.; Pottschimdt, K.; Hanke, M.; Boeck, M.
2010-01-01
We use the XMM-Newton EPIC-pn instrument in timing mode to extend spectral time-lag studies of hard state black hole X-ray binaries into the soft X-ray band. \\Ve show that variations of the disc blackbody emission substantially lead variations in the power-law emission, by tenths of a second on variability time-scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time-delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time-scales less than a second the disc lags the power-law variations by a few ms, consistent with the disc variations being dominated by X-ray heating by the power-law, with the short lag corresponding to the light-travel time between the power-law emitting region and the disc. Our results indicate that instabilities in the accretion disc are responsible for continuum variability on time-scales of seconds or longer and probably also on shorter time-scales.
NASA Astrophysics Data System (ADS)
Zhang, Q.; Xiong, S. L.; Song, L. M.
2018-04-01
Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of p. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with p > 2, there are still a few GRBs suggestive of a hard (p < 2) electron energy spectrum. Our previous work showed that GRB 091127 gave strong evidence for a double power-law hard electron energy (DPLH) spectrum with 1 < p 1 < 2, p 2 > 2 and an “injection break” assumed as γ b ∝ γ q in the highly relativistic regime, where γ is the bulk Lorentz factor of the jet. In this paper, we show that GRB 060614 and GRB 060908 provide further evidence for such a DPLH spectrum. We interpret the multiband afterglow of GRB 060614 with the DPLH model in a homogeneous interstellar medium by taking into account a continuous energy injection process, while, for GRB 060908, a wind-like circumburst density profile is used. The two bursts, along with GRB 091127, suggest a similar behavior in the evolution of the injection break, with q ∼ 0.5. Whether this represents a universal law of the injection break remains uncertain and more afterglow observations such as these are needed to test this conjecture.
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.
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.
Structure of ternary additive hard-sphere fluid mixtures.
Malijevský, Alexander; Malijevský, Anatol; Yuste, Santos B; Santos, Andrés; López de Haro, Mariano
2002-12-01
Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.
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.
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.
Power law inflation with electromagnetism
Luo, Xianghui; Isenberg, James, E-mail: isenberg@uoregon.edu
2013-07-15
We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as inmore » Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.« less
Power Law Distributions in Two Community Currencies
NASA Astrophysics Data System (ADS)
Kichiji, N.; Nishibe, M.
2007-07-01
The purpose of this paper is to highlight certain newly discovered social phenomena that accord with Zipf's law, in addition to the famous natural and social phenomena including word frequencies, earthquake magnitude, city size, income1 etc. that are already known to follow it. These phenomena have recently been discovered within the transaction amount (payments or receipts) distributions within two different Community Currencies (CC) that had been initiated as social experiments. One is a local CC circulating in a specific geographical area, such as a town. The other is a virtual CC used among members who belong to a certain community of interest (COI) on the Internet. We conducted two empirical studies to estimate the economic vitalization effects they had on their respective local economies. The results we found were that the amount of transactions (payments and receipts) of the two CCs was distributed according to a power-law distribution with a unity rank exponent. In addition, we found differences between the two CCs with regard to the shapes of their distribution over a low-transaction range. The result may originate from the difference in methods of issuing CCs or in the magnitudes of the minimum-value unit; however, this result calls for further investigation.
Non-thermal Power-Law Distributions in Solar and Space Plasmas
NASA Astrophysics Data System (ADS)
Oka, M.; Battaglia, M.; Birn, J.; Chaston, C. C.; Effenberger, F.; Eriksson, E.; Fletcher, L.; Hatch, S.; Imada, S.; Khotyaintsev, Y. V.; Kuhar, M.; Livadiotis, G.; Miyoshi, Y.; Retino, A.
2017-12-01
Particles are accelerated to very high, non-thermal energies in solar and space plasma environments. While energy spectra of accelerated particles often exhibit a power-law and are characterized by the power-law index δ, it remains unclear how particles are accelerated to high energies and how δ is determined. Here, we review previous observations of the power-law index δ in a variety of different plasma environments with a particular focus on sub-relativistic electrons. It appears that in regions more closely related to magnetic reconnection (such as the "above-the-looptop" solar hard X-ray source and the plasma sheet in Earth's magnetotail), the spectra are typically soft (δ> 4). This is in contrast to the typically hard spectra (δ< 4) that are observed in coincidence with shocks. The difference implies that shocks are more efficient in producing a larger fraction of non-thermal electron energies than magnetic reconnection. A caveat is that during active times in Earth's magnetotail, δ values seem spatially uniform in the plasma sheet, while power-law distributions still exist even in quiet times. The role of magnetotail reconnection in the electron power-law formation could therefore be confounded with these background conditions. Because different regions have been studied with different instrumentations and methodologies, we point out a need for more systematic and coordinated studies of power-law distributions for a better understanding of possible scaling laws in particle acceleration as well as their universality.
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.
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.
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.
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.
Power law analysis of the human microbiome.
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.
Relativity, nonextensivity, and extended power law distributions.
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.
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.
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.
Models of fragmentation with composite power laws
NASA Astrophysics Data System (ADS)
Tavassoli, Z.; Rodgers, G. J.
1999-06-01
Some models for binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the first model we assume a fixed rate of fragmentation for the largest fragment and two different rates of fragmentation in the two regions of sizes above and below the transition size. The model is solved exactly in the long time limit to reveal stable time-invariant solutions for the fragment size and mass distributions. These solutions exhibit composite power law behaviours; power laws with two different exponents for fragments in smaller and larger regions. A special case of the model with no fragmentation in the smaller size region is also examined. Another model is also introduced which have three regions of fragment sizes with different rates of fragmentation. The similarities between the stable distributions in our models and composite power law distributions from experimental work on shock fragmentation of long thin glass rods and thick clay plates are discussed.
Power law tails in phylogenetic systems.
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.
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 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.
Maximum Renyi entropy principle for systems with power-law Hamiltonians.
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 (0
Deformation of a Capsule in a Power-Law Shear Flow
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
Renormalization group approach to power-law modeling of complex metabolic networks.
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.
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.
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.
Universal Power Law Governing Pedestrian Interactions
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
Poissonian renormalizations, exponentials, and power laws.
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.
Power laws and fragility in flow networks.
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.
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.
Power-law spatial dispersion from fractional Liouville equation
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 scaling in synchronization of brain signals depends on cognitive load.
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.
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 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.
Fractional power-law spatial dispersion in electrodynamics
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
Power laws in citation distributions: evidence from Scopus.
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.
Research on hardness and tensile properties of A390 alloy with tin addition
NASA Astrophysics Data System (ADS)
Si, Yi
2018-03-01
The effect of tin content on hardness and tensile properties of A390 alloys has been discussed. The microstructure of the A390 alloy with tin addition has been surveyed by OM and investigated by SEM. Research showed that β-Sn in the alloy precipitation forms were mainly small blocks and thin strips, particles within the Al2Cu network or large blocks consisting of β-Sn and Al2Cu on Al/Si interfaces or α-Al grain boundaries. Spheroidization of the primary and eutectic silicon was improved due to Sn accretion. With the augment of element tin, hardness of casting alloy is much higher than that of alloy after heat treatment. The elongation and ultimate tensile strength (UTS) were increased in Sn addition from 0 to 1%, which is attributed to the multiple action of Sn.
López de Haro, Mariano; Tejero, Carlos F; Santos, Andrés
2013-04-28
The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures.
Statistical analyses support power law distributions found in neuronal avalanches.
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.
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.
Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources
NASA Technical Reports Server (NTRS)
Fiorito, Ralph; Titarchuk, Lev
2004-01-01
Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.
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.
Fractal ladder models and power law wave equations
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
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.
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.
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.
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.
Effects of Mn addition on microstructure and hardness of Al-12.6Si alloy
NASA Astrophysics Data System (ADS)
Biswas, Prosanta; Patra, Surajit; Mondal, Manas Kumar
2018-03-01
In this work, eutectic Al-12.6Si alloy with and without manganese (Mn) have been developed through gravity casting route. The effect of Mn concentration (0.0 wt.%, 1 wt%, 2 wt% and 3 wt%) on microstructural morphology and hardness property of the alloy has been investigated. The eutectic Al-12.6 Si alloy exhibits the presence of combine plate, needle and rod-like eutectic silicon phase with very sharp corners and coarser primary silicon particles within the α-Al phase. In addition of 1wt.% of Mn in the eutectic Al-12.6Si alloy, sharp corners of the primary Si and needle-like eutectic Si are became blunt and particles size is reduced. Further, increase in Mn concentration (2.0 wt.%) in the Al-12.6Si alloy, irregular plate shape Al6(Mn,Fe) intermetallics are formed inside the α-Al phase, but the primary and eutectic phase morphology is similar to the eutectic Al-12.6Si alloy. The volume fraction of Al6(Mn,Fe) increases and Al6(Mn,Fe) particles appear as like chain structure in the alloy with 3 wt.% Mn. An increase in Mn concentration in the Al-12.6Si alloys result in the increase in bulk hardness of the alloy as an effects of microstructure modification as well as the presence of harder Al6(Mn,Fe) phase in the developed alloy.
Statistical tests for power-law cross-correlated processes
NASA Astrophysics Data System (ADS)
Podobnik, Boris; Jiang, Zhi-Qiang; Zhou, Wei-Xing; Stanley, H. Eugene
2011-12-01
For stationary time series, the cross-covariance and the cross-correlation as functions of time lag n serve to quantify the similarity of two time series. The latter measure is also used to assess whether the cross-correlations are statistically significant. For nonstationary time series, the analogous measures are detrended cross-correlations analysis (DCCA) and the recently proposed detrended cross-correlation coefficient, ρDCCA(T,n), where T is the total length of the time series and n the window size. For ρDCCA(T,n), we numerically calculated the Cauchy inequality -1≤ρDCCA(T,n)≤1. Here we derive -1≤ρDCCA(T,n)≤1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ρDCCA within which the cross-correlations become statistically significant. For overlapping windows we numerically determine—and for nonoverlapping windows we derive—that the standard deviation of ρDCCA(T,n) tends with increasing T to 1/T. Using ρDCCA(T,n) we show that the Chinese financial market's tendency to follow the U.S. market is extremely weak. We also propose an additional statistical test that can be used to quantify the existence of cross-correlations between two power-law correlated time series.
Power laws for gravity and topography of Solar System bodies
NASA Astrophysics Data System (ADS)
Ermakov, A.; Park, R. S.; Bills, B. G.
2017-12-01
When a spacecraft visits a planetary body, it is useful to be able to predict its gravitational and topographic properties. This knowledge is important for determining the level of perturbations in spacecraft's motion as well as for planning the observation campaign. It has been known for the Earth that the power spectrum of gravity follows a power law, also known as the Kaula rule (Kaula, 1963; Rapp, 1989). A similar rule was derived for topography (Vening-Meinesz, 1951). The goal of this paper is to generalize the power law that can characterize the gravity and topography power spectra for bodies across a wide range of size. We have analyzed shape power spectra of the bodies that have either global shape and gravity field measured. These bodies span across five orders of magnitude in their radii and surface gravities and include terrestrial planets, icy moons and minor bodies. We have found that despite having different internal structure, composition and mechanical properties, the topography power spectrum of these bodies' shapes can be modeled with a similar power law rescaled by the surface gravity. Having empirically found a power law for topography, we can map it to a gravity power law. Special care should be taken for low-degree harmonic coefficients due to potential isostatic compensation. For minor bodies, uniform density can be assumed. The gravity coefficients are a linear function of the shape coefficients for close-to-spherical bodoes. In this case, the power law for gravity will be steeper than the power law of topography due to the factor (2n+1) in the gravity expansion (e.g. Eq. 10 in Wieczorek & Phillips, 1998). Higher powers of topography must be retained for irregularly shaped bodies, which breaks the linearity. Therefore, we propose the following procedure to derive an a priori constraint for gravity. First, a surface gravity needs to be determined assuming typical density for the relevant class of bodies. Second, the scaling coefficient of the
Power-law ansatz in complex systems: Excessive loss of information.
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.
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.
The speed-curvature power law of movements: a reappraisal.
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.
Power-law creep behavior of a semiflexible chain.
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.
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.
Robust Statistical Detection of Power-Law Cross-Correlation.
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.
General 2.5 power law of metallic glasses
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
A COSMIC COINCIDENCE: THE POWER-LAW GALAXY CORRELATION FUNCTION
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
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
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.
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.
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.
Constraints on cosmological parameters in power-law cosmology
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
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.
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
Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles
NASA Astrophysics Data System (ADS)
Paul, Sanku; Santhanam, M. S.
2018-03-01
It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.
Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L
2011-10-01
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws
Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.
2011-01-01
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.
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.
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.
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.
Diffusion with stochastic resetting at power-law times.
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 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.
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.
Model selection for identifying power-law scaling.
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.
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.
Bounds of memory strength for power-law series.
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.
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) .
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.
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.
Robust Statistical Detection of Power-Law Cross-Correlation
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
Gad, Mohammed M; Rahoma, Ahmed; Al-Thobity, Ahmad M
2018-06-20
The current study evaluated the effects of autoclave polymerization both with and without glass fiber (GF) reinforcement on the surface roughness and hardness of acrylic denture base material. Ninety disc specimens (30×2.5 mm) were prepared from Vertex resin and divided according to polymerization techniques into a water bath, short and long autoclave polymerization groups. Tested groups were divided into three subgroups according to the GF concentration (0, 2.5, and 5 wt%). Profilometer and Vickers hardness tests were performed to measure surface roughness and hardness. ANOVA and Tukey-Kramer multiple comparison tests analyzed the results, and p≤0.05 was considered statistically significant. Autoclave polymerization significantly decreased the surface roughness and increased the hardness of acrylic resin without GF reinforcement (p<0.05). However, 5 wt% GF addition significantly increased surface roughness and decreased hardness of the autoclave polymerized denture base resin (p<0.05). Surface properties of Polymethyl methacrylate (PMMA) denture base material improved with autoclave polymerization and negatively affected with GFs addition.
Simple inflationary quintessential model. II. Power law potentials
NASA Astrophysics Data System (ADS)
de Haro, Jaume; Amorós, Jaume; Pan, Supriya
2016-09-01
The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive
Scale Invariance in Landscape Evolution Models Using Stream Power Laws
NASA Astrophysics Data System (ADS)
Kwang, J. S.; Parker, G.
2014-12-01
Landscape evolution models (LEM) commonly utilize stream power laws to simulate river incision with formulations such as E = KAmSn, where E is a vertical incision rate [L/T], K is an erodibility constant [L1-2m/T], A is an upstream drainage area [L2], S is a local channel gradient [-], and m and n are positive exponents that describe the basin hydrology. In our reduced complexity model, the landscape approached equilibrium by balancing an incision rate with a constant, uniform, vertical rock uplift rate at every location in the landscape. From our simulations, for a combination of m and n, the landscape exhibited scale invariance. That is, regardless of the size and scale of the basin, the relief and vertical structure of the landscape remained constant. Therefore, the relief and elevation profile of the landscape at equilibrium were only dependent on the coefficients for erodibility and uplift and an equation that described how upstream area, A, increased as the length of a stream increased. In our analytical 1D models, we utilized two equations that described upslope area, (a) A = Bl, where B is the profile width [L], and l is the stream length from the ridge [L] and (b) A = Clh, Hack's Law, where C is a constant [L2-h] and h is a positive exponent. With these equations, (a) m = n and (b) hm = n resulted in scale invariance. In our numerical 2D models, the relationship between A and l was inherent in the actual structure of the drainage network. From our numerical 2D results, scale invariance occurred when 2m = n. Additionally, using reasonable values from the literature for exponents, n, m and h, resulted in singularities at the ridges in the landscape, which caused truncation error. In consequence, the elevation of the ridge increased as the number of grid cells in the domain increased in the numerical model, and the model was unable to converge. These singularities at the ridges appeared when (a) m ≥ n and (b) hm ≥ n in the analytical model and 2m ≥ n in
Qu, Jun; Zhou, Yan; Leonard, Donovan N
The objectives for this considerations described here are to; investigate the compatibility of engine lubricant antiwear (AW) additives, specifically conventional zinc dialkyldithiophosphate (ZDDP) and newly developed ionic liquids (ILs), with selected commercial hard coatings, and provide fundamental understanding to guide future development of engine lubricants.
van Mierlo, Trevor; Hyatt, Douglas; Ching, Andrew T
2015-06-25
Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by
Urban, Vanessa M; Lima, Thiago F; Bueno, Mirian G; Giannini, Marcelo; Arioli Filho, João N; de Almeida, Ana Lúcia P F; Neppelenbroek, Karin H
2015-04-01
While the incorporation of antimicrobial agents into soft denture liners has been suggested as a reliable alternative treatment for denture stomatitis, it may affect the liner's properties. The effect of addition of antimicrobial agents for the treatment of denture stomatitis on the surface roughness and Shore A hardness of soft lining materials was evaluated. The test groups comprised specimens (36 × 7 × 6 mm(3) ) of soft materials (Softone and Trusoft) without (control) or with incorporation of drugs (nystatin, miconazole, ketoconazole, chlorhexidine diacetate, and itraconazole). Hardness (Shore A) and roughness (Ra) were evaluated after immersion of specimens (n = 10) in distilled water at 37°C for 24 hours, 7 and 14 days. Data were analyzed by 3-way ANOVA/Tukey's test (α = 0.05). After 14 days, an increase (p < 0.05) was observed in the hardness of soft materials with time for the modified specimens, except for itraconazole. Addition of drugs increased the Softone roughness only for the addition of miconazole and chlorhexidine (p < 0.05), and did not increase the roughness of Trusoft with time. Only chlorhexidine and itraconazole altered the roughness compared to the control for each material (p < 0.05). The smallest changes of hardness and roughness with time in the modified groups compared to controls were observed for itraconazole groups for both materials. © 2014 by the American College of Prosthodontists.
Event-scale power law recession analysis: quantifying methodological uncertainty
NASA Astrophysics Data System (ADS)
Dralle, David N.; Karst, Nathaniel J.; Charalampous, Kyriakos; Veenstra, Andrew; Thompson, Sally E.
2017-01-01
The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship
Power laws, discontinuities and regional city size distributions
Garmestani, A.S.; Allen, Craig R.; Gallagher, C.M.
2008-01-01
Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classes in the city size distributions are snapshots of stable states within urban systems in flux.
Power-law tails in the distribution of order imbalance
NASA Astrophysics Data System (ADS)
Zhang, Ting; Gu, Gao-Feng; Xu, Hai-Chuan; Xiong, Xiong; Chen, Wei; Zhou, Wei-Xing
2017-10-01
We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and the order size. We find that the order imbalance distributions of individual stocks have power-law tails. However, the tail index fluctuates remarkably from stock to stock. We also investigate the distributions of aggregated order imbalance of all stocks at different timescales Δt. We find no clear trend in the tail index with respect Δt. All the analyses suggest that the distributions of order imbalance are asymmetric.
Elastohydrodynamic analysis using a power law pressure-viscosity relation
NASA Technical Reports Server (NTRS)
Loewenthal, S. H.; Zaretsky, E. V.
1973-01-01
An isothermal elastohydrodynamic (EHD) inlet analysis of the Grubin type which considers a power law pressure-viscosity relation and a finite pressure at the inlet edge of the Hertzian contact zone was performed. Comparisons made with published X-ray EHD film thickness data for a synthetic paraffinic oil and when conventional EHD theory showed that the present theory exhibits a slightly stronger film thickness load dependence than do previous isothermal EHD theories but far less than that exhibited by the measured 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.
COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS
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 Law Distributions of Patents as Indicators of Innovation
NASA Astrophysics Data System (ADS)
O'Neale, Dion; Hendy, Shaun
2013-03-01
The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Such figures however give an overly simplistic measure of innovation within a country. Here we present evidence that the distribution of patents amongst applicants within many countries is well-fitted to a power law distribution with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.
Power law "thermalization" of ion pickup and ionospheric outflows
NASA Astrophysics Data System (ADS)
Moore, T. E.; Ofman, L.; Glocer, A.; Gershman, D. J.; Khazanov, G. V.; Paterson, W. R.
2016-12-01
One observed feature of ionospheric outflows is that the active ion heating processes produce power law tails of the core plasma velocity distribution, as well as transverse or conic peaks in the angular distributions. This characteristic is shared with hot ion distributions produced by ion pickup in the solar wind, resulting from cometary or interstellar gas ionization, and with hot ions observed around the Space Transportation System during gas releases. We revisit relevant observations and consider the hypothesis that the ion pickup thermalization process tends to produce power law (𝛋) energy distributions, using a simulation of the instability of a simple pickup (ring) distribution. Simulation results are derived for cases representative of both solar wind pickup, where ion velocities exceed the local Alfvén speed, and ionospheric pickup, where the local Alfvén speed exceeds ion velocities. The sub-Alfvenic pickup ring distribution appears to have a slow growth rate (per ion gyro period), that is, the instability evolves more slowly in the latter case than in the former. Implications for ionospheric outflow are discussed.
Power-law Growth and Punctuated Equilibrium Dynamics in Water Resources Systems
NASA Astrophysics Data System (ADS)
Parolari, A.; Katul, G. G.; Porporato, A. M.
2015-12-01
The global rise in population-driven water scarcity and recent appreciation of strong dynamic coupling between human and natural systems has called for new approaches to predict the future sustainability of regional and global water resources systems. The dynamics of coupled human-water systems are driven by a complex set of social, environmental, and technological factors. Present projections of water resources systems range from a finite carrying capacity regulated by accessible freshwater, or `peak renewable water,' to punctuated evolution with new supplied and improved efficiency gained from technological and social innovation. However, these projections have yet to be quantified from observations or in a comprehensive theoretical framework. Using data on global water withdrawals and storage capacity of regional water supply systems, non-trivial dynamics are identified in water resources systems development over time, including power-law growth and punctuated equilibria. Two models are introduced to explain this behavior: (1) a delay differential equation and (2) a power-law with log-periodic oscillations, both of which rely on past conditions (or system memory) to describe the present rate of growth in the system. In addition, extension of the first model demonstrates how system delays and punctuated equilibria can emerge from coupling between human population growth and associated resource demands. Lastly, anecdotal evidence is used to demonstrate the likelihood of power-law growth in global water use from the agricultural revolution 3000 BC to the present. In a practical sense, the presence of these patterns in models with delayed oscillations suggests that current decision-making related to water resources development results from the historical accumulation of resource use decisions, technological and social changes, and their consequences.
Breaking the power law: Multiscale simulations of self-ion irradiated tungsten
NASA Astrophysics Data System (ADS)
Jin, Miaomiao; Permann, Cody; Short, Michael P.
2018-06-01
The initial stage of radiation defect creation has often been shown to follow a power law distribution at short time scales, recently so with tungsten, following many self-organizing patterns found in nature. The evolution of this damage, however, is dominated by interactions between defect clusters, as the coalescence of smaller defects into clusters depends on the balance between transport, absorption, and emission to/from existing clusters. The long-time evolution of radiation-induced defects in tungsten is studied with cluster dynamics parameterized with lower length scale simulations, and is shown to deviate from a power law size distribution. The effects of parameters such as dose rate and total dose, as parameters affecting the strength of the driving force for defect evolution, are also analyzed. Excellent agreement is achieved with regards to an experimentally measured defect size distribution at 30 K. This study provides another satisfactory explanation for experimental observations in addition to that of primary radiation damage, which should be reconciled with additional validation data.
Economic demography in fuzzy spatial dilemmas and power laws
NASA Astrophysics Data System (ADS)
Fort, H.; Pérez, N.
2005-03-01
Adaptive agents, playing the iterated Prisoner's Dilemma (IPD) in a two-dimensional spatial setting and governed by Pavlovian strategies ("higher success-higher chance to stay"), are used to approach the problem of cooperation between self-interested individuals from a novel angle: We investigate the effect of different possible measures of success (MS) used by players to asses their performance in the game. These MS involve quantities such as: the player's utilities U, his cumulative score (or "capital") W, his neighborhood "welfare", etc. To handle an imprecise concept like "success" the agents use fuzzy logic. The degree of cooperation, the "economic demography" and the "efficiency" attained by the system depend dramatically on the MS. Specifically, patterns of "segregation" or "exploitation" are observed for some MS. On the other hand, power laws, that may be interpreted as signatures of critical self-organization (SOC), constitute a common feature for all the MS.
Power-law rheology controls aftershock triggering and decay
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
Novel solution of power law for γ-bands
NASA Astrophysics Data System (ADS)
Gupta, J. B.
The power law expression E = aIb offers a single-term formula with just two parameters for expressing the level energies in the spectra of even-Z even-N nuclei. Its application to ground band spectra for a wide range of nuclei has been demonstrated in our earlier works. Here, we extend its application to the rotational bands built on an excited state of K = 2 γ-vibration band and Kπ = 0 2+ beta band. A novel assumption of a virtual level with spin zero for γ-bands is made and its validity and use is illustrated. Here, the constancy of the parameters “b” and “a” with spin, offers a more realistic view of the dependence of the nuclear core deformation on spin, in the excited bands. Also, it enables a spinwise view, not available in the other energy fit expressions.
Unexpected power-law stress relaxation of entangled ring polymers
KAPNISTOS, M.; LANG, M.; PYCKHOUT-HINTZEN, W.; RICHTER, D.; CHO, D.; CHANG, T.
2016-01-01
After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers. PMID:18953345
Radiative corrections in the (varying power)-law modified gravity
NASA Astrophysics Data System (ADS)
Hammad, Fayçal
2015-06-01
Although the (varying power)-law modified gravity toy model has the attractive feature of unifying the early- and late-time expansions of the Universe, thanks to the peculiar dependence of the scalar field's potential on the scalar curvature, the model still suffers from the fine-tuning problem when used to explain the actually observed Hubble parameter. Indeed, a more correct estimate of the mass of the scalar field needed to comply with actual observations gives an unnaturally small value. On the other hand, for a massless scalar field the potential would have no minimum and hence the field would always remain massless. What solves these issues are the radiative corrections that modify the field's effective potential. These corrections raise the field's effective mass, rendering the model free from fine-tuning, immune against positive fifth-force tests, and better suited to tackle the dark matter sector.
Power-law weighted networks from local attachments
NASA Astrophysics Data System (ADS)
Moriano, P.; Finke, J.
2012-07-01
This letter introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on extended power-law weighted networks with both a desired scaling exponent and a fixed clustering coefficient. The analytical results show that the connectivity distribution converges to the scaling behavior often found in social and engineering systems. To illustrate the approach of the proposed framework we generate network substrates that resemble steady state properties of the empirical citation distributions of i) publications indexed by the Institute for Scientific Information from 1981 to 1997; ii) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and iii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.
Bubble coalescence in a power-law fluid
NASA Astrophysics Data System (ADS)
Kamat, Pritish; Thete, Sumeet; Basaran, Osman
2015-11-01
As two spherical gas bubbles in a liquid are slowly brought together, the liquid film or sheet between them drains and ultimately ruptures, forming a circular hole that connects them. The high curvature near the edge of the liquid sheet drives flow radially outward, causing the film to retract and the radius of the hole to increase with time. Recent experimental and theoretical work in this area has uncovered self-similarity and universal scaling regimes when two bubbles coalesce in a Newtonian fluid. Motivated by applications such as polymer and composites processing, food and drug manufacture, and aeration/deaeration systems where the liquids often exhibit deformation-rate thinning rheology, we extend the recent Newtonian studies to bubble coalescence in power-law fluids. In our work, we use a combination of thin-film theory and full 3D, axisymmetric computations to probe the dynamics in the aftermath of the singularity.
Deviations from uniform power law scaling in nonstationary time series
NASA Technical Reports Server (NTRS)
Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.
1997-01-01
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
Power law f(𝒢,T) gravity models supporting wormhole solutions
NASA Astrophysics Data System (ADS)
Shamir, M. Farasat; Ahmad, Mushtaq
This work provides some feasible regions for the existence of traversable wormhole geometries in modified f(𝒢,T) gravity. For this purpose, three different matter contents have been studied with special emphasis on anisotropic fluid by considering a specific f(𝒢,T) gravity power law model. It has been shown that the null energy conditions for the effective energy-momentum tensor are widely violated for the ordinary matter content. However, some small feasible regions to support the wormhole solutions have been noted. Furthermore, the stability of the anisotropic feasible regions for the wormhole solutions has been discussed. It is concluded that the wormhole geometries threaded by the ordinary matter actually exist and are well stable in f(𝒢,T) gravity.
Power laws and extreme values in antibody repertoires
NASA Astrophysics Data System (ADS)
Boyer, Sebastien; Biswas, Dipanwita; Scaramozzino, Natale; Kumar, Ananda Soshee; Nizak, Clément; Rivoire, Olivier
2015-03-01
Evolution by natural selection involves the succession of three steps: mutations, selection and proliferation. We are interested in describing and characterizing the result of selection over a population of many variants. After selection, this population will be dominated by the few best variants, with highest propensity to be selected, or highest ``selectivity.'' We ask the following question: how is the selectivity of the best variants distributed in the population? Extreme value theory, which characterizes the extreme tail of probability distributions in terms of a few universality class, has been proposed to describe it. To test this proposition and identify the relevant universality class, we performed quantitative in vitro experimental selections of libraries of >105 antibodies using the technique of phage display. Data obtained by high-throughput sequencing allows us to fit the selectivity distribution over more than two decades. In most experiments, the results show a striking power law for the selectivity distribution of the top antibodies, consistent with extreme value theory.
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.
The Discrepancy between Einstein Mass and Dynamical Mass for SIS and Power-law Mass Models
NASA Astrophysics Data System (ADS)
Li, Rui; Wang, Jiancheng; Shu, Yiping; Xu, Zhaoyi
2018-03-01
We investigate the discrepancy between the two-dimensional projected lensing mass and the dynamical mass for an ensemble of 97 strong gravitational lensing systems discovered by the Sloan Lens ACS Survey, the BOSS Emission-Line Lens Survey (BELLS), and the BELLS for GALaxy-Lyα EmitteR sYstems Survey. We fit the lensing data to obtain the Einstein mass and use the velocity dispersion of the lensing galaxies provided by the Sloan Digital Sky Survey to get the projected dynamical mass within the Einstein radius by assuming the power-law mass approximation. The discrepancy is found to be obvious and quantified by Bayesian analysis. For the singular isothermal sphere mass model, we obtain that the Einstein mass is 20.7% more than the dynamical mass, and the discrepancy increases with the redshift of the lensing galaxies. For the more general power-law mass model, the discrepancy still exists within a 1σ credible region. We suspect the main reason for this discrepancy is mass contamination, including all invisible masses along the line of sight. In addition, the measurement errors and the approximation of the mass models could also contribute to the discrepancy.
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.
Fickl, Stefan; Zuhr, Otto; Wachtel, Hannes; Kebschull, Moritz; Hürzeler, Markus B
2009-10-01
The aim of this study was to histometrically assess alterations of the ridge following socket preservation alone and socket preservation with additional buccal overbuilding. In five beagle dogs four extraction sites were randomly subjected to one of the following treatments: Tx 1: The socket was filled with BioOss Collagen and covered with a free gingival graft from the palate. Tx 2: The buccal bone plate was augmented using the GBR-technique, the socket was filled with BioOss Collagen and covered with a free gingival graft. Tx 3: The buccal bone plate was forced into a buccal direction using a manual bone spreader. The socket was filled with BioOss Collagen and covered with a free gingival graft from the palate. Tx 4: The socket was filled with BioOss Collagen and a combined free gingival/connective tissue graft was used to cover the socket and for buccal tissue augmentation. For each experimental site, two histological sections were subjected to histometric analysis and evaluated for (i) vertical bone dimensions and (ii) horizontal bone dimensions. All treatment groups showed horizontal and vertical bone loss. The mean vertical bone loss of the buccal bone plate was significantly lower in Tx 4 than in the other groups, while no statistical significant differences could be detected among the groups in the horizontal dimension. Overbuilding the buccal aspect in combination with socket preservation does not seem to be a suitable technique to compensate for the alterations after tooth extraction.
Power Laws, Scale Invariance and the Generalized Frobenius Series:
NASA Astrophysics Data System (ADS)
Visser, Matt; Yunes, Nicolas
We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to
Mutually cooperative epidemics on power-law networks
NASA Astrophysics Data System (ADS)
Cui, Peng-Bi; Colaiori, Francesca; Castellano, Claudio
2017-08-01
The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favoring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial role in these cooperative dynamics. We consider a susceptible-infected-removed-type model with two mutually cooperative pathogens: An individual already infected with one disease has an increased probability of getting infected by the other. We present a heterogeneous mean-field theoretical approach to the coinfection dynamics on generic uncorrelated power-law degree-distributed networks and validate its results by means of numerical simulations. We show that, when the second moment of the degree distribution is finite, the epidemic transition is continuous for low cooperativity, while it is discontinuous when cooperativity is sufficiently high. For scale-free networks, i.e., topologies with diverging second moment, the transition is instead always continuous. In this way we clarify the effect of heterogeneity and system size on the nature of the transition, and we validate the physical interpretation about the origin of the discontinuity.
One loop back reaction on power law inflation
Abramo, L.R.; Woodard, R.P.
1999-08-01
We consider quantum-mechanical corrections to a homogeneous, isotropic, and spatially flat geometry whose scale factor expands classically as a general power of the comoving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger [J. Math. Phys. {bold 2}, 407 (1961); {ital Particles, Sources and Fields} (Addison, Wesley, Reading, MA, 1970)] with the Feynman rules recently developed by Iliopoulos {ital et al.} [Nucl. Phys. B {bold 534}, 419 (1998)]. We find no significant effect, in marked contrast to the result obtained by Mukhanov and co-workers [Phys. Rev. Lett.more » {bold 78}, 1624 (1998); Phys. Rev. D {bold 56}, 3248 (1997)] for chaotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov and co-workers to the exponential potentials of power law inflation, we show that the two methods produce the same results, within the approximations employed, for these backgrounds. We therefore conclude that the shape of the inflaton potential can have an enormous impact on the one loop back reaction. {copyright} {ital 1999} {ital The American Physical Society}« less
There is More than a Power Law in Zipf
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
The Epidemics of Donations: Logistic Growth and Power-Laws
Schweitzer, Frank; Mach, Robert
2008-01-01
This paper demonstrates that collective social dynamics resulting from individual donations can be well described by an epidemic model. It captures the herding behavior in donations as a non-local interaction between individual via a time-dependent mean field representing the mass media. Our study is based on the statistical analysis of a unique dataset obtained before and after the tsunami disaster of 2004. We find a power-law behavior for the distributions of donations with similar exponents for different countries. Even more remarkably, we show that these exponents are the same before and after the tsunami, which accounts for some kind of universal behavior in donations independent of the actual event. We further show that the time-dependent change of both the number and the total amount of donations after the tsunami follows a logistic growth equation. As a new element, a time-dependent scaling factor appears in this equation which accounts for the growing lack of public interest after the disaster. The results of the model are underpinned by the data analysis and thus also allow for a quantification of the media influence. PMID:18213367
The speed–curvature power law in Drosophila larval locomotion
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
Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs
NASA Astrophysics Data System (ADS)
van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.
2018-04-01
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299-2361, 2012). It was proved that when the degrees obey a power law with exponent τ \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.
The speed-curvature power law in Drosophila larval locomotion.
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.
Reciprocity and the Emergence of Power Laws in Social Networks
NASA Astrophysics Data System (ADS)
Schnegg, Michael
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.
Power-law tail probabilities of drainage areas in river basins
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.
Power law signature of media exposure in human response waiting time distributions
NASA Astrophysics Data System (ADS)
Crane, Riley; Schweitzer, Frank; Sornette, Didier
2010-05-01
We study the humanitarian response to the destruction brought by the tsunami generated by the Sumatra earthquake of December 26, 2004, as measured by donations, and find that it decays in time as a power law ˜1/tα with α=2.5±0.1 . This behavior is suggested to be the rare outcome of a priority queuing process in which individuals execute tasks at a rate slightly faster than the rate at which new tasks arise. We believe this to be an empirical evidence documenting the recently predicted [G. Grinstein and R. Linsker, Phys. Rev. E 77, 012101 (2008)] regime, and provide additional independent evidence that suggests that this “highly attentive regime” arises as a result of the intense focus placed on this donation “task” by the media.
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.
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.
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.
Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T
2012-06-01
The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.
Power-Law Template for IR Point Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renee;
2011-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Power-Law Template for Infrared Point-Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark J.; Halpern, Mark; Hincks, Adam D; Hlozek, Renee;
2012-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ?(sup Beta)B(?, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
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
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.
Power law versus exponential state transition dynamics: application to sleep-wake architecture.
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.
Can power-law scaling and neuronal avalanches arise from stochastic dynamics?
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.
Gent, David H.; Mehra, Lucky K.; Christie, David; Magarey, Roger
2017-01-01
Empirical and mechanistic modeling indicate that pathogens transmitted via aerially dispersed inoculum follow a power law, resulting in dispersive epidemic waves. The spread parameter (b) of the power law model, which is an indicator of the distance of the epidemic wave front from an initial focus per unit time, has been found to be approximately 2 for several animal and plant diseases over a wide range of spatial scales under conditions favorable for disease spread. Although disease spread and epidemic expansion can be influenced by several factors, the stability of the parameter b over multiple epidemic years has not been determined. Additionally, the size of the initial epidemic area is expected to be strongly related to the final epidemic extent for epidemics, but the stability of this relationship is also not well established. Here, empirical data of cucurbit downy mildew epidemics collected from 2008 to 2014 were analyzed using a spatio-temporal model of disease spread that incorporates logistic growth in time with a power law function for dispersal. Final epidemic extent ranged from 4.16 ×108 km2 in 2012 to 6.44 ×108 km2 in 2009. Current epidemic extent became significantly associated (P < 0.0332; 0.56 < R2 < 0.99) with final epidemic area beginning near the end of April, with the association increasing monotonically to 1.0 by the end of the epidemic season in July. The position of the epidemic wave-front became exponentially more distant with time, and epidemic velocity increased linearly with distance. Slopes from the temporal and spatial regression models varied with about a 2.5-fold range across epidemic years. Estimates of b varied substantially ranging from 1.51 to 4.16 across epidemic years. We observed a significant b ×time (or distance) interaction (P < 0.05) for epidemic years where data were well described by the power law model. These results suggest that the spread parameter b may not be stable over multiple epidemic years. However, b
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.
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.
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.
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.
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.
Exploring the effect of power law social popularity on language evolution.
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.
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.
Fitting power-laws in empirical data with estimators that work for all exponents
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
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.
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.
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.
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.
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.
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.
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.
NASA Astrophysics Data System (ADS)
Prifiharni, Siska; Anwar, Moch. Syaiful; Nikitasari, Arini; Mabruri, Efendi
2018-05-01
In this work, the effect of 2% W, 1%Nb, and 1% V addition on the hardness, microstructure, and pitting resistance to austenitic stainless steel Fe25Ni15Cr was investigated. The specimens were prepared in induction melting furnace, followed by homogenizing at 1100°C for 24 h. Then, the specimens were solution treated at 975°C for 2 h followed by water quenching and aging at 725°C for 15 h. The hardness was measured by using Rockwell hardness B, and metallographic observation was conducted using optical microscope and SEM-EDS. The results show that the increament of W, Nb, and V in the austenitic stainless steel Fe25Ni15Crby increased the hardness. The metal carbide precipitation occurred at grain boundaries in niobium free alloy. The addition of Nb in the alloy promotes the Laves phase transformation, and addition of V increase Nb content in the Laves phase. Laves phase formation in alloys containing niobium during aging heat treatments lead to an increase in hardness. Addition of W, Nb, and V also increase pitting resistance of the Fe25Ni15Cr austenitic stainless steel. This can be attributed to an increasing level of niobium in the matrix.
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.
The statistical overlap theory of chromatography using power law (fractal) statistics.
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.
Analytical time-domain Green’s functions for power-law media
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
Power-law modeling based on least-squares minimization criteria.
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.
Entanglement and fluctuations in the XXZ model with power-law interactions
NASA Astrophysics Data System (ADS)
Frérot, Irénée; Naldesi, Piero; Roscilde, Tommaso
2017-06-01
We investigate the ground-state properties of the spin-1 /2 XXZ model with power-law-decaying (1 /rα ) interactions, which describe spins interacting with long-range transverse (XX) ferromagnetic interactions and longitudinal (Z) antiferromagnetic interactions, or hard-core bosons with long-range repulsion and hopping. The long-range nature of the couplings allows us to quantitatively study the spectral, correlation, and entanglement properties of the system by making use of linear spin-wave theory, supplemented with density-matrix renormalization group in one-dimensional systems. Our most important prediction is the existence of three distinct coupling regimes, depending on the decay exponent α and number of dimensions d : (1) a short-range regime for α >d +σc (where σc=1 in the gapped Néel antiferromagnetic phase exhibited by the XXZ model, and σc=2 in the gapless XY ferromagnetic phase), sharing the same properties as those of finite-range interactions (α =∞ ); (2) a long-range regime α
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3
Why credit risk markets are predestined for exhibiting log-periodic power law structures
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Leker, Jens
2014-01-01
Recent research has established the existence of log-periodic power law (LPPL) patterns in financial institutions’ credit default swap (CDS) spreads. The main purpose of this paper is to clarify why credit risk markets are predestined for exhibiting LPPL structures. To this end, the credit risk prediction of two variants of logistic regression, i.e. polynomial logistic regression (PLR) and kernel logistic regression (KLR), are firstly compared to the standard logistic regression (SLR). In doing so, the question whether the performances of rating systems based on balance sheet ratios can be improved by nonlinear transformations of the explanatory variables is resolved. Building on the result that nonlinear balance sheet ratio transformations hardly improve the SLR’s predictive power in our case, we secondly compare the classification performance of a multivariate SLR to the discriminative powers of probabilities of default derived from three different capital market data, namely bonds, CDSs, and stocks. Benefiting from the prompt inclusion of relevant information, the capital market data in general and CDSs in particular increasingly outperform the SLR while approaching the time of the credit event. Due to the higher classification performances, it seems plausible for creditors to align their investment decisions with capital market-based default indicators, i.e., to imitate the aggregate opinion of the market participants. Since imitation is considered to be the source of LPPL structures in financial time series, it is highly plausible to scan CDS spread developments for LPPL patterns. By establishing LPPL patterns in governmental CDS spread trajectories of some European crisis countries, the LPPL’s application to credit risk markets is extended. This novel piece of evidence further strengthens the claim that credit risk markets are adequate breeding grounds for LPPL patterns.
Apparent power-law distributions in animal movements can arise from intraspecific interactions
Breed, Greg A.; Severns, Paul M.; Edwards, Andrew M.
2015-01-01
Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight. PMID:25519992
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
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.
Tippett, Michael K; Cohen, Joel E
2016-02-29
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.
NASA Astrophysics Data System (ADS)
Tippett, Michael K.; Cohen, Joel E.
2016-02-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from `outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.
Power-law decay of the spatial correlation function in exciton-polariton condensates
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
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.
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.
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.
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.
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.
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.
Timing of continuous motor imagery: the two-thirds power law originates in trajectory planning.
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.
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.
Dilatonic BTZ black holes with power-law field
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Sheykhi, A.
2017-04-01
Motivated by low energy effective action of string theory and numerous applications of BTZ black holes, we will consider minimal coupling between dilaton and nonlinear electromagnetic fields in three dimensions. The main goal is studying thermodynamical structure of black holes in this set up. Temperature and heat capacity of these black holes are investigated and a picture regarding their phase transitions is given. In addition, the role and importance of studying the mass of black holes is highlighted. We will see how different parameters modify thermodynamical quantities, hence thermodynamical structure of these black holes. In addition, geometrical thermodynamics is used to investigate thermodynamical properties of these black holes. In this regard, the successful method is presented and the nature of interaction around bound and phase transition points is studied.
Numerical simulation of heat transfer in power law fluid flow through a stenosed artery
NASA Astrophysics Data System (ADS)
Talib, Amira Husni; Abdullah, Ilyani
2017-11-01
A numerical study of heat transfer in a power law fluid is investigated in this paper. The blood flow is treated as power law fluid with a presence of cosine shaped stenosis. This study reveals the effect of stenosis on the heat transfer and velocity of blood flowing in the constricted artery. The governing and energy equations are formulated in a cylindrical coordinate system. Hence, the set of equations and boundary conditions are solved numerically by Marker and Cell (MAC) method. The graphical result shows the profile of blood temperature is increased while the blood velocity is decreased at the critical height of stenosis.
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
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.
NASA Astrophysics Data System (ADS)
Lillo, F.
2007-02-01
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons.
On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy
Ahnen, Max L., E-mail: m.knoetig@gmail.com
The high-energy non-thermal universe is dominated by power-law-like spectra. Therefore, results in high-energy astronomy are often reported as parameters of power-law fits, or, in the case of a non-detection, as an upper limit assuming the underlying unseen spectrum behaves as a power law. In this paper, I demonstrate a simple and powerful one-to-one relation of the integral upper limit in the two-dimensional power-law parameter space into the spectrum parameter space and use this method to unravel the so-far convoluted question of the sensitivity of astroparticle telescopes.
NASA Technical Reports Server (NTRS)
Smalheer, C. V.
1973-01-01
The chemistry of lubricant additives is discussed to show what the additives are chemically and what functions they perform in the lubrication of various kinds of equipment. Current theories regarding the mode of action of lubricant additives are presented. The additive groups discussed include the following: (1) detergents and dispersants, (2) corrosion inhibitors, (3) antioxidants, (4) viscosity index improvers, (5) pour point depressants, and (6) antifouling agents.
Power law of distribution of emergency situations on main gas pipeline
NASA Astrophysics Data System (ADS)
Voronin, K. S.; Akulov, K. A.
2018-05-01
The article presents the results of the analysis of emergency situations on a main gas pipeline. A power law of distribution of emergency situations is revealed. The possibility of conducting further scientific research to ensure the predictability of emergency situations on pipelines is justified.
Imaging viscoelastic properties of live cells by AFM: power-law rheology on the nanoscale.
Hecht, Fabian M; Rheinlaender, Johannes; Schierbaum, Nicolas; Goldmann, Wolfgang H; Fabry, Ben; Schäffer, Tilman E
2015-06-21
We developed force clamp force mapping (FCFM), an atomic force microscopy (AFM) technique for measuring the viscoelastic creep behavior of live cells with sub-micrometer spatial resolution. FCFM combines force-distance curves with an added force clamp phase during tip-sample contact. From the creep behavior measured during the force clamp phase, quantitative viscoelastic sample properties are extracted. We validate FCFM on soft polyacrylamide gels. We find that the creep behavior of living cells conforms to a power-law material model. By recording short (50-60 ms) force clamp measurements in rapid succession, we generate, for the first time, two-dimensional maps of power-law exponent and modulus scaling parameter. Although these maps reveal large spatial variations of both parameters across the cell surface, we obtain robust mean values from the several hundreds of measurements performed on each cell. Measurements on mouse embryonic fibroblasts show that the mean power-law exponents and the mean modulus scaling parameters differ greatly among individual cells, but both parameters are highly correlated: stiffer cells consistently show a smaller power-law exponent. This correlation allows us to distinguish between wild-type cells and cells that lack vinculin, a dominant protein of the focal adhesion complex, even though the mean values of viscoelastic properties between wildtype and knockout cells did not differ significantly. Therefore, FCFM spatially resolves viscoelastic sample properties and can uncover subtle mechanical signatures of proteins in living cells.
Power laws reveal phase transitions in landscape controls of fire regimes
Donald McKenzie; Maureen C. Kennedy
2012-01-01
Understanding the environmental controls on historical wildfires, and how they changed across spatial scales, is difficult because there are no surviving explicit records of either weather or vegetation (fuels). Here we show how power laws associated with fire-event time series arise in limited domains of parameters that represent critical transitions in the controls...
Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?
ERIC Educational Resources Information Center
Bauer, Ben
2009-01-01
Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less…
Branching random walk with step size coming from a power law
NASA Astrophysics Data System (ADS)
Bhattacharya, Ayan; Subhra Hazra, Rajat; Roy, Parthanil
2015-09-01
In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.
THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.
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.
Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence
USDA-ARS?s Scientific Manuscript database
The binary power law (BPL) has been successfully used to characterize heterogeneity (over dispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial...
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.
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.
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
ERIC Educational Resources Information Center
Thelwall, Mike; Wilkinson, David
2003-01-01
Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)
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
Cioslowski, Jerzy
2010-12-21
Constituting the simplest generalization of spherical Coulomb crystals, assemblies of N equicharged particles confined by radial potentials proportional to the λth power of distance are amenable to rigorous analysis within the recently introduced shell model. Thanks to the power scaling of the confining potential and the resulting pruning property of the shell configurations (i.e., the lists of shell occupancies), the shell-model estimates of the energies and the mean radii of such assemblies at equilibrium geometries follow simple recursive formulas. The formulas greatly facilitate derivations of the first two leading terms in the large-N asymptotics of these estimates, which are given by power series in ξ(4/3) N(-2/3), where -(ξ/2) n(3/2) is the leading angular-correlation correction to the minimum energy of n electrons on the surface of a sphere with a unit radius (the solution of the Thomson problem). Although the scaled occupancies of the outermost shells conform to a universal scaling law, the actual filling of the shells tends to follow rather irregular patterns that vary strongly with λ. However, the number of shells K(N) for a given N decreases in general upon an increase in the power-law exponent, which is due to the (λ + 1)(2) ξ(2) dependence of shell capacities that roughly measure the maximum numbers of particles sustainable within individual shells. Several types of configuration transitions (i.e., the changes in the number of shells upon addition of one particle) are observed in the crystals with up to 10,000 particles and integer values of λ between 1 and 10, but the rule |K(N + 1)-K(N)| ≤ 1 is found to be strictly obeyed.
Earthquake cycle simulations with rate-and-state friction and power-law viscoelasticity
NASA Astrophysics Data System (ADS)
Allison, Kali L.; Dunham, Eric M.
2018-05-01
We simulate earthquake cycles with rate-and-state fault friction and off-fault power-law viscoelasticity for the classic 2D antiplane shear problem of a vertical, strike-slip plate boundary fault. We investigate the interaction between fault slip and bulk viscous flow with experimentally-based flow laws for quartz-diorite and olivine for the crust and mantle, respectively. Simulations using three linear geotherms (dT/dz = 20, 25, and 30 K/km) produce different deformation styles at depth, ranging from significant interseismic fault creep to purely bulk viscous flow. However, they have almost identical earthquake recurrence interval, nucleation depth, and down-dip coseismic slip limit. Despite these similarities, variations in the predicted surface deformation might permit discrimination of the deformation mechanism using geodetic observations. Additionally, in the 25 and 30 K/km simulations, the crust drags the mantle; the 20 K/km simulation also predicts this, except within 10 km of the fault where the reverse occurs. However, basal tractions play a minor role in the overall force balance of the lithosphere, at least for the flow laws used in our study. Therefore, the depth-integrated stress on the fault is balanced primarily by shear stress on vertical, fault-parallel planes. Because strain rates are higher directly below the fault than far from it, stresses are also higher. Thus, the upper crust far from the fault bears a substantial part of the tectonic load, resulting in unrealistically high stresses. In the real Earth, this might lead to distributed plastic deformation or formation of subparallel faults. Alternatively, fault pore pressures in excess of hydrostatic and/or weakening mechanisms such as grain size reduction and thermo-mechanical coupling could lower the strength of the ductile fault root in the lower crust and, concomitantly, off-fault upper crustal stresses.
Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise, and multifractality.
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.
PLNoise: a package for exact numerical simulation of power-law noises
NASA Astrophysics Data System (ADS)
Milotti, Edoardo
2006-08-01
Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1<β⩽1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v1_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B
NASA Astrophysics Data System (ADS)
Javidani, M.; Arreguin-Zavala, J.; Danovitch, J.; Tian, Y.; Brochu, M.
2017-04-01
This paper aims to study the manufacturing of the AlSi10Mg alloy with direct energy deposition (DED) process. Following fabrication, the macro- and microstructural evolution of the as-processed specimens was initially investigated using optical microscopy and scanning electron microscopy. Columnar dendritic structure was the dominant solidification feature of the deposit; nevertheless, detailed microstructural analysis revealed cellular morphology near the substrate and equiaxed dendrites at the top end of the deposit. Moreover, the microstructural morphology in the melt pool boundary of the deposit differed from the one in the core of the layers. The remaining porosity of the deposit was evaluated by Archimedes' principle and by image analysis of the polished surface. Crystallographic texture in the deposit was also assessed using electron backscatter diffraction and x-ray diffraction analysis. The dendrites were unidirectionally oriented at an angle of 80° to the substrate. EPMA line scans were performed to evaluate the compositional variation and elemental segregation in different locations. Eventually, microhardness (HV) tests were conducted in order to study the hardness gradient in the as-DED-processed specimen along the deposition direction. The presented results, which exhibited a deposit with an almost defect free structure, indicate that the DED process can suitable for the deposition of Al-Si-based alloys with a highly consolidated structure.
USDA-ARS?s Scientific Manuscript database
Empirical and mechanistic modeling indicate that aerially transmitted pathogens follow a power law, resulting in dispersive epidemic waves. The spread parameter (b) of the power law model, which defines the distance travelled by the epidemic wave front, has been found to be approximately 2 for sever...
Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock
NASA Astrophysics Data System (ADS)
Fareo, A. G.; Mason, D. P.
2016-06-01
Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.
NASA Astrophysics Data System (ADS)
Umansky, Moti; Weihs, Daphne
2012-08-01
parameters and quality of fit are provided. After all single trajectory time-averaged MSDs are fit, we obtain cutoffs from the user to categorize and segment the power laws into groups; cutoff are either in exponents of the power laws, time of appearance of the fits, or both together. The trajectories are sorted according to the cutoffs and the time- and ensemble-averaged MSD of each group is provided, with histograms of the distributions of the exponents in each group. The program then allows the user to generate new trajectory files with trajectories segmented according to the determined groups, for any further required analysis. Additional comments: README file giving the names and a brief description of all the files that make-up the package and clear instructions on the installation and execution of the program is included in the distribution package. Running time: On an i5 Windows 7 machine with 4 GB RAM the automated parts of the run (excluding data loading and user input) take less than 45 minutes to analyze and save all stages for an 844 trajectory file, including optional PDF save. Trajectory length did not affect run time (tested up to 3600 frames/trajectory), which was on average 3.2±0.4 seconds per trajectory.
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
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.
Focus-based filtering + clustering technique for power-law networks with small world phenomenon
NASA Astrophysics Data System (ADS)
Boutin, François; Thièvre, Jérôme; Hascoët, Mountaz
2006-01-01
Realistic interaction networks usually present two main properties: a power-law degree distribution and a small world behavior. Few nodes are linked to many nodes and adjacent nodes are likely to share common neighbors. Moreover, graph structure usually presents a dense core that is difficult to explore with classical filtering and clustering techniques. In this paper, we propose a new filtering technique accounting for a user-focus. This technique extracts a tree-like graph with also power-law degree distribution and small world behavior. Resulting structure is easily drawn with classical force-directed drawing algorithms. It is also quickly clustered and displayed into a multi-level silhouette tree (MuSi-Tree) from any user-focus. We built a new graph filtering + clustering + drawing API and report a case study.
Power law-based local search in spider monkey optimisation for lower order system modelling
NASA Astrophysics Data System (ADS)
Sharma, Ajay; Sharma, Harish; Bhargava, Annapurna; Sharma, Nirmala
2017-01-01
The nature-inspired algorithms (NIAs) have shown efficiency to solve many complex real-world optimisation problems. The efficiency of NIAs is measured by their ability to find adequate results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. This paper presents a solution for lower order system modelling using spider monkey optimisation (SMO) algorithm to obtain a better approximation for lower order systems and reflects almost original higher order system's characteristics. Further, a local search strategy, namely, power law-based local search is incorporated with SMO. The proposed strategy is named as power law-based local search in SMO (PLSMO). The efficiency, accuracy and reliability of the proposed algorithm is tested over 20 well-known benchmark functions. Then, the PLSMO algorithm is applied to solve the lower order system modelling problem.
Market reaction to a bid-ask spread change: A power-law relaxation dynamics
NASA Astrophysics Data System (ADS)
Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N.
2009-07-01
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.
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.
A Simple Power Law Governs Many Sensory Amplifications and Multisensory Enhancements.
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.
Slow domain reconfiguration causes power-law kinetics in a two-state enzyme.
Grossman-Haham, Iris; Rosenblum, Gabriel; Namani, Trishool; Hofmann, Hagen
2018-01-16
Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.
Numerical simulation of nanofluids based on power-law fluids with flow and heat transfer
NASA Astrophysics Data System (ADS)
Li, Lin; Jiang, Yongyue; Chen, Aixin
2017-04-01
In this paper, we investigate the heat transfer of nanofluids based on power-law fluids and movement of nanoparticles with the effect of thermophoresis in a rotating circular groove. The velocity of circular groove rotating is a constant and the temperature on the wall is kept to be zero all the time which is different from the temperature of nanofluids in the initial time. The effects of thermophoresis and Brownian diffusion are considered in temperature and concentration equations, and it is assumed that the thermal conductivity of nanofluids is a function of concentration of nanoparticles. Based on numerical results, it can be found that nanofluids improve the process of heat transfer than base fluids in a rotating circular groove. The enhancement of heat transfer increases as the power law index of base fluids decreases.
Power-Laws and Scaling in Finance: Empirical Evidence and Simple Models
NASA Astrophysics Data System (ADS)
Bouchaud, Jean-Philippe
We discuss several models that may explain the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are rather robust and suggest universality. However, many of the models that appear naturally (for example, to account for the distribution of wealth) contain some multiplicative noise, which generically leads to non universal exponents. Recent progress in the empirical study of the volatility suggests that the volatility results from some sort of multiplicative cascade. A convincing `microscopic' (i.e. trader based) model that explains this observation is however not yet available. We discuss a rather generic mechanism for long-ranged volatility correlations based on the idea that agents constantly switch between active and inactive strategies depending on their relative performance.
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.
Hypersonic aerodynamic characteristics of a family of power-law, wing body configurations
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1973-01-01
The configurations analyzed are half-axisymmetric, power-law bodies surmounted by thin, flat wings. The wing planform matches the body shock-wave shape. Analytic solutions of the hypersonic small disturbance equations form a basis for calculating the longitudinal aerodynamic characteristics. Boundary-layer displacement effects on the body and the wing upper surface are approximated. Skin friction is estimated by using compressible, laminar boundary-layer solutions. Good agreement was obtained with available experimental data for which the basic theoretical assumptions were satisfied. The method is used to estimate the effects of power-law, fineness ratio, and Mach number variations at full-scale conditions. The computer program is included.
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.
NASA Technical Reports Server (NTRS)
Raj, S. V.; Pharr, G. M.
1989-01-01
Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.
Mandel, Yael; Weissman, Amir; Schick, Revital; Barad, Lili; Novak, Atara; Meiry, Gideon; Goldberg, Stanislav; Lorber, Avraham; Rosen, Michael R; Itskovitz-Eldor, Joseph; Binah, Ofer
2012-02-21
The sinoatrial node is the main impulse-generating tissue in the heart. Atrioventricular conduction block and arrhythmias caused by sinoatrial node dysfunction are clinically important and generally treated with electronic pacemakers. Although an excellent solution, electronic pacemakers incorporate limitations that have stimulated research on biological pacing. To assess the suitability of potential biological pacemakers, we tested the hypothesis that the spontaneous electric activity of human embryonic stem cell-derived cardiomyocytes (hESC-CMs) and induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) exhibit beat rate variability and power-law behavior comparable to those of human sinoatrial node. We recorded extracellular electrograms from hESC-CMs and iPSC-CMs under stable conditions for up to 15 days. The beat rate time series of the spontaneous activity were examined in terms of their power spectral density and additional methods derived from nonlinear dynamics. The major findings were that the mean beat rate of hESC-CMs and iPSC-CMs was stable throughout the 15-day follow-up period and was similar in both cell types, that hESC-CMs and iPSC-CMs exhibited intrinsic beat rate variability and fractal behavior, and that isoproterenol increased and carbamylcholine decreased the beating rate in both hESC-CMs and iPSC-CMs. This is the first study demonstrating that hESC-CMs and iPSC-CMs exhibit beat rate variability and power-law behavior as in humans, thus supporting the potential capability of these cell sources to serve as biological pacemakers. Our ability to generate sinoatrial-compatible spontaneous cardiomyocytes from the patient's own hair (via keratinocyte-derived iPSCs), thus eliminating the critical need for immunosuppression, renders these myocytes an attractive cell source as biological pacemakers.
Huo, Yunlong; Choy, Jenny Susana; Wischgoll, Thomas; Luo, Tong; Teague, Shawn D; Bhatt, Deepak L; Kassab, Ghassan S
2013-04-06
Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length-volume scaling power law ( where L(c) and V(c) are crown length and volume) were found for both the high-fat and control groups (R(2) = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, K(LV), decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow-length scaling power law, however, was nearly unaffected by the positive remodelling. The length-volume and flow-length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. K(LV) < 18 in the length-volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans.
Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields
Steffen, J. H.; Baumbaugh, A.; Chou, A. S.
2010-12-31
We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Power-law distributions for a trapped ion interacting with a classical buffer gas.
DeVoe, Ralph G
2009-02-13
Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment.
DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K., E-mail: lzhao@fit.edu
2016-04-10
A double power law or a power law with exponential rollover at a few to tens of MeV nucleon{sup −1} of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochasticmore » approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon{sup −1} is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.« less
Logarithmic and power law input-output relations in sensory systems with fold-change detection.
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.
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
NASA Technical Reports Server (NTRS)
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
The power laws of violence against women: rescaling research and policies.
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.
Orbits in elementary, power-law galaxy bars - 1. Occurrence and role of single loops
NASA Astrophysics Data System (ADS)
Struck, Curtis
2018-05-01
Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit fits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second-order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighbourhood of perturbation solutions reveal zero or one actual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librating companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single-loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.
Q-Space Scattering Power Laws and the Interior Fields of Particles
2016-02-12
SECURITY CLASSIFICATION OF: This work studied the relationship between light scattered by particles of any shape and the interior field of that...Release; Distribution Unlimited UU UU UU UU 12-02-2016 7-Jul-2014 6-Apr-2015 Final Report: Q-space Scattering Power Laws and the Interior Fields of...the Army position, policy or decision, unless so designated by other documentation. 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S
The Power Laws of Violence against Women: Rescaling Research and Policies
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
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.
The Forbes 400, the Pareto power-law and efficient markets
NASA Astrophysics Data System (ADS)
Klass, O. S.; Biham, O.; Levy, M.; Malcai, O.; Solomon, S.
2007-01-01
Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.
Epitrochoid Power-Law Nozzle Rapid Prototype Build/Test Project (Briefing Charts)
2015-02-01
Production Approved for public release; distribution is unlimited. PA clearance # 15122. 4 Epitrochoid Power-Law Nozzle Build/Test Build on SpaceX ...Multiengine Approach SpaceX ) Approved for public release; distribution is unlimited. PA clearance # 15122. Engines: Merlin 1D on Falcon 9 v1.1 (Photo 5...to utilize features of high performance engines advances and the economies of scale of the multi-engine approach of SpaceX Falcon 9 – Rapid Prototype
Tippett, Michael K.; Cohen, Joel E.
2016-01-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from ‘outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954–2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210
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
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.
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.
NASA Astrophysics Data System (ADS)
Huang, M.; Wada, R.; Chen, Z.; Keutgen, T.; Kowalski, S.; Hagel, K.; Barbui, M.; Bonasera, A.; Bottosso, C.; Materna, T.; Natowitz, J. B.; Qin, L.; Rodrigues, M. R. D.; Sahu, P. K.; Schmidt, K. J.; Wang, J.
2010-11-01
Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, asym/T, extracted in previous work and that of the pairing term, ap/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I=N-Z value, the corrected yields of isotopes relative to the yield of C12 show a power law distribution Y(N,Z)/Y(12C)~A-τ in the mass range 1⩽A⩽30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted τ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be τprim=2.4±0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.
Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.
Zhao, Cunlu; Yang, Chun
2013-03-01
EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
A stability analysis of the power-law steady state of marine size spectra.
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.
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.
Power-law scaling in daily rainfall patterns and consequences in urban stream discharges
NASA Astrophysics Data System (ADS)
Park, Jeryang; Krueger, Elisabeth H.; Kim, Dongkyun; Rao, Suresh C.
2016-04-01
Poissonian rainfall has been frequently used for modelling stream discharge in a catchment at the daily scale. Generally, it is assumed that the daily rainfall depth is described by memoryless exponential distribution which is transformed to stream discharge, resulting in an analytical pdf for discharge [Gamma distribution]. While it is true that catchment hydrological filtering processes (censored by constant rate ET losses, and first-order recession) increases "memory", reflected in 1/f noise in discharge time series. Here, we show that for urban watersheds in South Korea: (1) the observation of daily rainfall depths follow power-law pdfs, and spectral slopes range between 0.2 ~ 0.4; and (2) the stream discharge pdfs have power-law tails. These observation results suggest that multiple hydro-climatic factors (e.g., non-stationarity of rainfall patterns) and hydrologic filtering (increasing impervious area; more complex urban drainage networks) influence the catchment hydrologic responses. We test the role of such factors using a parsimonious model, using different types of daily rainfall patterns (e.g., power-law distributed rainfall depth with Poisson distribution in its frequency) and urban settings to reproduce patterns similar to those observed in empirical records. Our results indicate that fractality in temporally up-scaled rainfall, and the consequences of large extreme events are preserved as high discharge events in urbanizing catchments. Implications of these results to modeling urban hydrologic responses and impacts on receiving waters are discussed.
Comment on "Time needed to board an airplane: a power law and the structure behind it".
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the "back-to-front" strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.
NASA Astrophysics Data System (ADS)
Chahtour, C.; Ben Hamed, H.; Beji, H.; Guizani, A.; Alimi, W.
2018-01-01
We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.
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.
Evidence for intermittency and a truncated power law from highly resolved aphid movement data.
Mashanova, Alla; Oliver, Tom H; Jansen, Vincent A A
2010-01-06
Power laws are increasingly used to describe animal movement. Despite this, the use of power laws has been criticized on both empirical and theoretical grounds, and alternative models based on extensions of conventional random walk theory (Brownian motion) have been suggested. In this paper, we analyse a large volume of data of aphid walking behaviour (65,068 data points), which provides a highly resolved dataset to investigate the pattern of movement. We show that aphid movement is intermittent--with alternations of a slow movement with frequent change of direction and a fast, relatively directed movement--and that the fast movement consists of two phases--a strongly directed phase that gradually changes into an uncorrelated random walk. By measuring the mean-squared displacement and the duration of non-stop movement episodes we found that both spatial and temporal aspects of aphid movement are best described using a truncated power law approach. We suggest that the observed spatial pattern arises from the duration of non-stop movement phases rather than from correlations in turning angles. We discuss the implications of these findings for interpreting movement data, such as distinguishing between movement and non-movement, and the effect of the range of data used in the analysis on the conclusions.
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.
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.
Dust-acoustic waves and stability in the permeating dusty plasma. II. Power-law distributions
Gong Jingyu; Du Jiulin; Liu Zhipeng
2012-08-15
The dust-acoustic waves and the stability theory for the permeating dusty plasma with power-law distributions are studied by using nonextensive q-statistics. In two limiting physical cases, when the thermal velocity of the flowing dusty plasma is much larger than, and much smaller than the phase velocity of the waves, we derived the dust-acoustic wave frequency, the instability growth rate, and the instability critical flowing velocity. As compared with the formulae obtained in part I [Gong et al., Phys. Plasmas 19, 043704 (2012)], all formulae of the present cases and the resulting plasma characteristics are q-dependent, and the power-law distribution ofmore » each plasma component of the permeating dusty plasma has a different q-parameter and thus has a different nonextensive effect. Further, we make numerical analyses of an example that a cometary plasma tail is passing through the interplanetary space dusty plasma and we show that these power-law distributions have significant effects on the plasma characteristics of this kind of plasma environment.« less
Mobility of power-law and Carreau fluids through fibrous media.
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.
NASA Astrophysics Data System (ADS)
Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.
2014-09-01
We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.
NASA Astrophysics Data System (ADS)
Kumar, Jagadish; Ananthakrishna, G.
2018-01-01
Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum
Kumar, Jagadish; Ananthakrishna, G
2018-01-01
Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum
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
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.
Tripathi, Arvind; Gupta, Ashutosh; Bagchi, Soumyojeet; Mishra, Lallan; Gautam, Abhina; Madhok, Riti
2016-04-01
To observe the effects of incorporating cyanoacrylate, epoxy resins, and gum arabic on the abrasion resistance of type IV gypsum die materials. Forty specimens were prepared and divided into four groups (10 specimens in each group), namely group A (control), group B (die stone mixed with cyanoacrylate), group C (die stone mixed with epoxy resin), group D (die stone mixed with gum arabic). All the specimens were subjected to abrasion testing, wear volume analysis, Fourier transform infrared spectroscopy (FT-IR), and scanning electron microscope (SEM) analysis. Abrasion testing showed maximum wear in the control group and minimum wear in the gum arabic group. Intergroup differences were statistically significant (p < 0.001). The largest mean difference was between control and gum arabic. The lowest was between cyanoacrylate and the control group. The mean wear volume was lowest in the gum arabic group (4.23 mm(3) ) and highest in the control group (6.78 mm(3) ). The FT-IR graphs of the gum arabic models showed the presence of CH2 , which is responsible for its binding activity. SEM revealed that the irregular particles of gum arabic display an interlocking arrangement. This jigsaw puzzle pattern results in stronger physical bond formation. Observations from this study showed that the addition of gum arabic increases resistance to abrasion in type IV gypsum. Cyanoacrylates are good adhesives as well, but a major drawback is that they have very low resistance to chemical action with water and physical actions such as sunlight. Epoxy resins are powerful adhesives, but they attain their full efficiency when cured with heat. Cyanoacrylate and epoxy resin displayed poor physical bonding, primarily because of inhomogeneity. © 2015 by the American College of Prosthodontists.
New version of PLNoise: a package for exact numerical simulation of power-law noises
NASA Astrophysics Data System (ADS)
Milotti, Edoardo
2007-08-01
In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0<α⩽2. Here I extend the algorithm to generate 1/f noises with 2<α⩽4 (black noises). The method is exact in the sense that it produces a sampled process with a theoretically guaranteed range-limited power-law spectrum for any arbitrary sequence of sampling intervals, i.e. the sampling times may be unevenly spaced. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v2_0.html Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press
CT-based Diagnosis of Diffuse Coronary Artery Disease on the Basis of Scaling Power Laws
Huo, Yunlong; Wischgoll, Thomas; Choy, Jenny Susana; Sola, Srikanth; Navia, Jose L.; Teague, Shawn D.; Bhatt, Deepak L.
2013-01-01
Purpose: To provide proof of concept for a diagnostic method to assess diffuse coronary artery disease (CAD) on the basis of coronary computed tomography (CT) angiography. Materials and Methods: The study was approved by the Cleveland Clinic Institutional Review Board, and all subjects gave informed consent. Morphometric data from the epicardial coronary artery tree, determined with CT angiography in 120 subjects (89 patients with metabolic syndrome and 31 age- and sex-matched control subjects) were analyzed on the basis of the scaling power law. Results obtained in patients with metabolic syndrome and control subjects were compared statistically. Results: The mean lumen cross-sectional area (ie, lumen cross-sectional area averaged over each vessel of an epicardial coronary artery tree) and sum of intravascular volume in patients with metabolic syndrome (0.039 cm2 ± 0.015 [standard deviation] and 2.71 cm3 ± 1.75, respectively) were significantly less than those in control subjects (0.054 cm2± 0.015 and 3.29 cm3± 1.77, respectively; P < .05). The length-volume power law showed coefficients of 27.0 cm−4/3 ± 9.0 (R2 = 0.91 ± 0.08) for patients with metabolic syndrome and 19.9 cm−4/3 ± 4.3 (R2 = 0.92 ± 0.07) for control subjects (P < .05). The probability frequency shows that more than 65% of patients with metabolic syndrome had a coefficient of 23 or more for the length-volume scaling power law, whereas approximately 90% of the control subjects had a coefficient of less than 23. Conclusion: The retrospective scaling analysis provides a quantitative rationale for diagnosis of diffuse CAD. © RSNA, 2013 Supplemental material: http://radiology.rsna.org/lookup/suppl/doi:10.1148/radiol.13122181/-/DC1 PMID:23616633
Power laws in microrheology experiments on living cells: Comparative analysis and modeling
NASA Astrophysics Data System (ADS)
Balland, Martial; Desprat, Nicolas; Icard, Delphine; Féréol, Sophie; Asnacios, Atef; Browaeys, Julien; Hénon, Sylvie; Gallet, François
2006-08-01
We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a microbead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient Ge(ω) is retrieved. Both J(t) and Ge(ω) exhibit power law behaviors: J(t)=A0(t/t0)α and ∣Ge(ω)∣=G0(ω/ω0)α , with the same exponent α≈0.2 . This power law behavior is very robust; α is distributed over a narrow range, and shows almost no dependence on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors A0 and G0 appear very sensitive to these parameters. Whereas the exponents α are normally distributed over the cell population, the prefactors A0 and G0 follow a log-normal repartition. These results are compared with other data published in the literature. We propose a global interpretation, based on a semiphenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: τm˜1000s .
Power laws in microrheology experiments on living cells: Comparative analysis and modeling.
Balland, Martial; Desprat, Nicolas; Icard, Delphine; Féréol, Sophie; Asnacios, Atef; Browaeys, Julien; Hénon, Sylvie; Gallet, François
2006-08-01
We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a microbead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient Ge(omega) is retrieved. Both J(t) and Ge(omega) exhibit power law behaviors: J(t) = A0(t/t0)alpha and absolute value (Ge(omega)) = G0(omega/omega0)alpha, with the same exponent alpha approximately 0.2. This power law behavior is very robust; alpha is distributed over a narrow range, and shows almost no dependence on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors A0 and G0 appear very sensitive to these parameters. Whereas the exponents alpha are normally distributed over the cell population, the prefactors A0 and G0 follow a log-normal repartition. These results are compared with other data published in the literature. We propose a global interpretation, based on a semiphenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: tau(m) approximately 1000 s.
Effects of diversity and procrastination in priority queuing theory: The different power law regimes
NASA Astrophysics Data System (ADS)
Saichev, A.; Sornette, D.
2010-01-01
Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law ˜1/tα with 0<α≤1 over a time scale of years. We present a simple model for this persistence phenomenon, framed within the standard priority queuing theory, of a target task which has the lowest priority compared to all other tasks that flow on the computer of an individual. We identify a “time deficit” control parameter β and a bifurcation to a regime where there is a nonzero probability for the target task to never be completed. The distribution of waiting time T until the completion of the target task has the power law tail ˜1/t1/2 , resulting from a first-passage solution of an equivalent Wiener process. Taking into account a diversity of time deficit parameters in a population of individuals, the power law tail is changed into 1/tα , with αɛ(0.5,∞) , including the well-known case 1/t . We also study the effect of “procrastination,” defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks. This regime provides an explanation for even slower apparent decay and longer persistence.
Power-Law Modeling of Cancer Cell Fates Driven by Signaling Data to Reveal Drug Effects
Zhang, Fan; Wu, Min; Kwoh, Chee Keong; Zheng, Jie
2016-01-01
Extracellular signals are captured and transmitted by signaling proteins inside a cell. An important type of cellular responses to the signals is the cell fate decision, e.g., apoptosis. However, the underlying mechanisms of cell fate regulation are still unclear, thus comprehensive and detailed kinetic models are not yet available. Alternatively, data-driven models are promising to bridge signaling data with the phenotypic measurements of cell fates. The traditional linear model for data-driven modeling of signaling pathways has its limitations because it assumes that the a cell fate is proportional to the activities of signaling proteins, which is unlikely in the complex biological systems. Therefore, we propose a power-law model to relate the activities of all the measured signaling proteins to the probabilities of cell fates. In our experiments, we compared our nonlinear power-law model with the linear model on three cancer datasets with phosphoproteomics and cell fate measurements, which demonstrated that the nonlinear model has superior performance on cell fates prediction. By in silico simulation of virtual protein knock-down, the proposed model is able to reveal drug effects which can complement traditional approaches such as binding affinity analysis. Moreover, our model is able to capture cell line specific information to distinguish one cell line from another in cell fate prediction. Our results show that the power-law data-driven model is able to perform better in cell fate prediction and provide more insights into the signaling pathways for cancer cell fates than the linear model. PMID:27764199
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.
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.
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.
Laboratory constraints on chameleon dark energy and power-law fields
Steffen, Jason H.; /Fermilab; Upadhye, Amol
2010-10-01
We report results from the GammeV Chameleon Afterglow Search - a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
NASA Astrophysics Data System (ADS)
Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco
2015-06-01
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps.
Grossmann, S; Holthaus, M
1997-11-10
After discussing the idea underlying the Maxwell's Demon ensemble, we employ this ensemble for calculating fluctuations of ideal Bose gas condensates in traps with power-law single-particle energy spectra. Two essentially different cases have to be distinguished. If the heat capacity is continuous at the condensation point, the fluctuations of the number of condensate particles vanish linearly with temperature, independent of the trap characteristics. In this case, microcanonical and canonical fluctuations are practically indistinguishable. If the heat capacity is discontinuous, the fluctuations vanish algebraically with temperature, with an exponent determined by the trap, and the micro-canonical fluctuations are lower than their canonical counterparts.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
Bakalis, Evangelos, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it
2015-06-07
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
Effects of Power-Law Plasticity on Deformation Fields underneath Vickers Indenter
NASA Astrophysics Data System (ADS)
Chollacoop, Nuwong; Srikant, Gollapudi; Ramamurty, Upadrasta
The effects of power-law plasticity (yield strength σy and strain hardening exponent n) on the plastic strain distribution underneath a Vickers indenter was explicitly investigated by recourse to macro- and micro-indentation experiments on heat-treated Al-Zn-Mg alloy. With carefully designed aging profile, Al alloy can achieve similar σy with different n, and vice versa. Using the Vickers tip, the samples were macro-indented, sectioned and micro-indented to construct the sub-surface strain distribution. Thus, the effects of σy and n on stain distribution underneath Vickers indenter were revealed.
Pressure driven laminar flow of a power-law fluid in a T-channel
NASA Astrophysics Data System (ADS)
Dyakova, O. A.; Frolov, O. Yu
2017-10-01
Planar flow of a non-Newtonian fluid in a T-channel is investigated. The viscosity is determined by the Ostwald-de Waele power law. Motion of the fluid is caused by pressure drop given in boundary sections of the T-channel. On the solid walls, the no slip boundary condition is used. The problem is numerically solved with using a finite difference method based on the SIMPLE procedure. As a result of this study, characteristic flow regimes have been found. Influence of main parameters on the flow pattern has been demonstrated. Criteria dependences describing basic characteristics of the flow under conditions of the present work have been shown.
Highly excited bound-state resonances of short-range inverse power-law potentials
NASA Astrophysics Data System (ADS)
Hod, Shahar
2017-11-01
We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form V(r)=-β _n r^{-n} with n>2. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius R, we derive a compact analytical formula for the threshold energy E^{ {max}}_l=E^{ {max}}_l(n,β _n,R), which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.
NASA Astrophysics Data System (ADS)
Mercan, Kadir; Demir, Çiǧdem; Civalek, Ömer
2016-01-01
In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.
Power law expansion of the early universe for a V (a) = kan potential
NASA Astrophysics Data System (ADS)
Freitas, Augusto S.
2018-01-01
In a recent paper, He, Gao and Cai [Phys. Rev. D 89, 083510 (2014)], found a rigorous proof, based on analytical solutions of the Wheeler-DeWitt (WDWE) equation, of the spontaneous creation of the universe from nothing. The solutions were obtained from a classical potential V = ka2, where a is the scale factor. In this paper, we present a complementary (to that of He, Gao and Cai) solution to the WDWE equation with V = kan. I have found an exponential expansion of the true vacuum bubble for all scenarios. In all scenarios, we found a power law behavior of the scale factor result which is in agreement with another studies.
Unification of small and large time scales for biological evolution: deviations from power law.
Chowdhury, Debashish; Stauffer, Dietrich; Kunwar, Ambarish
2003-02-14
We develop a unified model that describes both "micro" and "macro" evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the "microevolution" over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the "macroevolution" over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.
Hoogenboom, Jacob P; van Dijk, Erik M H P; Hernando, Jordi; van Hulst, Niek F; García-Parajó, María F
2005-08-26
We exploit the strong excitonic coupling in a superradiant trimer molecule to distinguish between long-lived collective dark states and photobleaching events. The population and depopulation kinetics of the dark states in a single molecule follow power-law statistics over 5 orders of magnitude in time. This result is consistent with the formation of a radical unit via electron tunneling to a time-varying distribution of trapping sites in the surrounding polymer matrix. We furthermore demonstrate that this radicalization process forms the dominant pathway for molecular photobleaching.
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
Power-law statistics of neurophysiological processes analyzed using short signals
NASA Astrophysics Data System (ADS)
Pavlova, Olga N.; Runnova, Anastasiya E.; Pavlov, Alexey N.
2018-04-01
We discuss the problem of quantifying power-law statistics of complex processes from short signals. Based on the analysis of electroencephalograms (EEG) we compare three interrelated approaches which enable characterization of the power spectral density (PSD) and show that an application of the detrended fluctuation analysis (DFA) or the wavelet-transform modulus maxima (WTMM) method represents a useful way of indirect characterization of the PSD features from short data sets. We conclude that despite DFA- and WTMM-based measures can be obtained from the estimated PSD, these tools outperform the standard spectral analysis when characterization of the analyzed regime should be provided based on a very limited amount of data.
Complex motion of a vehicle through a series of signals controlled by power-law phase
NASA Astrophysics Data System (ADS)
Nagatani, Takashi
2017-07-01
We study the dynamic motion of a vehicle moving through the series of traffic signals controlled by the position-dependent phase of power law. All signals are controlled by both cycle time and position-dependent phase. The dynamic model of the vehicular motion is described in terms of the nonlinear map. The vehicular motion varies in a complex manner by varying cycle time for various values of the power of the position-dependent phase. The vehicle displays the periodic motion with a long cycle for the integer power of the phase, while the vehicular motion exhibits the very complex behavior for the non-integer power of the phase.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; ...
2015-12-30
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron–positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power lawmore » $${\\gamma }^{-\\alpha }$$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.« less
Power-law scaling in Bénard-Marangoni convection at large Prandtl numbers
NASA Astrophysics Data System (ADS)
Boeck, Thomas; Thess, André
2001-08-01
Bénard-Marangoni convection at large Prandtl numbers is found to exhibit steady (nonturbulent) behavior in numerical experiments over a very wide range of Marangoni numbers Ma far away from the primary instability threshold. A phenomenological theory, taking into account the different character of thermal boundary layers at the bottom and at the free surface, is developed. It predicts a power-law scaling for the nondimensional velocity (Peclet number) and heat flux (Nusselt number) of the form Pe~Ma2/3, Nu~Ma2/9. This prediction is in good agreement with two-dimensional direct numerical simulations up to Ma=3.2×105.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane.
Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco
2015-06-07
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
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.
Stable target opinion through power-law bias in information exchange.
Datta, Amitava
2018-04-01
We study a model of binary decision making when a certain population of agents is initially seeded with two different opinions, "+" and "-," with fractions p_{1} and p_{2}, respectively, p_{1}+p_{2}=1. Individuals can reverse their initial opinion only once based on this information exchange. We study this model on a completely connected network, where any pair of agents can exchange information, and a two-dimensional square lattice with periodic boundary conditions, where information exchange is possible only between the nearest neighbors. We propose a model in which each agent maintains two counters of opposite opinions and accepts opinions of other agents with a power-law bias until a threshold is reached, when they fix their final opinion. Our model is inspired by the study of negativity bias and positive-negative asymmetry, which has been known in the psychology literature for a long time. Our model can achieve a stable intermediate mix of positive and negative opinions in a population. In particular, we show that it is possible to achieve close to any fraction p_{3}, 0≤p_{3}≤1, of "-" opinion starting from an initial fraction p_{1} of "-" opinion by applying a bias through adjusting the power-law exponent of p_{3}.
Interplay of ICP and IXP over the Internet with power-law features
NASA Astrophysics Data System (ADS)
Fan, Zhongyan; Tang, Wallace Kit-Sang
The Internet is the largest artificial network consisting of billions of IP devices, managed by tens of thousands of autonomous systems (ASes). Due to its importance, the Internet has received much attention and its topological features, mainly in AS-level, have been widely explored from the complex network perspective. However, most of the previous studies assume a homogeneous model in which nodes are indistinguishable in nature. It may be good for a general study of topological structure, but unfortunately it fails to reflect the functionality. The Internet ecology is in fact heterogeneous and highly complex. It consists of various elements such as Internet Exchange Points (IXPs), Internet Content Providers (ICPs), and normal Autonomous System (ASes), realizing different roles in the Internet. In this paper, we propose level-structured network models for investigating how ICP performs under the AS-topology with power-law features and how IXP enhances its performance from a complex network perspective. Based on real data, our results reveal that the power-law nature of the Internet facilitates content delivery not only in efficiency but also in path redundancy. Moreover, the proposed multi-level framework is able to clearly illustrate the significant benefits gained by ICP from IXP peerings.
“Slimming” of power-law tails by increasing market returns
NASA Astrophysics Data System (ADS)
Sornette, D.
2002-06-01
We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r> rδ corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power-law exponent and thus the thinner is the tail of the distribution of price returns.
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.
Viscous-elastic dynamics of power-law fluids within an elastic cylinder
NASA Astrophysics Data System (ADS)
Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.
2017-07-01
In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.
NASA Astrophysics Data System (ADS)
Desplentere, Frederik; Six, Wim; Bonte, Hilde; Debrabandere, Eric
2013-04-01
In predictive engineering for polymer processes, the proper prediction of material microstructure from known processing conditions and constituent material properties is a critical step forward properly predicting bulk properties in the finished composite. Operating within the context of long-fiber thermoplastics (LFT, length > 15mm) this investigation concentrates on the influence of the power law index on the final fiber length distribution within the injection molded part. To realize this, the Autodesk Simulation Moldflow Insight Scandium 2013 software has been used. In this software, a fiber breakage algorithm is available from this release on. Using virtual material data with realistic viscosity levels allows to separate the influence of the power law index on the fiber breakage from the other material and process parameters. Applying standard settings for the fiber breakage parameters results in an obvious influence on the fiber length distribution through the thickness of the part and also as function of position in the part. Finally, the influence of the shear rate constant within the fiber breakage model has been investigated illustrating the possibility to fit the virtual fiber length distribution to the possible experimentally available data.
Stable target opinion through power-law bias in information exchange
NASA Astrophysics Data System (ADS)
Datta, Amitava
2018-04-01
We study a model of binary decision making when a certain population of agents is initially seeded with two different opinions, "+" and "-," with fractions p1 and p2, respectively, p1+p2=1 . Individuals can reverse their initial opinion only once based on this information exchange. We study this model on a completely connected network, where any pair of agents can exchange information, and a two-dimensional square lattice with periodic boundary conditions, where information exchange is possible only between the nearest neighbors. We propose a model in which each agent maintains two counters of opposite opinions and accepts opinions of other agents with a power-law bias until a threshold is reached, when they fix their final opinion. Our model is inspired by the study of negativity bias and positive-negative asymmetry, which has been known in the psychology literature for a long time. Our model can achieve a stable intermediate mix of positive and negative opinions in a population. In particular, we show that it is possible to achieve close to any fraction p3, 0 ≤p3≤1 , of "-" opinion starting from an initial fraction p1 of "-" opinion by applying a bias through adjusting the power-law exponent of p3.
Nonuniversal power law scaling in the probability distribution of scientific citations
Peterson, George J.; Pressé, Steve; Dill, Ken A.
2010-01-01
We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations (“classics”) are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The “tipping point” at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975–1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited. PMID:20805513
NASA Astrophysics Data System (ADS)
Hong, S. Lee; Bodfish, James W.; Newell, Karl M.
2006-03-01
We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.
Nonlinear and linear wave equations for propagation in media with frequency power law losses
NASA Astrophysics Data System (ADS)
Szabo, Thomas L.
2003-10-01
The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.
NASA Astrophysics Data System (ADS)
Simakin, A.; Ghassemi, A.
2005-03-01
A poroviscoelastic constitutive model is developed and used to study coupled rock deformation and fluid flow. The model allows the relaxation of both shear and symmetric components of the effective stress. Experimental results are usually interpreted in terms of the power law viscous material. However, in this work the effect of strain damage on viscosity is considered by treating the viscosity as a dynamic time-dependent parameter that varies proportionally to the second invariant of the strain rate. Healing is also taken into account so that the dynamic power law viscosity has a constant asymptotic at a given strain rate. The theoretical model is implemented in a finite element (FE) formulation that couples fluid flow and mechanical equilibrium equations. The FE method is applied to numerically study the triaxial compression of partially melted rocks at elevated PT conditions. It is found that the numerically calculated stress-strain curves demonstrate maxima similar to those observed in laboratory experiments. Also, the computed pattern of melt redistribution and strain localization at the contact between the rock sample and a stiff spacer is qualitatively similar to the experimental observations. The results also indicate that the matrix sensitivity to damage affects the scale of strain localization and melt redistribution.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Transition from Exponential to Power Law Income Distributions in a Chaotic Market
NASA Astrophysics Data System (ADS)
Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.
So You Think the Crab is Described by a Power-Law Spectrum
NASA Technical Reports Server (NTRS)
Weisskopf, Martin C.
2008-01-01
X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.
Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales
NASA Technical Reports Server (NTRS)
Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.
2006-01-01
The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.
Duality symmetry and power-law fading of frustration in a quantum multiconnected superconductor
Sun, S.N.; Ralston, J.P.
1991-03-01
We generalize the Alexander--de Gennes equations to a new system of superconducting-wire networks, allowing for variation of the cross-sectional area of wires. The generalized equations are solved for a square lattice of different cross-sectional-area ratios {lambda} in the {ital x} and {ital y} directions. A symmetry of {lambda}{r arrow}1/{lambda} is related to the Aubry-Andre duality and an obvious geometric property. We find that even a slight geometric asymmetry can soften the fine structure of the magnetic phase boundary considerably. We obtain a power-law dependence on the parameter {lambda} as {lambda}{r arrow}{infinity} and {lambda}{r arrow}0. For a finite-area ratio {lambda}, wemore » speculate that a simple analytic fit incorporating the dual symmetry is close to the exact nonperturbative behavior. The system is also related analytically to a recent study of Hu and Chen, which revealed a power-law behavior for a rectangular lattice.« less
The US business cycle: power law scaling for interacting units with complex internal structure
NASA Astrophysics Data System (ADS)
Ormerod, Paul
2002-11-01
In the social sciences, there is increasing evidence of the existence of power law distributions. The distribution of recessions in capitalist economies has recently been shown to follow such a distribution. The preferred explanation for this is self-organised criticality. Gene Stanley and colleagues propose an alternative, namely that power law scaling can arise from the interplay between random multiplicative growth and the complex structure of the units composing the system. This paper offers a parsimonious model of the US business cycle based on similar principles. The business cycle, along with long-term growth, is one of the two features which distinguishes capitalism from all previously existing societies. Yet, economics lacks a satisfactory theory of the cycle. The source of cycles is posited in economic theory to be a series of random shocks which are external to the system. In this model, the cycle is an internal feature of the system, arising from the level of industrial concentration of the agents and the interactions between them. The model-in contrast to existing economic theories of the cycle-accounts for the key features of output growth in the US business cycle in the 20th century.
Underestimating extreme events in power-law behavior due to machine-dependent cutoffs
NASA Astrophysics Data System (ADS)
Radicchi, Filippo
2014-11-01
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subject to severe machine-dependent limitations. As a result, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, which are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies, they also pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.
Birth and death of protein domains: A simple model of evolution explains power law behavior
Karev, Georgy P; Wolf, Yuri I; Rzhetsky, Andrey Y; Berezovskaya, Faina S; Koonin, Eugene V
2002-01-01
Background Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. Results A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, are considered
Birth and death of protein domains: a simple model of evolution explains power law behavior.
Karev, Georgy P; Wolf, Yuri I; Rzhetsky, Andrey Y; Berezovskaya, Faina S; Koonin, Eugene V
2002-10-14
Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, are considered in details and the
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.
Listing triangles in expected linear time on a class of power law graphs.
Nordman, Daniel J.; Wilson, Alyson G.; Phillips, Cynthia Ann
Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysismore » for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically
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
Akiba, M., E-mail: akiba@nict.go.jp; Tsujino, K.
This paper offers a theoretical explanation of the temperature and temporal dependencies of transient dark count rates (DCRs) measured for a linear-mode silicon avalanche photodiode (APD) and the dependencies of afterpulsing that were measured in Geiger-mode Si and InGaAs/InP APDs. The temporal dependencies exhibit power-law behavior, at least to some extent. For the transient DCR, the value of the DCR for a given time period increases with decreases in temperature, while the power-law behavior remains unchanged. The transient DCR is attributed to electron emissions from traps in the multiplication layer of the APD with a high electric field, and itsmore » temporal dependence is explained by a continuous change in the electron emission rate as a function of the electric field strength. The electron emission rate is calculated using a quantum model for phonon-assisted tunnel emission. We applied the theory to the temporal dependence of afterpulsing that was measured for Si and InGaAs/InP APDs. The power-law temporal dependence is attributed to the power-law function of the electron emission rate from the traps as a function of their position across the p–n junction of the APD. Deviations from the power-law temporal dependence can be derived from the upper and lower limits of the electric field strength.« less
NASA Astrophysics Data System (ADS)
Chakraborty, Ahana; Sensarma, Rajdeep
2018-03-01
The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.
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.
A two-parameter family of double-power-law biorthonormal potential-density expansions
NASA Astrophysics Data System (ADS)
Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn
2018-05-01
We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.
Perihelion precession from power law central force and magnetic-like force
NASA Astrophysics Data System (ADS)
Xu, Feng
2011-04-01
By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury’s 43”/century is reproduced, and 2) spherically distributed dark matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.
Perihelion precession from power law central force and magnetic-like force
Xu Feng
2011-04-15
By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury's 43''/century is reproduced, and 2) spherically distributed darkmore » matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.« less
NASA Technical Reports Server (NTRS)
Choi, Sung R.; Gyekenyesi, John P.
2002-01-01
The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.
A power-law coupled three-form dark energy model
NASA Astrophysics Data System (ADS)
Yao, Yan-Hong; Yan, Yang-Jie; Meng, Xin-He
2018-02-01
We consider a field theory model of coupled dark energy which treats dark energy as a three-form field and dark matter as a spinor field. By assuming the effective mass of dark matter as a power-law function of the three-form field and neglecting the potential term of dark energy, we obtain three solutions of the autonomous system of evolution equations, including a de Sitter attractor, a tracking solution and an approximate solution. To understand the strength of the coupling, we confront the model with the latest Type Ia Supernova, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation observations, with the conclusion that the combination of these three databases marginalized over the present dark matter density parameter Ω _{m0} and the present three-form field κ X0 gives stringent constraints on the coupling constant, - 0.017< λ <0.047 (2σ confidence level), by which we present the model's applicable parameter range.
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 two-parameter family of double-power-law biorthonormal potential-density expansions
NASA Astrophysics Data System (ADS)
Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn
2018-07-01
We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.
Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.
Namikawa, Jun
2005-08-01
Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.
Slow synaptic dynamics in a network: From exponential to power-law forgetting
NASA Astrophysics Data System (ADS)
Luck, J. M.; Mehta, A.
2014-09-01
We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√t relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.
A two-parameter family of double-power-law biorthonormal potential-density expansions
NASA Astrophysics Data System (ADS)
Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn
2018-05-01
We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.
NASA Astrophysics Data System (ADS)
Makinde, O. D.
2014-12-01
In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.
Effect of acoustic coupling on power-law flame acceleration in spherical confinement
NASA Astrophysics Data System (ADS)
Akkerman, V'yacheslav; Law, Chung K.
2013-01-01
A model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach number flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into an existing theory of self-similar flame acceleration in free space [V. Akkerman, C. K. Law, and V. Bychkov, "Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering," Phys. Rev. E 83, 026305 (2011)], 10.1103/PhysRevE.83.026305. Being reflected from the chamber wall, flame-generated acoustics interact with the flamefront and the attendant hydrodynamic flamefront cellular instability. This in turn affects the subsequent flame morphology and propagation speed. It is shown that the acoustics modify the power-law flame acceleration, concomitantly facilitating or inhibiting the transition to detonation in confinement, which allows reconciliation of a discrepancy in experimental measurements of different groups.
A comment on power-law inflation with a dark radiation component
NASA Astrophysics Data System (ADS)
Di Valentino, Eleonora; Bouchet, François R.
2016-10-01
Tram et al. 2016 recently pointed out in [1] that power-law inflation in presence of a dark radiation component may relieve the 3.3 σ tension which exists within standard ΛCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) [2] and the value derived from CMB anisotropy data [3] by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the σ8 tension between the Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from Planck HFI data [4] are included in the analysis, the H0 tension reappears and this scenario looses appeal.
Power law of shear viscosity in Einstein-Maxwell-Dilaton-Axion model
NASA Astrophysics Data System (ADS)
Ling, Yi; Xian, Zhuoyu; Zhou, Zhenhua
2017-02-01
We construct charged black hole solutions with hyperscaling violation in the infrared (IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is verified numerically at low temperature T, namely, η/s ˜ T κ , where the values of exponent κ coincide with the analytical results. We also find that the exponent κ is not affected by irrelevant current, but is reduced by the relevant current. Supported by National Natural Science Foundation of China (11275208, 11575195), Opening Project of Shanghai Key Laboratory of High Temperature Superconductors (14DZ2260700) and Jiangxi Young Scientists (JingGang Star) Program and 555 Talent Project of Jiangxi Province
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.
Power law X- and gamma-ray emission from relativistic thermal plasmas
NASA Technical Reports Server (NTRS)
Zdziarski, A. A.
1984-01-01
Pair equilibrium in thermal plasmas emitting power law photon spectra by repeated Compton scatterings of a soft photon source active galactic nuclei was studied. Dependence of the spectral index on optical thickness and on temperature of the plasma is discussed. The equation for pair equilibrium is solved for the maximum steady luminosity. Analytical solutions for the subrelativistic region, and for the ultrarelativistic region are found. In the transrelativistic region the solutions are expressed by single integrals over the pair production cross sections, performed numerically. The constraints on soft photon source imposed by the condition that the soft photon flux cannot exceed the black-body flux are considered. For the Comptonized synchrotron radiation model a relation between magnetic field strength and output luminosity is found.
On the Measurement of Power Law Creep Parameters from Instrumented Indentation
NASA Astrophysics Data System (ADS)
Sudharshan Phani, P.; Oliver, W. C.; Pharr, G. M.
2017-11-01
Recently the measurement of the creep response of materials at small scales has received renewed interest largely because the equipment required to perform high-temperature nanomechanical testing has become available to an increasing number of researchers. Despite that increased access, there remain several significant experimental and modeling challenges in small-scale mechanical testing at elevated temperatures that are as yet unresolved. In this regard, relating the creep response observed with high-temperature instrumented indentation experiments to macroscopic uniaxial creep response is of great practical value. In this review, we present an overview of various methods currently being used to measure creep with instrumented indentation, with a focus on geometrically self-similar indenters, and their relative merits and demerits from an experimental perspective. A comparison of the various methods to use those instrumented indentation results to predict the uniaxial power law creep response of a wide range of materials will be presented to assess their validity.
NASA Astrophysics Data System (ADS)
Fan, Qingju; Wu, Yonghong
2015-08-01
In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.
Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons
Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves
2009-01-01
Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of Vm activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the Vm reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the “effective” connectivity responsible for the dynamical signature of the population signals measured
Undersampling power-law size distributions: effect on the assessment of extreme natural hazards
Geist, Eric L.; Parsons, Thomas E.
2014-01-01
The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and by attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historic data.
Musical rhythm spectra from Bach to Joplin obey a 1/f power law.
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.
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
El Boustani, Sami; Marre, Olivier; Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves
2009-09-01
Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m) activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m) reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the "effective" connectivity responsible for the dynamical signature of the population signals measured
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.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
NASA Technical Reports Server (NTRS)
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
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.
NASA Astrophysics Data System (ADS)
Sachs, M. K.; Yoder, M. R.; Turcotte, D. L.; Rundle, J. B.; Malamud, B. D.
2012-05-01
Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.
GPU accelerated simulations of three-dimensional flow of power-law fluids in a driven cube
NASA Astrophysics Data System (ADS)
Jin, K.; Vanka, S. P.; Agarwal, R. K.; Thomas, B. G.
2017-01-01
Newtonian fluid flow in two- and three-dimensional cavities with a moving wall has been studied extensively in a number of previous works. However, relatively a fewer number of studies have considered the motion of non-Newtonian fluids such as shear thinning and shear thickening power law fluids. In this paper, we have simulated the three-dimensional, non-Newtonian flow of a power law fluid in a cubic cavity driven by shear from the top wall. We have used an in-house developed fractional step code, implemented on a Graphics Processor Unit. Three Reynolds numbers have been studied with power law index set to 0.5, 1.0 and 1.5. The flow patterns, viscosity distributions and velocity profiles are presented for Reynolds numbers of 100, 400 and 1000. All three Reynolds numbers are found to yield steady state flows. Tabulated values of velocity are given for the nine cases studied, including the Newtonian cases.
A growth model for directed complex networks with power-law shape in the out-degree distribution
Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.
2015-01-01
Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141
A simple marriage model for the power-law behaviour in the frequency distributions of family names
NASA Astrophysics Data System (ADS)
Wu, Hao-Yun; Chou, Chung-I.; Tseng, Jie-Jun
2011-01-01
In many countries, the frequency distributions of family names are found to decay as a power law with an exponent ranging from 1.0 to 2.2. In this work, we propose a simple marriage model which can reproduce this power-law behaviour. Our model, based on the evolution of families, consists of the growth of big families and the formation of new families. Preliminary results from the model show that the name distributions are in good agreement with empirical data from Taiwan and Norway.
Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements
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
Power-law modulation of the scalar power spectrum from a heavy field with a monomial potential
NASA Astrophysics Data System (ADS)
Huang, Qing-Guo; Pi, Shi
2018-04-01
The effects of heavy fields modulate the scalar power spectrum during inflation. We analytically calculate the modulations of the scalar power spectrum from a heavy field with a separable monomial potential, i.e. V(phi)~ phin. In general the modulation is characterized by a power-law oscillation which is reduced to the logarithmic oscillation in the case of n=2.
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.
Interrelation of soft and hard X-ray emissions during solar flares. I - Observations
NASA Technical Reports Server (NTRS)
Winglee, R. M.; Kiplinger, A. L.; Zarro, D. M.; Dulk, G. A.; Lemen, J. R.
1991-01-01
The interrelation between the acceleration and heating of electrons and ions during impulsive solar flares is determined on the basis of simulataneous observations of hard and soft X-ray emission from the Solar Maximum Mission at high time resolution (6 s). For all the flares, the hard X-rays are found to have a power-law spectrum which breaks down during the rise phase and beginning of the decay phase. After that, the spectrum changes to either a single power law or a power law that breaks up at high energies. The characteristics of the soft X-ray are found to depend on the flare position. It is suggested that small-scale quasi-static electric fields are important for determining the acceleration of the X-ray-producing electrons and the outflowing chromospheric ions.
Temperature fluctuation in Rayleigh-Bénard convection: Logarithmic vs power-law
NASA Astrophysics Data System (ADS)
He, Yu-Hao; Xia, Ke-Qing
2016-11-01
We present an experimental measurement of the rms temperature (σT) profile in two regions inside a large aspect ratio (Γ = 4 . 2) rectangular Rayleigh-Bénard convection cell. The Rayleigh number (Ra) is from 3 . 2 ×107 to 1 . 9 ×108 at fixed Prandtl number (Pr = 4 . 34). It is found that, in one region, where the boundary layer is sheared by a large-scale wind, σT versus the distance (z) above the bottom plate, obeys power law over one decade, whereas in another region, where plumes concentrate and move upward (plume-ejection region), the profile of σT has a logarithmic dependence on z. When normalized by a typical temperature scale θ*, the profiles of σT at different Rayleigh numbers collapse onto a single curve, indicating a university of σT profile with respect to Ra . This work is supported by the Hong Kong Research Grant Council under Grant Number N_CUHK437/15.
Critical spreading dynamics of parity conserving annihilating random walks with power-law branching
NASA Astrophysics Data System (ADS)
Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.
2018-09-01
We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.
Analysis of log-periodic power law singularity patterns in time series related to credit risk
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Sornette, Didier
2015-04-01
The log-periodic (super-exponential) power law singularity (LPPLS) has become a promising tool for predicting extreme behavior of self-organizing systems in natural sciences and finance. Some researchers have recently proposed to employ the LPPLS on credit risk markets. The review article at hand summarizes four papers in this field and shows how they are linked. After structuring the research questions, we collect the corresponding answers from the four articles. This eventually gives us an overall picture of the application of the LPPLS to credit risk data. Our literature review begins with grounding the view that credit default swap (CDS) spreads are hotbeds for LPPLS patterns and it ends up with drawing attention to the recently proposed alarm index for the prediction of institutional bank runs. By presenting a new field of application for the LPPLS, the reviewed strand of literature further substantiates the LPPLS hypothesis. Moreover, the results suggest that CDS spread trajectories belong to a different universality class than, for instance, stock prices.
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Denz, Cornelia
2013-09-01
We employ the log-periodic power law (LPPL) to analyze the late-2000 financial crisis from the perspective of critical phenomena. The main purpose of this study is to examine whether LPPL structures in the development of credit default swap (CDS) spreads can be used for default classification. Based on the different triggers of Bear Stearns’ near bankruptcy during the late-2000 financial crisis and Ford’s insolvency in 2009, this study provides a quantitative description of the mechanism behind bank runs. We apply the Johansen-Ledoit-Sornette (JLS) positive feedback model to explain the rise of financial institutions’ CDS spreads during the global financial crisis 2007-2009. This investigation is based on CDS spreads of 40 major banks over the period from June 2007 to April 2009 which includes a significant CDS spread increase. The qualitative data analysis indicates that the CDS spread variations have followed LPPL patterns during the global financial crisis. Furthermore, the univariate classification performances of seven LPPL parameters as default indicators are measured by Mann-Whitney U tests. The present study supports the hypothesis that discrete scale-invariance governs the dynamics of financial markets and suggests the application of new and fast updateable default indicators to capture the buildup of long-range correlations between creditors.
Phase boundaries of power-law Anderson and Kondo models: A poor man's scaling study
NASA Astrophysics Data System (ADS)
Cheng, Mengxing; Chowdhury, Tathagata; Mohammed, Aaron; Ingersent, Kevin
2017-07-01
We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states ρ (ɛ ) ∝|ɛ| r , either vanishing (for r >0 ) or diverging (for r <0 ) at the Fermi energy ɛ =0 , that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., r >0 ), we find the phase boundary for (a) 0
The flow of power law fluids in elastic networks and porous media.
Sochi, Taha
2016-02-01
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer
NASA Astrophysics Data System (ADS)
Castillo, Luciano; Hussain, Fazle
2017-02-01
Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ' + and the Reynolds shear stress, u'v'¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50 ≤y+≤170 ). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u' 2 ¯+ and v'θ'¯+ change little with the strength of acceleration, while v'+, w'+, and u'v'¯+ continue to decay in the flow direction. Furthermore, θ'+ and u'θ'¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for "transient growth" generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, "Coherent structure generation near-wall turbulence," J. Fluid Mech. 453, 57-108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.
Signal detection in power-law noise: effect of spectrum exponents.
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.
Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
NASA Astrophysics Data System (ADS)
Ito, Yuta; Nishimura, Jun; Tsuchiya, Asato
2015-11-01
Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to N = 512, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value N c ≃ 110, we find that (3+1)D expanding universe emerges dynamically with a clear large- N scaling property. Furthermore, the observed increase of the spatial extent with time t at sufficiently late times is consistent with a power-law behavior t 1/2, which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original supersymmetric model including fermionic matrices.
Fourth-power law structure of the shock wave fronts in metals and ceramics
NASA Astrophysics Data System (ADS)
Bayandin, Yuriy; Naimark, Oleg; Saveleva, Natalia
2017-06-01
The plate impact experiments were performed for solids during last fifty years. It was established that the dependence between the strain rate and the shock wave amplitude for metals and ceramics expressed by a fourth-power law. Present study is focused on the theoretical investigation and numerical simulation of plane shock wave propagation in metals and ceramics. Statistically based constitutive model of solid with defects (microcracks and microshears) was developed to provide the relation between damage induced mechanisms of structural relaxation, thermally activated plastic flow and material reactions for extreme loading conditions. Original approach based on the wide range constitutive equations was proposed for the numerical simulation of multiscale damage-failure transition mechanisms and plane shock wave propagation in solids with defects in the range of strain rate 103 -108s-1 . It was shown that mechanisms of plastic relaxation and damage-failure transitions are linked to the multiscale kinetics of defects leading to the self-similar nature of shock wave fronts in metals and ceramics. The work was supported by the Russian Science Foundation (Project No. 14-19-01173).
Inertial migration of elastic particles in a pressure-driven power-law fluid
NASA Astrophysics Data System (ADS)
Bowie, Samuel; Alexeev, Alexander
2016-11-01
Using three-dimensional computer simulations, we study the cross-stream migration of deformable particles in a channel filled with a non-Newtonian fluid driven by a pressure gradient. Our numerical approach integrates lattice Boltzmann method and lattice spring method in order to model fluid structural interactions of the elastic particle and the surrounding power fluid in the channel. The particles are modeled as elastic shells filled with a viscous fluid that are initially spherical. We focus on the regimes where the inertial effects cannot be neglected and cause cross-stream drift of particles. We probe the flow with different power law indexes including both the shear thickening and thinning fluids. We also examine migration of particles of with different elasticity and relative size. To isolate the non-Newtonian effects on particle migration, we compare the results with the inertial migration results found in the case where the channel is filled with a simple Newtonian fluid. The results can be useful for applications requiring high throughput separation, sorting, and focusing of both synthetic particles and biological cells in microfluidic devices. Financial support provided by National Science Foundation (NSF) Grant No. CMMI1538161.
Numerical evaluation of a single ellipsoid motion in Newtonian and power-law fluids
NASA Astrophysics Data System (ADS)
Férec, Julien; Ausias, Gilles; Natale, Giovanniantonio
2018-05-01
A computational model is developed for simulating the motion of a single ellipsoid suspended in a Newtonian and power-law fluid, respectively. Based on a finite element method (FEM), the approach consists in seeking solutions for the linear and angular particle velocities using a minimization algorithm, such that the net hydrodynamic force and torque acting on the ellipsoid are zero. For a Newtonian fluid subjected to a simple shear flow, the Jeffery's predictions are recovered at any aspect ratios. The motion of a single ellipsoidal fiber is found to be slightly disturbed by the shear-thinning character of the suspending fluid, when compared with the Jeffery's solutions. Surprisingly, the perturbation can be completely neglected for a particle with a large aspect ratio. Furthermore, the particle centroid is also found to translate with the same linear velocity as the undisturbed simple shear flow evaluated at particle centroid. This is confirmed by recent works based on experimental investigations and modeling approach (1-2).
Emergence of power-law scalings in shock-driven mixing transition
NASA Astrophysics Data System (ADS)
Vorobieff, Peter; Wayne, Patrick; Olmstead, Dell; Simons, Dylan; Truman, C. Randall; Kumar, Sanjay
2016-11-01
We present an experimental study of transition to turbulence due to shock-driven instability evolving on an initially cylindrical, diffuse density interface between air and a mixture of sulfur hexafluoride (SF6) and acetone. The plane of the shock is at an initial angle θ with the axis of the heavy-gas cylinder. We present the cases of planar normal (θ = 0) and oblique (θ =20°) shock interaction with the initial conditions. Flow is visualized in two perpendicular planes with planar laser-induced fluorescence (PLIF) triggered in acetone with a pulsed ultraviolet laser. Statistics of the flow are characterized in terms of the second-order structure function of the PLIF intensity. As instabilities in the flow evolve, the structure functions begin to develop power-law scalings, at late times manifesting over a range of scales spanning more than two orders of magnitude. We discuss the effects of the initial conditions on the emergence of these scalings, comparing the fully three-dimensional case (oblique shock interaction) with the quasi-two-dimensional case (planar normal shock interaction). We also discuss the flow anisotropy apparent in statistical differences in data from the two visualization planes. This work is funded by NNSA Grant DE-NA0002913.
Transport on percolation clusters with power-law distributed bond strengths.
Alava, Mikko; Moukarzel, Cristian F
2003-05-01
The simplest transport problem, namely finding the maximum flow of current, or maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed bond strengths of the type P(sigma) approximately sigma(-alpha). Assuming that only cutting bonds determine the flow, the maxflow critical exponent v is found to be v(alpha)=(d-1)nu+1/(1-alpha). This prediction is confirmed with excellent accuracy using large-scale numerical simulation in two and three dimensions. However, in the region of anomalous bond capacity distributions (0< or =alpha< or =1) we demonstrate that, due to cluster-structure fluctuations, it is not the cutting bonds but the blobs that set the transport properties of the backbone. This "blob dominance" avoids a crossover to a regime where structural details, the distribution of the number of red or cutting bonds, would set the scaling. The restored scaling exponents, however, still follow the simplistic red bond estimate. This is argued to be due to the existence of a hierarchy of so-called minimum cut configurations, for which cutting bonds form the lowest level, and whose transport properties scale all in the same way. We point out the relevance of our findings to other scalar transport problems (i.e., conductivity).
Exact, E = 0, classical and quantum solutions for general power-law oscillators
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Daboul, Jamil
1995-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
Power Law and Logarithmic Ricci Dark Energy Models in Hořava-Lifshitz Cosmology
NASA Astrophysics Data System (ADS)
Pasqua, Antonio; Chattopadhyay, Surajit; Khurshudyan, Martiros; Myrzakulov, Ratbay; Hakobyan, Margarit; Movsisyan, Artashes
2015-03-01
In this work, we studied the Power Law and the Logarithmic Entropy Corrected versions of the Ricci Dark Energy (RDE) model in a spatially non-flat universe and in the framework of Hořava-Lifshitz cosmology. For the two cases containing non-interacting and interacting RDE and Dark Matter (DM), we obtained the exact differential equation that determines the evolutionary form of the RDE energy density. Moreover, we obtained the expressions of the deceleration parameter q and, using a parametrization of the equation of state (EoS) parameter ω D given by the relation ω D ( z) = ω 0+ ω 1 z, we derived the expressions of both ω 0 and ω 1. We interestingly found that the expression of ω 0 is the same for both non-interacting and interacting case. The expression of ω 1 for the interacting case has strong dependence from the interacting parameter b 2. The parameters derived in this work are done in small redshift approximation and for low redshift expansion of the EoS parameter.
Shock-driven transition to turbulence: Emergence of power-law scaling
Olmstead, D.; Wayne, P.; Simons, D.; ...
2017-05-25
Here, we consider two cases of interaction between a planar shock and a cylindrical density interface. In the first case (planar normal shock), the axis of the gas cylinder is parallel to the shock front and baroclinic vorticity deposited by the shock is predominantly two dimensional (directed along the axis of the cylinder). In the second case, the cylinder is tilted, resulting in an oblique shock interaction and a fully-three-dimensional shock-induced vorticity field. Furthermore, the statistical properties of the flow for both cases are analyzed based on images from two orthogonal visualization planes, using structure functions of the intensity mapsmore » of fluorescent tracer premixed with heavy gas. And at later times, these structure functions exhibit power-law-like behavior over a considerable range of scales. Manifestation of this behavior is remarkably consistent in terms of dimensionless time τ defined based on Richtmyer's linear theory within the range of Mach numbers from 1.1 to 2.0 and the range of gas cylinder tilt angles with respect to the plane of the shock front (0–30°).« less
NASA Astrophysics Data System (ADS)
Xie, Y.; Zhang, S.
2011-12-01
The observed correlations, between the characteristic ages and dipole surface magnetic field strengths of all pulsars, can be well explained by magnetic field decay with core temperatures of 2×108 K, ˜2×107 K, and ˜105 K, for magnetars, normal radio pulsars, and millisecond pulsars, respectively; assuming that their characteristic ages are about two orders of magnitude larger than their true ages, the required core temperatures may be reduced by about a factor of 10. The magnetic decay follows a power-law and is dominated by the solenoidal component of the ambipolar diffusion mode. In this model, all NSs are assumed to have the same initial magnetic field strength, but different core temperature which does not change as the magnetic field decays. This suggests that the key distinguishing property between magnetars and normal pulsars is that magnetars were born much hotter than normal pulsars, and thus have much longer magnetic field decay time scales, resulting in higher surface magnetic field strength even with the same ages of normal pulsars. The above conclusion agrees well with the observed correlations between the surface temperatures of magnetars and other young NSs, which do not agree with the cooling dominated evolution of neutron stars. This suggests a possible scenario that heating, perhaps due to magnetic field decay, balances neutron star cooling for observed pulsars.
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.
A unified econophysics explanation for the power-law exponents of stock market activity
NASA Astrophysics Data System (ADS)
Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, Eugene
2007-08-01
We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.
X-ray Properties of an Unbiased Hard X-ray Detected Sample of AGN
NASA Technical Reports Server (NTRS)
Winter, Lisa M.; Mushotzky, Richard F.; Tueller, Jack; Markwardt, Craig
2007-01-01
The SWIFT gamma ray observatory's Burst Alert Telescope (BAT) has detected a sample of active galactic nuclei (AGN) based solely on their hard X-ray flux (14-195keV). In this paper, we present for the first time XMM-Newton X-ray spectra for 22 BAT AGXs with no previously analyzed X-ray spectra. If our sources are a representative sample of the BAT AGN, as we claim, our results present for the first time global X-ray properties of an unbiased towards absorption (n(sub H) < 3 x 10(exp 25)/sq cm), local (< z >= 0.03), AGN sample. We find 9/22 low absorption (n(sub H) < 10(exp 23)/sq cm), simple power law model sources, where 4 of these sources have a statistically significant soft component. Among these sources, we find the presence of a warm absorber statistically significant for only one Seyfert 1 source, contrasting with the ASCA results of Reynolds (1997) and George et al. (1998), who find signatures of warm absorption in half or more of their Seyfert 1 samples at similar redshifts. Additionally, the remaining sources (13122) have more complex spectra, well-fit by an absorbed power law at E > 2.0 keV. Five of the complex sources (NGC 612, ESO 362-G018, MRK 417, ESO 506-G027, and NGC 6860) are classified as Compton-thick candidates. Further, we find four more sources (SWIFT J0641.3+3257, SWIFT J0911.2+4533, SWIFT J1200.8+0650, and NGC 4992) with properties consistent with the hidden/buried AGN reported by Ueda et al. (2007). Finally, we include a comparison of the XMM EPIC spectra with available SWIFT X-ray Telescope (XRT) observations. From these comparisons, we find 6/16 sources with varying column densities, 6/16 sources with varying power law indices, and 13/16 sources with varying fluxes, over periods of hours to months. Flux and power law index are correlated for objects where both parameters vary.
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.
Katerndahl, David A
2009-06-01
Although symptoms of anxiety and depression correlate, they may covary in irregular and unpredictable ways. This non-linear covariation may be important to psychiatric diagnosis, treatment and relapse. This non-linear anxiety-depression interaction suggests that power laws may be observed. Power laws are statistical distributions found when systems vary in complex ways at the interface between chaotic dynamics and periodic dynamics, such that data points vary randomly but are still partially correlated with each other. Such non-linear dynamics and relationships should result in characteristic patterns of interaction among patients, stressors and treatment. This is important because non-linear dynamics could affect our understanding of mental disorders, the need for varied treatment approaches and patterns of early response to treatment. To determine whether the relationships between anxiety and depression levels, changes and rates of change follow power law distributions among patients with newly diagnosed major depressive episode (MDE), panic disorder (PD) and neither disorder (controls). Time series of hourly mood variation. Setting Acute and continuity primary care clinics. Five adult patients presenting each with MDE, PD and controls based on DSM-IV criteria. Four patients in each group completed 30 days of assessments. MAIN AND SECONDARY OUTCOME MEASURES: Hourly self-assessments (while awake) of levels of anxiety and depression using visual analogue scales for a 30-day period. Covariation in level of symptoms, in the change of symptoms and in the rate of change were assessed. Anxiety-depression matrices were prepared for pooled subjects. Power laws were sought using log-log plots of frequency versus order of that frequency. Although visual inspection of plots for symptoms levels, change and rates of change all suggest power laws, statistical assessments provide stronger support for power laws in symptom change than for either symptom levels or rates of change
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
Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.
Sardar, Tridip; Saha, Bapi
2017-06-01
In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R 0 ). It is shown that if R 0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. Copyright © 2017 Elsevier Inc. All rights reserved.
Bubble Motion through a Generalized Power-Law Fluid Flowing in a Vertical Tube
Mukundakrishnan, Karthik; Eckmann, David M.; Ayyaswamy, P. S.
2009-01-01
Intravascular gas embolism may occur with decompression in space flight, as well as during cardiac and vascular surgery. Intravascular bubbles may be deposited into any end organ, such as the heart or the brain. Surface interactions between the bubble and the endothelial cells lining the vasculature result in serious impairment of blood flow and can lead to heart attack, stroke, or even death. To develop effective therapeutic strategies, there is a need for understanding the dynamics of bubble motion through blood and its interaction with the vessel wall through which it moves. Toward this goal, we numerically investigate the axisymmetric motion of a bubble moving through a vertical circular tube in a shear-thinning generalized power-law fluid, using a front-tracking method. The formulation is characterized by the inlet Reynolds number, capillary number, Weber number, and Froude number. The flow dynamics and the associated wall shear stresses are documented for a combination of two different inlet flow conditions (inlet Reynolds numbers) and three different effective bubble radii (ratio of the undeformed bubble radii to the tube radii). The results of the non-Newtonian model are then compared with that of the model assuming a Newtonian blood viscosity. Specifically, for an almost occluding bubble (effective bubble radius = 0.9), the wall shear stress and the bubble residence time are compared for both Newtonian and non-Newtonian cases. Results show that at low shear rates, for a given pressure gradient the residence time for a non-Newtonian flow is higher than that for a Newtonian flow. PMID:19426324
Spaide, Richard F
2016-10-01
To investigate flow characteristics of the choriocapillaris using optical coherence tomography angiography. Retrospective observational case series. Visualization of flow in individual choriocapillary vessels is below the current resolution limit of optical coherence tomography angiography instruments, but areas of absent flow signal, called flow voids, are resolvable. The central macula was imaged with the Optovue RTVue XR Avanti using a 10-μm slab thickness in 104 eyes of 80 patients who ranged in age from 24 to 99 years of age. Automatic local thresholding of the resultant raw data with the Phansalkar method was analyzed with generalized estimating equations. The distribution of flow voids vs size of the voids was highly skewed. The data showed a linear log-log plot and goodness-of-fit methods showed the data followed a power law distribution over the relevant range. A slope intercept relationship was also evaluated for the log transform and significant predictors for variables included age, hypertension, pseudodrusen, and the presence of late age-related macular degeneration (AMD) in the fellow eye. The pattern of flow voids forms a scale invariant pattern in the choriocapillaris starting at a size much smaller than a choroidal lobule. Age and hypertension affect the choriocapillaris, a flat layer of capillaries that may serve as an observable surrogate for the neural or systemic microvasculature. Significant alterations detectable in the flow pattern in eyes with pseudodrusen and in eyes with late AMD in the fellow eye offer diagnostic possibilities and impact theories of disease pathogenesis. Copyright © 2016 Elsevier Inc. All rights reserved.
Enhanced dust emissivity power-law index along the western H α filament of NGC 1569
NASA Astrophysics Data System (ADS)
Suzuki, T.; Kaneda, H.; Onaka, T.; Yamagishi, M.; Ishihara, D.; Kokusho, T.; Tsuchikawa, T.
2018-07-01
We used a data set from AKARI and Herschel images at wavelengths from 7 to 500 μm to catch the evidence of dust processing in galactic winds in NGC 1569. Images show a diffuse infrared (IR) emission extending from the galactic disc into the halo region. The most prominent filamentary structure seen in the diffuse IR emission is spatially in good agreement with the western H α filament (western arm). The spatial distribution of the F350/F500 map shows high values in regions around the super-star clusters (SSCs) and towards the western arm, which are not found in the F250/F350 map. The colour-colour diagram of F250/F350-F350/F500 indicates high values of the emissivity power-law index (βc) of the cold dust component in those regions. From a spectral decomposition analysis on a pixel-by-pixel basis, a βc map shows values ranging from ˜1 to ˜2 over the whole galaxy. In particular, high βc values of ˜2 are observed only in the regions indicated by the colour-colour diagram. Since the average cold dust temperature in NGC 1569 is ˜30 K, βc < 2.0 in the far-IR and sub-mm region theoretically suggests emission from amorphous grains, while βc = 2.0 suggests that from crystal grains. Given that the enhanced βc regions are spatially confined by the H I ridge that is considered to be a birthplace of the SSCs, the spatial coincidences may indicate that dust grains around the SSCs are grains of relatively high crystallinity injected by massive stars originating from starburst activities and that those grains are blown away along the H I ridge and thus the western arm.
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.
Hirose, H
1997-01-01
This paper proposes a new treatment for electrical insulation degradation. Some types of insulation which have been used under various circumstances are considered to degrade at various rates in accordance with their stress circumstances. The cross-linked polyethylene (XLPE) insulated cables inspected by major Japanese electric companies clearly indicate such phenomena. By assuming that the inspected specimen is sampled from one of the clustered groups, a mixed degradation model can be constructed. Since the degradation of the insulation under common circumstances is considered to follow a Weibull distribution, a mixture model and a Weibull power law can be combined. This is called The mixture Weibull power law model. By using the maximum likelihood estimation for the newly proposed model to Japanese 22 and 33 kV insulation class cables, they are clustered into a certain number of groups by using the AIC and the generalized likelihood ratio test method. The reliability of the cables at specified years are assessed.
Seasonal evolution of the Arctic marginal ice zone and its power-law obeying floe size distribution
NASA Astrophysics Data System (ADS)
Zhang, J.; Stern, H. L., III; Schweiger, A. J. B.; Steele, M.; Hwang, P. B.
2017-12-01
A thickness, floe size, and enthalpy distribution (TFED) sea ice model, implemented numerically into the Pan-arctic Ice-Ocean Modeling and Assimilation System (PIOMAS), is used to investigate the seasonal evolution of the Arctic marginal ice zone (MIZ) and its floe size distribution. The TFED sea ice model, by coupling the Zhang et al. [2015] sea ice floe size distribution (FSD) theory with the Thorndike et al. [1975] ice thickness distribution (ITD) theory, simulates 12-category FSD and ITD explicitly and jointly. A range of ice thickness and floe size observations were used for model calibration and validation. The model creates FSDs that generally obey a power law or upper truncated power law, as observed by satellites and aerial surveys. In this study, we will examine the role of ice fragmentation and lateral melting in altering FSDs in the Arctic MIZ. We will also investigate how changes in FSD impact the seasonal evolution of the MIZ by modifying the thermodynamic processes.
Takahashi, Ryosuke; Okajima, Takaharu, E-mail: okajima@ist.hokudai.ac.jp
We present multi-frequency force modulation atomic force microscopy (AFM) for mapping the complex shear modulus G* of living cells as a function of frequency over the range of 50–500 Hz in the same measurement time as the single-frequency force modulation measurement. The AFM technique enables us to reconstruct image maps of rheological parameters, which exhibit a frequency-dependent power-law behavior with respect to G{sup *}. These quantitative rheological measurements reveal a large spatial variation in G* in this frequency range for single cells. Moreover, we find that the reconstructed images of the power-law rheological parameters are much different from those obtained inmore » force-curve or single-frequency force modulation measurements. This indicates that the former provide information about intracellular mechanical structures of the cells that are usually not resolved with the conventional force measurement methods.« less
NASA Astrophysics Data System (ADS)
Wu, P.; Wang, H.; van der Wal, W.
2006-12-01
Modern geodetic measurements from GPS, satellite altimetry, tide-gauges, Satellite Laser Ranging (SLR) and space-borne gravimetry (such as GRACE) have been used to monitor global change. Since these measurements contain contributions from glacial isostatic adjustment (GIA) and other tectonic processes, they must be modeled and removed in order to observe current climate change. In the past, most GIA models assumed that the earth is laterally homogeneous and the rheology is linear. The aim of this paper is to investigate the effects of lateral heterogeneity and Power-Law rheology on GIA induced land uplift rate, horizontal velocities, relative sealevels, J-dot and the secular gravity rate of change in the southern part of Hudson Bay, which is detected by the GRACE mission. Here, GIA is modeled with a spherical, self-gravitating, compressible viscoelastic, laterally heterogeneous earth using the Finite-Element Method. The effect of gravitationally self-consistent sea levels in realistic oceans is also included. Lateral variations in mantle viscosities and lithospheric thickness are inferred from the seismic tomography model S20A using well known scaling relationships. Power-Law rheologies in the whole mantle or in combination with linear rheologies in the upper or lower mantle are also investigated. Both ICE-5G and ICE-4G deglaciation models are used to investigate their effect on the pattern of rebound. Preliminary results show that both lateral heterogeneity and power-law rheology have strong effects on the direction and magnitude of horizontal velocities. The effects of lateral heterogeneity and power-law rheology are also large enough to be detected in land uplift rate, relative sealevels, J-dot and gravity rate of change. Their implication on observing the effects of global warming will also be discussed.
Marshall, Najja; Timme, Nicholas M.; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M.
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of “neural avalanches” (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods—power-law fitting, avalanche shape collapse, and neural complexity—have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox. PMID:27445842
NASA Astrophysics Data System (ADS)
Nigmatullin, R. R.; Arbuzov, A. A.; Salehli, F.; Giz, A.; Bayrak, I.; Catalgil-Giz, H.
2007-01-01
For the first time we achieved incontestable evidence that the real process of dielectric relaxation during the polymerization reaction of polyvinylpyrrolidone (PVP) is described in terms of the fractional kinetic equations containing complex-power-law exponents. The possibility of the existence of the fractional kinetics containing non-integer complex-power-law exponents follows from the general theory of dielectric relaxation that has been suggested recently by one of the authors (R.R.N). Based on the physical/geometrical meaning of the fractional integral with complex exponents there is a possibility to develop a general theory of dielectric relaxation based on the self-similar (fractal) character of the reduced (averaged) microprocesses that take place in the mesoscale region. This theory contains some essential predictions related to existence of the non-integer power-law kinetics and the results of this paper can be considered as the first confirmation of existence of the kinetic phenomena that are described by fractional derivatives with complex-power-law exponents. We want to stress here that with the help of a new complex fitting function for the complex permittivity it becomes possible to describe the whole process for real and imaginary parts simultaneously throughout the admissible frequency range (30 Hz-13 MHz). The fitting parameters obtained for the complex permittivity function for three temperatures (70, 90 and 110 °C) confirm in general the picture of reaction that was known qualitatively before. They also reveal some new features, which improve the interpretation of the whole polymerization process. We hope that these first results obtained in the paper will serve as a good stimulus for other researches to find the traces of the existence of new fractional kinetics in other relaxation processes unrelated to the dielectric relaxation. These results should lead to the reconsideration and generalization of irreversibility and kinetic phenomena that
Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
Salje, Ekhard K H; Planes, Antoni; Vives, Eduard
2017-10-01
Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.
Evidence for power-law frequency dependence of intrinsic dielectric response in the Ca Cu3 Ti4 O12
NASA Astrophysics Data System (ADS)
Tselev, Alexander; Brooks, Charles M.; Anlage, Steven M.; Zheng, Haimei; Salamanca-Riba, Lourdes; Ramesh, R.; Subramanian, M. A.
2004-10-01
We investigated the dielectric response of CaCu3Ti4O12 (CCTO) thin films grown epitaxially on LaAlO3 (001) substrates by pulsed laser deposition. The dielectric response of the films was found to be strongly dominated by a power law in frequency, typical of materials with localized hopping charge carriers, in contrast to the Debye-like response of the bulk material. The film conductivity decreases with annealing in oxygen, and it suggests that oxygen deficit is a cause of the relatively high film conductivity. With increase of the oxygen content, the room temperature frequency response of the CCTO thin films changes from the response indicating the presence of some relatively low conducting capacitive layers to purely power law, and then toward a frequency independent response with a relative dielectric constant ɛ'˜102 . The film conductance and dielectric response decrease upon decrease of the temperature, with dielectric response being dominated by the power-law frequency dependence. Below ˜80K , the dielectric response of the films is frequency independent with ɛ' close to 102 . The results provide another piece of evidence for an extrinsic, Maxwell-Wagner type, origin of the colossal dielectric response of the bulk CCTO material, connected with electrical inhomogeneity of the bulk material.
NASA Astrophysics Data System (ADS)
Holway, Kevin; Thaxton, Christopher S.; Calantoni, Joseph
2012-11-01
Morphodynamic models of coastal evolution require relatively simple parameterizations of sediment transport for application over larger scales. Calantoni and Thaxton (2008) [6] presented a transport parameterization for bimodal distributions of coarse quartz grains derived from detailed boundary layer simulations for sheet flow and near sheet flow conditions. The simulation results, valid over a range of wave forcing conditions and large- to small-grain diameter ratios, were successfully parameterized with a simple power law that allows for the prediction of the transport rates of each size fraction. Here, we have applied the simple power law to a two-dimensional cellular automaton to simulate sheet flow transport. Model results are validated with experiments performed in the small oscillating flow tunnel (S-OFT) at the Naval Research Laboratory at Stennis Space Center, MS, in which sheet flow transport was generated with a bed composed of a bimodal distribution of non-cohesive grains. The work presented suggests that, under the conditions specified, algorithms that incorporate the power law may correctly reproduce laboratory bed surface measurements of bimodal sheet flow transport while inherently incorporating vertical mixing by size.
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.
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.
2015-10-01
We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.
Langbein, John O.
2012-01-01
Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.
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.
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.
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
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.
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 flow of a power-law fluid in the near-wake of a flat plate
NASA Astrophysics Data System (ADS)
Zhou, Min; Ladeinde, Foluso; Bluestein, Danny
2006-08-01
The analysis of the near-wake flow downstream of a flat plate is reported in this paper for the case of a non-Newtonian (power-law) constitutive model. To our knowledge, the present paper is the first to address this problem, as previous work on near-wakes has been limited to the use of a Newtonian model. The motivation for this work comes from the biomedical engineering problem of blood flow around the bileaflet of a mechanical heart valve. In the present paper, the series method has been used to calculate the flow near the centerline of the wake, while an asymptotic method has been used for larger distances from the centerline. The effects of power-law inlet conditions on the wake flow are reported for various values of the power-law index n, within the range 0.7≤n ≤1.3. The present analysis has been successfully validated by comparing the results for n =1 to the near-wake results by Goldstein [Proc. Cambridge Philos. Soc. 26, 1 (1930)]. We generalized the equations for arbitrary values of n, without any special considerations for n =1. Therefore, the accurate results observed for n =1 validate our procedure as a whole. The first major finding is that a fluid with smaller n develops faster downstream, such that decreasing n leads to monotonically increasing velocities compared to fluids with large n values. Another finding is that the non-Newtonian effects become more significant as the downstream distance increases. Finally, these effects tend to be more pronounced in the vicinity of the wake centerline compared to larger y locations.
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.
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
NASA Astrophysics Data System (ADS)
Mehedi Faruk, Mir; Sazzad Hossain, Md.; Muktadir Rahman, Md.
2016-02-01
The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U=\\sumi=1dci\\vert xi/ai\\vertni are studied carefully. Detailed calculation of Kim et al. (J. Phys. Condens. Matter 11 (1999) 10269) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume CV are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.
The effect of power-law body forces on a thermally driven flow between concentric rotating spheres
NASA Technical Reports Server (NTRS)
Macaraeg, M. G.
1986-01-01
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
The effect of power law body forces on a thermally-driven flow between concentric rotating spheres
NASA Technical Reports Server (NTRS)
Macaraeg, M. G.
1985-01-01
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
NASA Astrophysics Data System (ADS)
Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu
2014-03-01
We start from Gibrat's law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.
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;
2011-01-01
Vela X is a large, 3 deg x 2 deg, radio-emitting pulsar wind nebula (PWN) powered by the Vela pulsar in the Vela supernova remnant. Using four Suzaku/XIS observations pointed just outside Vela X, we find hard X-ray emission extending throughout the fields of view. The hard X-ray spectra are well represented by a power-law. The photon index is measured to be constant at Gamma approximates 2.4, similar to that of the southern outer part of Vela X. The power-law flux decreases with increasing distance from the pulsar. These properties lead us to propose that the hard X-ray emission is associated with the Vela PWN. The larger X-ray extension found in this work strongly suggests that distinct populations relativistic electrons form the X-ray PWN and Vela X, as was recently inferred from multiwavelength spectral modeling of Vela X.
Stochastic modeling of the migration of Cs-137 in the soil considering a power law tailing in space
NASA Astrophysics Data System (ADS)
Oka, Hiroki; Hatano, Yuko
2016-04-01
We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. In our past study, we derived the analytic solution under the generalized Robin boundary condition (Oka-Yamamoto solution). This is a generalization of the He-Walling solution (1996). We compared our solution with the Fukushima soil data of for 3 years after the accident and found that the concentration of Cs-137 has a discrepancy from our solution, specifically in a deep part because the depth profiles have a power law tailing. Therefore, we improved our model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x,t|D) in terms of the diffusion coefficient D and calculate C(x,t)=∫_(0~∞) C(x,t|D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.
Hu, Bin; Kieweg, Sarah L
2012-07-15
Gravity-driven thin film flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. There have been many prior works on gravity-driven thin films. However, the incorporation of surface tension effect has not been well studied for non-Newtonian fluids. After surface tension effect was incorporated into our 2D (i.e. 1D spreading) power-law model, we found that surface tension effect not only impacted the spreading speed of the microbicide gel, but also had an influence on the shape of the 2D spreading profile. We observed a capillary ridge at the front of the fluid bolus. Previous literature shows that the emergence of a capillary ridge is strongly related to the contact line fingering instability. Fingering instabilities during epithelial coating may change the microbicide gel distribution and therefore impact how well it can protect the epithelium. In this study, we focused on the capillary ridge in 2D flow and performed a series of simulations and showed how the capillary ridge height varies with other parameters, such as surface tension coefficient, inclination angle, initial thickness, and power-law parameters. As shown in our results, we found that capillary ridge height increased with higher surface tension, steeper inclination angle, bigger initial thickness, and more Newtonian fluids. This study provides the initial insights of how to optimize the flow and prevent the appearance of a capillary ridge and fingering instability.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock
NASA Astrophysics Data System (ADS)
Fareo, A. G.; Mason, D. P.
2013-12-01
The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.
Power-law distributions for the areas of the basins of attraction on a potential energy landscape.
Massen, Claire P; Doye, Jonathan P K
2007-03-01
Energy landscape approaches have become increasingly popular for analyzing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy landscape into basins of attraction surrounding the minima. Here, we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids. We find that this probability distribution is a power law over a large number of decades with the lower-energy minima having larger basins of attraction. Interestingly, the exponent for this power law is approximately the same as that for a high-dimensional Apollonian packing, providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. These results suggest that the basins of attraction provide a fractal-like tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.
NASA Astrophysics Data System (ADS)
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; López-López, M. G.; Alvarado-Martínez, V. M.
2018-03-01
In this paper, the two-dimensional projectile motion was studied; for this study two cases were considered, for the first one, we considered that there is no air resistance and, for the second case, we considered a resisting medium k . The study was carried out by using fractional calculus. The solution to this study was obtained by using fractional operators with power law, exponential decay and Mittag-Leffler kernel in the range of γ \\in (0,1] . These operators were considered in the Liouville-Caputo sense to use physical initial conditions with a known physical interpretation. The range and the maximum height of the projectile were obtained using these derivatives. With the aim of exploring the validity of the obtained results, we compared our results with experimental data given in the literature. A multi-objective particle swarm optimization approach was used for generating Pareto-optimal solutions for the parameters k and γ for different fixed values of velocity v0 and angle θ . The results showed some relevant qualitative differences between the use of power law, exponential decay and Mittag-Leffler law.
NASA Astrophysics Data System (ADS)
Kalkanis, G.; Rosso, E.
1989-09-01
Results of an accelerated test on the lifetime of a mylar-polyurethane laminated dc high voltage insulating structure are reported. This structure consists of mylar ribbons placed side by side in a number of layers, staggered and glued together with a polyurethane adhesive. The lifetime until breakdown as a function of extremely high values of voltage stress is measured and represented by a mathematical model, the inverse power law model with a 2-parameter Weibull lifetime distribution. The statistical treatment of the data — either by graphical or by analytical methods — allowed us to estimate the lifetime distribution and confidence bounds for any required normal voltage stress. The laminated structure under consideration is, according to the analysis, a very reliable dc hv insulating material, with a very good life performance according to the inverse power law model, and with an exponent of voltage stress equal to 6. A large insulator of cylindrical shape with this kind of laminated structure can be constructed by winding helically a mylar ribbon in a number of layers.
NASA Technical Reports Server (NTRS)
Schubert, G.; Lingenfelter, R. E.
1973-01-01
Investigations have continued into the possibility that significant information on stream flow rates can be obtained from aerial and satellite imagery of river meander patterns by seeking a correlation between the meander and discharge spectra of rivers. Such a correlation could provide the basis for a simple and inexpensive technique for remote sensing of the water resources of large geographical areas, eliminating the need for much hydrologic recording. The investigation of the nature of the meander and discharge spectra and their interrelationship can also contribute to a more fundamental understanding of the processes of both river meander formation and drainage of large basins. It has been found that floods decay with an inverse power law dependence on time. The exponent of this dependence varies from river to river and even from station to station along the same river. This power law time dependence makes possible the forecasting of river discharge with an uncertainty of about 5% for as long as a month following the flood peak.
MHD mixed convection analysis of non-Newtonian power law fluid in an open channel with round cavity
NASA Astrophysics Data System (ADS)
Bose, Pritom; Rakib, Tawfiqur; Das, Sourav; Rabbi, Khan Md.; Mojumder, Satyajit
2017-06-01
In this study, magneto-hydrodynamic (MHD) mixed convection flow through a channel with a round cavity at bottom wall using non-Newtonian power law fluid is analysed numerically. The cavity is kept at uniformly high temperature whereas rest of the bottom wall is insulated and top wall of the channel is maintained at a temperature lower than cavity temperature. Grid independency test and code validation are performed to justify the computational accuracy before solving the present problem. Galerkin weighted residual method is appointed to solve the continuity, momentum and energy equations. The problem is solved for wide range of pertinent parameters like Rayleigh number (Ra= 103 - 105), Hartmann number (Ha= 0 - 60) and power law index (n= 0.5 - 1.5) at constant Richardson number Ri= 1.0. The flow and thermal field have been thoroughly discussed through streamline and isothermal lines respectively. The heat transfer performance of the given study is illustrated by average Nusselt number plots. Result of this investigation indicates that heat transfer is highest for dilatant fluids at this configuration and they perform better (47% more heat transfer) in absence of magnetic field. The retardation of heat transfer is offset by shear thickening nature of non-Newtonian fluid.
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.
Dieterich, J.H.; Kilgore, B.D.
1996-01-01
A procedure has been developed to obtain microscope images of regions of contact between roughened surfaces of transparent materials, while the surfaces are subjected to static loads or undergoing frictional slip. Static loading experiments with quartz, calcite, soda-lime glass and acrylic plastic at normal stresses to 30 MPa yield power law distributions of contact areas from the smallest contacts that can be resolved (3.5 ??m2) up to a limiting size that correlates with the grain size of the abrasive grit used to roughen the surfaces. In each material, increasing normal stress results in a roughly linear increase of the real area of contact. Mechanisms of contact area increase are by growth of existing contacts, coalescence of contacts and appearance of new contacts. Mean contacts stresses are consistent with the indentation strength of each material. Contact size distributions are insensitive to normal stress indicating that the increase of contact area is approximately self-similar. The contact images and contact distributions are modeled using simulations of surfaces with random fractal topographies. The contact process for model fractal surfaces is represented by the simple expedient of removing material at regions where surface irregularities overlap. Synthetic contact images created by this approach reproduce observed characteristics of the contacts and demonstrate that the exponent in the power law distributions depends on the scaling exponent used to generate the surface topography.
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2017-01-01
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference
ERIC Educational Resources Information Center
Kolata, Gina
1985-01-01
To determine how hard it is for computers to solve problems, researchers have classified groups of problems (polynomial hierarchy) according to how much time they seem to require for their solutions. A difficult and complex proof is offered which shows that a combinatorial approach (using Boolean circuits) may resolve the problem. (JN)
NASA Astrophysics Data System (ADS)
Hyman, J. D.; Aldrich, G.; Viswanathan, H.; Makedonska, N.; Karra, S.
2016-08-01
We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. These observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.
NASA Astrophysics Data System (ADS)
Hyman, J.; Aldrich, G. A.; Viswanathan, H. S.; Makedonska, N.; Karra, S.
2016-12-01
We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semi-correlation, and non-correlation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same.We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. These observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.
Hyman, Jeffrey De'Haven; Aldrich, Garrett Allen; Viswanathan, Hari S.; ...
2016-08-01
We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected somore » that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. Lastly, these observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.« less
Chatterjee, Biplab K.; Ghosh, C. K.; Chattopadhyay, K. K., E-mail: kalyan-chattopadhyay@yahoo.com
2014-10-21
The thermal variation of magnetic anisotropy (K) and saturation magnetization (M{sub S}) for uniaxial nickel ferrite (NiFe₂O₄) nanomagnets are investigated. Major magnetic hysteresis loops are measured for the sample at temperatures over the range 5–280 K using a vibrating sample magnetometer. The high-field regimes of the hysteresis loops are modeled using the law of approach to saturation, based on the assumption that at sufficiently high field only direct rotation of spin-moment take place, with an additional forced magnetization term that is linear with applied field. The uniaxial anisotropy constant K is calculated from the fitting of the data to the theoreticalmore » equation. As temperature increases from 5 K to 280 K, a 49% reduction of K, accompanied by an 85% diminution of M{sub S} is observed. Remarkably, K is linearly proportional to M{sub S}₂.₆ in the whole temperature range violating the existing theoretical model by Callen and Callen. The unusual power-law behavior for the NiFe₂O₄ uniaxial nanomagnets is ascribed to the non-negligible contributions from inter-sublattice pair interactions, Neel surface anisotropy, and higher order anisotropies. A complete realization of the unusual anisotropy-magnetization scaling behavior for nanoscale two-sublattice magnetic materials require a major modification of the existing theory by considering the exact mechanism of each contributions to the effective anisotropy.« less
Hyman, Jeffrey De'Haven; Aldrich, Garrett Allen; Viswanathan, Hari S.
We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected somore » that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. Lastly, these observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.« less
NASA Astrophysics Data System (ADS)
Pedretti, Daniele
2017-04-01
Power-law (PL) distributions are widely adopted to define the late-time scaling of solute breakthrough curves (BTCs) during transport experiments in highly heterogeneous media. However, from a statistical perspective, distinguishing between a PL distribution and another tailed distribution is difficult, particularly when a qualitative assessment based on visual analysis of double-logarithmic plotting is used. This presentation aims to discuss the results from a recent analysis where a suite of statistical tools was applied to evaluate rigorously the scaling of BTCs from experiments that generate tailed distributions typically described as PL at late time. To this end, a set of BTCs from numerical simulations in highly heterogeneous media were generated using a transition probability approach (T-PROGS) coupled to a finite different numerical solver of the flow equation (MODFLOW) and a random walk particle tracking approach for Lagrangian transport (RW3D). The T-PROGS fields assumed randomly distributed hydraulic heterogeneities with long correlation scales creating solute channeling and anomalous transport. For simplicity, transport was simulated as purely advective. This combination of tools generates strongly non-symmetric BTCs visually resembling PL distributions at late time when plotted in double log scales. Unlike other combination of modeling parameters and boundary conditions (e.g. matrix diffusion in fractures), at late time no direct link exists between the mathematical functions describing scaling of these curves and physical parameters controlling transport. The results suggest that the statistical tests fail to describe the majority of curves as PL distributed. Moreover, they suggest that PL or lognormal distributions have the same likelihood to represent parametrically the shape of the tails. It is noticeable that forcing a model to reproduce the tail as PL functions results in a distribution of PL slopes comprised between 1.2 and 4, which are the
Formation and relaxation of quasistationary states in particle systems with power-law interactions
NASA Astrophysics Data System (ADS)
Marcos, B.; Gabrielli, A.; Joyce, M.
2017-09-01
We explore the formation and relaxation of the so-called quasistationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential V (r →∞ ) ˜1 /rγ with γ >0 , and either a soft core or hard core regularization at small r . In the first part of the paper, we generalize, for any spatial dimension d ≥2 , Chandrasekhar's approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two-body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for γ >d -1 , the rate diverges in the large particle number N (mean-field) limit, unless a sufficiently large soft core is present; for γ
Second-order small disturbance theory for hypersonic flow over power-law bodies. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1974-01-01
A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.
NASA Astrophysics Data System (ADS)
Huang, Y.; Song, Q. W.; Tan, B. L.
2018-04-01
It is first proposed a theoretical scaling law respectively for the coronal magnetic field strength B and electron power-law index δ versus frequency and coronal height in solar microwave burst sources. Based on the non-thermal gyro-synchrotron radiation model (Ramaty in Astrophys. J. 158:753, 1969), B and δ are uniquely solved by the observable optically-thin spectral index and turnover (peak) frequency, the other parameters (plasma density, temperature, view angle, low and high energy cutoffs, etc.) are relatively insensitive to the calculations, thus taken as some typical values. Both of B and δ increase with increasing of radio frequency but with decreasing of coronal height above photosphere, and well satisfy a square or cubic logarithmic fitting.
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 .
NASA Astrophysics Data System (ADS)
Li, Qiang; Popov, Valentin L.
2018-03-01
Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation.
Warren, Keith; Craciun, Gheorghe; Anderson-Butcher, Dawn
2005-04-01
This paper develops a simple random network model of peer contagion in aggressive behavior among inner-city elementary school boys during recess periods. The model predicts a distribution of aggressive behaviors per recess period with a power law tail beginning at two aggressive behaviors and having a slope of approximately -1.5. Comparison of these values with values derived from observations of aggressive behaviors during recess at an inner-city elementary school provides empirical support for the model. These results suggest that fluctuations in aggressive behaviors during recess arise from the interactions between students, rather than from variations in the behavior of individual students. The results therefore support those interventions that aim to change the pattern of interaction between students.
Wen, Rui-Tao, E-mail: Ruitao.Wen@angstrom.uu.se; Granqvist, Claes G.; Niklasson, Gunnar A.
2014-10-20
Ni-oxide-based thin films were produced by reactive direct-current magnetron sputtering and were characterized by X-ray diffraction and Rutherford backscattering spectroscopy. Intercalation of Li{sup +} ions was accomplished by cyclic voltammetry (CV) in an electrolyte of LiClO{sub 4} in propylene carbonate, and electrochromism was documented by spectrophotometry. The charge density exchange, and hence the optical modulation span, decayed gradually upon repeated cycling. This phenomenon was accurately described by an empirical power law, which was valid for at least 10{sup 4} cycles when the applied voltage was limited to 4.1 V vs Li/Li{sup +}. Our results allow lifetime assessments for one of themore » essential components in an electrochromic device such as a “smart window” for energy-efficient buildings.« less
2011-01-01
Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520
NASA Astrophysics Data System (ADS)
Cao, Shuo; Biesiada, Marek; Yao, Meng; Zhu, Zong-Hong
2016-09-01
We use 118 strong gravitational lenses observed by the SLACS, BOSS emission-line lens survey (BELLS), LSD and SL2S surveys to constrain the total mass profile and the profile of luminosity density of stars (light tracers) in elliptical galaxies up to redshift z ˜ 1. Assuming power-law density profiles for the total mass density, ρ = ρ0(r/r0)-α, and luminosity density, ν = ν0(r/r0)-δ, we investigate the power-law index and its first derivative with respect to the redshift. Using Monte Carlo simulations of the posterior likelihood taking the Planck's best-fitting cosmology as a prior, we find γ = 2.132 ± 0.055 with a mild trend ∂γ/∂zl = -0.067 ± 0.119 when α = δ = γ, suggesting that the total density profile of massive galaxies could have become slightly steeper over cosmic time. Furthermore, similar analyses performed on sub-samples defined by different lens redshifts and velocity dispersions indicate the need of treating low-, intermediate- and high-mass galaxies separately. Allowing δ to be a free parameter, we obtain α = 2.070 ± 0.031, ∂α/∂zl = -0.121 ± 0.078 and δ = 2.710 ± 0.143. The model in which mass traces light is rejected at >95 per cent confidence, and our analysis robustly indicates the presence of dark matter in the form of a mass component that is differently spatially extended than the light. In this case, intermediate-mass elliptical galaxies (200 km s-1 <σap ≤ 300 km s-1) show the best consistency with the singular isothermal sphere as an effective model of galactic lenses.
Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics.
Teka, Wondimu W; Upadhyay, Ranjit Kumar; Mondal, Argha
2017-09-01
Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. Copyright © 2017 Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Thompson, Rodger I.
2018-04-01
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar ϕ with respect to the natural log of the scale factor a, β (φ )=d φ /d ln (a). Once the beta function is specified, modulo a boundary condition, the evolution of the scalar ϕ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated "beta potential" is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are that are not calculable using only the model action. As an example this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that ΛCDM is part of the family of quintessence cosmology power law potentials with a power of zero.
NASA Astrophysics Data System (ADS)
Thompson, Rodger I.
2018-07-01
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar φ with respect to the natural log of the scale factor a, β (φ)=d φ/d ln (a). Once the beta function is specified, modulo a boundary condition, the evolution of the scalar φ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated `beta potential' is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are not calculable using only the model action. As an example, this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that Λ cold dark matter is part of the family of quintessence cosmology power-law potentials with a power of zero.
Aziz, Asim; Ali, Yasir; Aziz, Taha; Siddique, J. I.
2015-01-01
In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined. PMID:26407162
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.
Esquivel-Gómez, J.; Arjona-Villicaña, P. D.; Stevens-Navarro, E.; Pineda-Rico, U.; Balderas-Navarro, R. E.; Acosta-Elias, J.
2015-01-01
The out-degree distribution is one of the most reported topological properties to characterize real complex networks. This property describes the probability that a node in the network has a particular number of outgoing links. It has been found that in many real complex networks the out-degree has a behavior similar to a power-law distribution, therefore some network growth models have been proposed to approximate this behavior. This paper introduces a new growth model that allows to produce out-degree distributions that decay as a power-law with an exponent in the range from 1 to ∞. PMID:25765763
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.
Hard diffraction and deep inelastic scattering
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
Does price efficiency increase with trading volume? Evidence of nonlinearity and power laws in ETFs
NASA Astrophysics Data System (ADS)
Caginalp, Gunduz; DeSantis, Mark
2017-02-01
Whether efficiency increases with increasing volume is an important issue that may illuminate trader strategies and distinguish between market theories. This relationship is tested using 124,236 daily observations comprising 68 large and liquid U.S. equity exchange traded funds (ETFs). ETFs have the advantage that efficiency can be measured in terms of the deviation between the trading price and the underlying net asset value that is reported each day. Our findings support the hypothesis that the relationship between volume and efficiency is nonlinear. Indeed, efficiency increases as volume increases from low to moderately high levels, but then decreases as volume increases further. The first part tends to support the idea that higher volume simply facilitates transactions and maintains efficiency, while the latter part, i.e., even higher volumes, supports the ansatz that increased volume is associated with increased speculation that ignores valuation and decreases efficiency. The results are consistent with the hypothesis that valuation is only part of the motivation for traders. Our methodology accounts for fund heterogeneity and contemporaneous correlations. Similar results are obtained when daily price volatility is introduced as an additional independent variable.
A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues.
Nicolle, S; Vezin, P; Palierne, J-F
2010-03-22
Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s(-1) to 0.7s(-1). Copyright (c) 2009 Elsevier Ltd. All rights reserved.
Zhang, Kai; Fan, Meng; Liu, Yanhui
When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate R{sub c}, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. R{sub c} (or the corresponding critical casting thickness d{sub c}) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small R{sub c} < 10{sup −2} K/s, pure metals and most alloys are typically poor glass-formers with large R{sub c} > 10{sup 10} K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with R{sub c} approachingmore » that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important
Scocchia, Lisa; Bolognini, Nadia; Convento, Silvia; Stucchi, Natale
2015-11-16
Human movements conform to specific kinematic laws of motion. One of such laws, the "two-thirds power law", describes the systematic co-variation between curvature and velocity of body movements. Noticeably, the same law also influences the perception of moving stimuli: the velocity of a dot moving along a curvilinear trajectory is perceived as uniform when the dot kinematics complies with the two-thirds power law. Instead, if the dot moves at constant speed, its velocity is perceived as highly non-uniform. This dynamic visual illusion points to a strong coupling between action and perception; however, how this coupling is implemented in the brain remains elusive. In this study, we tested whether the premotor cortex (PM) and the primary visual cortex (V1) play a role in the illusion by means of transcranial Direct Current Stimulation (tDCS). All participants underwent three tDCS sessions during which they received active or sham cathodal tDCS (1.5mA) over PM or V1 of the left hemisphere. During tDCS, participants were required to adjust the velocity of a dot moving along an elliptical trajectory until it looked uniform across the whole trajectory. Results show that occipital tDCS decreases the illusion variability both within and across participants, as compared to sham tDCS. This means that V1 stimulation increases individual sensitivity to the illusory motion and also increases coherence across different observers. Conversely, the illusion seems resistant to tDCS in terms of its magnitude, with cathodal stimulation of V1 or PM not affecting the amount of the illusory effect. Our results provide evidence for strong visuo-motor coupling in visual perception: the velocity of a dot moving along an elliptical trajectory is perceived as uniform only when its kinematics closely complies to the same law of motion that constrains human movement production. Occipital stimulation by cathodal tDCS can stabilize such illusory percept. Copyright © 2015 Elsevier Ireland Ltd
Catalina Segura; Davide Lazzati; Arumugam Sankarasubramanian
2013-01-01
A recent study employed a broken power-law (BPL) distribution for understanding the scaling frequency of bankfull discharge in snowmelt-dominated basins. This study, grounded from those findings, investigated the ability of a BPL function to describe the distribution of daily flows above the mean annual flow in 1217 sites across the conterminous U.S. (CONUS). The...
NASA Technical Reports Server (NTRS)
Goodman, Michael L.; Kwan, Chiman; Ayhan, Bulent; Shang, Eric L.
2017-01-01
A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model pre- dicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic & Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q-s, above an AR dependent threshold value of Q, where 0.3952 < or = s < or = 0.5298 with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. Observations show that the number of occurrences N(E) of coronal flares with a total energy released > or = E obeys the same type of distribution, N(E) / E-S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.
NASA Technical Reports Server (NTRS)
Goodman, Michael L.; Kwan, Chiman; Ayhan, Bulent; Shang, Eric L.
2017-01-01
A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model predicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q-s, above an AR dependent threshold value of Q, where 0.3952 < or = s < or = 0.5298 with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. Observations show that the number of occurrences N(E) of coronal flares with a total energy released > or = E obeys the same type of distribution, N(E) / E-S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.
NASA Astrophysics Data System (ADS)
Iorio, L.
2012-07-01
We put independent model dynamical constraints on the net electric charge Q of some astronomical and astrophysical objects by assuming that their exterior spacetimes are described by the Reissner-Nordström, metric, which induces an additional potential {U_RN ∝ Q^2 r^{-2}}. From the current bounds {Δ dot \\varpi} on any anomalies in the secular perihelion rate {dot \\varpi} of Mercury and the Earth-mercury ranging Δ ρ, we have {|Q_{⊙}| ≲ 1-0.4 × 10^{18} C}. Such constraints are 60-200 times tighter than those recently inferred in literature. For the Earth, the perigee precession of the Moon, determined with the Lunar Laser Ranging technique, and the intersatellite ranging Δ ρ for the GRACE mission yield {|Q_{⊕} | ≲ 5-0.4 × 10^{14} C}. The periastron rate of the double pulsar PSR J0737-3039A/B system allows to infer {|Q_NS | ≲ 5× 10^{19} C}. According to the perinigricon precession of the main sequence S2 star in Sgr A*, the electric charge carried by the compact object hosted in the Galactic Center may be as large as {|Q_{bullet} | ≲ 4× 10^{27} C}. Our results extend to other hypothetical power-law interactions inducing extra-potentials {U_pert = Ψ r^{-2}} as well. It turns out that the terrestrial GRACE mission yields the tightest constraint on the parameter {Ψ}, assumed as a universal constant, amounting to {|Ψ| ≲ 5× 109 {m^4 s^{-2}}}.
Wong, Wing-Cheong; Ng, Hong-Kiat; Tantoso, Erwin; Soong, Richie; Eisenhaber, Frank
2018-02-12
Though earlier works on modelling transcript abundance from vertebrates to lower eukaroytes have specifically singled out the Zip's law, the observed distributions often deviate from a single power-law slope. In hindsight, while power-laws of critical phenomena are derived asymptotically under the conditions of infinite observations, real world observations are finite where the finite-size effects will set in to force a power-law distribution into an exponential decay and consequently, manifests as a curvature (i.e., varying exponent values) in a log-log plot. If transcript abundance is truly power-law distributed, the varying exponent signifies changing mathematical moments (e.g., mean, variance) and creates heteroskedasticity which compromises statistical rigor in analysis. The impact of this deviation from the asymptotic power-law on sequencing count data has never truly been examined and quantified. The anecdotal description of transcript abundance being almost Zipf's law-like distributed can be conceptualized as the imperfect mathematical rendition of the Pareto power-law distribution when subjected to the finite-size effects in the real world; This is regardless of the advancement in sequencing technology since sampling is finite in practice. Our conceptualization agrees well with our empirical analysis of two modern day NGS (Next-generation sequencing) datasets: an in-house generated dilution miRNA study of two gastric cancer cell lines (NUGC3 and AGS) and a publicly available spike-in miRNA data; Firstly, the finite-size effects causes the deviations of sequencing count data from Zipf's law and issues of reproducibility in sequencing experiments. Secondly, it manifests as heteroskedasticity among experimental replicates to bring about statistical woes. Surprisingly, a straightforward power-law correction that restores the distribution distortion to a single exponent value can dramatically reduce data heteroskedasticity to invoke an instant increase in
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.
NASA Astrophysics Data System (ADS)
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
NASA Astrophysics Data System (ADS)
Biham, Ofer; Malcai, Ofer; Levy, Moshe; Solomon, Sorin
1998-08-01
The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form wi(t+1)=λ(t)wi(t)+aw¯(t)-bwi(t)w¯(t) is studied by computer simulations. The variables wi, i=1,...,N, are the individual system components and w¯(t)=(1/N)∑iwi(t) is their average. The parameters a and b are constants, while λ(t) is randomly chosen at each time step from a given distribution. Models of this type describe the temporal evolution of a large variety of systems such as stock markets and city populations. These systems are characterized by a large number of interacting objects and the dynamics is dominated by multiplicative processes. The instantaneous probability distribution P(w,t) of the system components wi turns out to fulfill a Pareto power law P(w,t)~w-1-α. The time evolution of w¯(t) presents intermittent fluctuations parametrized by a Lévy-stable distribution with the same index α, showing an intricate relation between the distribution of the wi's at a given time and the temporal fluctuations of their average.
Zhang, Qun; Zhang, Qunzhi; Sornette, Didier
2016-01-01
We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the “S&P 500 1987” bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs. PMID:27806093
NASA Astrophysics Data System (ADS)
Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.
2016-10-01
Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent dynamics. The present work strengthens this connection by providing a general picture of the relaxation process of isolated lattice many-body quantum systems that are routinely studied in experiments with cold atoms, ions traps, and nuclear magnetic resonance. We show numerically and analytically that the long-time decay of the probability for finding the system in its initial state necessarily shows a power-law behavior ∝t-γ . This happens independently of the details of the system, such as integrability, level repulsion, and the presence or absence of disorder. Information about the spectrum, the structure of the initial state, and the number of particles that interact simultaneously is contained in the value of γ . From it, we can anticipate whether the initial state will or will not thermalize.
Zhang, Qun; Zhang, Qunzhi; Sornette, Didier
2016-01-01
We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the "S&P 500 1987" bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs.
Magnetic Pumping as a Source of Particle Heating and Power-law Distributions in the Solar Wind
NASA Astrophysics Data System (ADS)
Lichko, E.; Egedal, J.; Daughton, W.; Kasper, J.
2017-12-01
Based on the rate of expansion of the solar wind, the plasma should cool rapidly as a function of distance to the Sun. Observations show this is not the case. In this work, a magnetic pumping model is developed as a possible explanation for the heating and the generation of power-law distribution functions observed in the solar wind plasma. Most previous studies in this area focus on the role that the dissipation of turbulent energy on microscopic kinetic scales plays in the overall heating of the plasma. However, with magnetic pumping, particles are energized by the largest-scale turbulent fluctuations, thus bypassing the energy cascade. In contrast to other models, we include the pressure anisotropy term, providing a channel for the large-scale fluctuations to heat the plasma directly. A complete set of coupled differential equations describing the evolution, and energization, of the distribution function are derived, as well as an approximate closed-form solution. Numerical simulations using the VPIC kinetic code are applied to verify the model’s analytical predictions. The results of the model for realistic solar wind scenario are computed, where thermal streaming of particles are important for generating a phase shift between the magnetic perturbations and the pressure anisotropy. In turn, averaged over a pump cycle, the phase shift permits mechanical work to be converted directly to heat in the plasma. The results of this scenario show that magnetic pumping may account for a significant portion of the solar wind energization.
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
NASA Astrophysics Data System (ADS)
Scott, James F.; Evans, Donald M.; Katiyar, Ram S.; McQuaid, Raymond G. P.; Gregg, J. Marty
2017-08-01
Since the 1935 work of Landau-Lifshitz and of Kittel in 1946 all ferromagnetic, ferroelectric, and ferroelastic domains have been thought to be straight-sided with domain widths proportional to the square root of the sample thickness. We show in the present work that this is not true. We also discover period doubling domains predicted by Metaxas et al (2008 Phys. Rev. Lett. 99 217208) and modeled by Wang and Zhao (2015 Sci. Rep. 5 8887). We examine non-equilibrium ferroic domain structures in perovskite oxides with respect to folding, wrinkling, and relaxation and suggest that structures are kinetically limited and in the viscous flow regime predicted by Metaxas et al in 2008 but never observed experimentally. Comparisons are made with liquid crystals and hydrodynamic instabilities, including chevrons, and fractional power-law relaxation. As Shin et al (2016 Soft Matter 12 3502) recently emphasized: ‘An understanding of how these folds initiate, propagate, and interact with each other is still lacking’. Inside each ferroelastic domain are ferroelectric 90° nano-domains with 10 nm widths and periodicity in agreement with the 10 nm theoretical minima predicted by Feigl et al (2014 Nat. Commun. 5 4677). Evidence is presented for domain-width period doubling, which is common in polymer films but unknown in ferroic domains. A discussion of the folding-to-period doubling phase transition model of Wang and Zhao is included.
Size effect and scaling power-law for superelasticity in shape-memory alloys at the nanoscale.
Gómez-Cortés, Jose F; Nó, Maria L; López-Ferreño, Iñaki; Hernández-Saz, Jesús; Molina, Sergio I; Chuvilin, Andrey; San Juan, Jose M
2017-08-01
Shape-memory alloys capable of a superelastic stress-induced phase transformation and a high displacement actuation have promise for applications in micro-electromechanical systems for wearable healthcare and flexible electronic technologies. However, some of the fundamental aspects of their nanoscale behaviour remain unclear, including the question of whether the critical stress for the stress-induced martensitic transformation exhibits a size effect similar to that observed in confined plasticity. Here we provide evidence of a strong size effect on the critical stress that induces such a transformation with a threefold increase in the trigger stress in pillars milled on [001] L2 1 single crystals from a Cu-Al-Ni shape-memory alloy from 2 μm to 260 nm in diameter. A power-law size dependence of n = -2 is observed for the nanoscale superelasticity. Our observation is supported by the atomic lattice shearing and an elastic model for homogeneous martensite nucleation.
Cai, PingGen; Takahashi, Ryosuke; Kuribayashi-Shigetomi, Kaori; Subagyo, Agus; Sueoka, Kazuhisa; Maloney, John M; Van Vliet, Krystyn J; Okajima, Takaharu
2017-08-08
Changes in the cytoskeletal organization within cells can be characterized by large spatial and temporal variations in rheological properties of the cell (e.g., the complex shear modulus G ∗ ). Although the ensemble variation in G ∗ of single cells has been elucidated, the detailed temporal variation of G ∗ remains unknown. In this study, we investigated how the rheological properties of individual fibroblast cells change under a spatially confined environment in which the cell translational motion is highly restricted and the whole cell shape remains unchanged. The temporal evolution of single-cell rheology was probed at the same measurement location within the cell, using atomic force microscopy-based oscillatory deformation. The measurements reveal that the temporal variation in the power-law rheology of cells is quantitatively consistent with the ensemble variation, indicating that the cell system satisfies an ergodic hypothesis in which the temporal statistics are identical to the ensemble statistics. The autocorrelation of G ∗ implies that the cell mechanical state evolves in the ensemble of possible states with a characteristic timescale. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
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.
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 .
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.
Magnetic Pumping as a Source of Particle Heating and Power-Law Distributions in the Solar Wind
Lichko, Emily Rose; Egedal, Jan; Daughton, William Scott
Based on the rate of expansion of the solar wind, the plasma should cool rapidly as a function of distance to the Sun. Observations show this is not the case. In this work, a magnetic pumping model is developed as a possible explanation for the heating and the generation of power-law distribution functions observed in the solar wind plasma. Most previous studies in this area focus on the role that the dissipation of turbulent energy on microscopic kinetic scales plays in the overall heating of the plasma. However, with magnetic pumping, particles are energized by the largest-scale turbulent fluctuations, thusmore » bypassing the energy cascade. In contrast to other models, we include the pressure anisotropy term, providing a channel for the large-scale fluctuations to heat the plasma directly. A complete set of coupled differential equations describing the evolution, and energization, of the distribution function are derived, as well as an approximate closed-form solution. Numerical simulations using the VPIC kinetic code are applied to verify the model's analytical predictions. The results of the model for realistic solar wind scenario are computed, where thermal streaming of particles are important for generating a phase shift between the magnetic perturbations and the pressure anisotropy. In turn, averaged over a pump cycle, the phase shift permits mechanical work to be converted directly to heat in the plasma. Here, the results of this scenario show that magnetic pumping may account for a significant portion of the solar wind energization.« less
Magnetic Pumping as a Source of Particle Heating and Power-Law Distributions in the Solar Wind
Lichko, Emily Rose; Egedal, Jan; Daughton, William Scott; ...
2017-11-27
Based on the rate of expansion of the solar wind, the plasma should cool rapidly as a function of distance to the Sun. Observations show this is not the case. In this work, a magnetic pumping model is developed as a possible explanation for the heating and the generation of power-law distribution functions observed in the solar wind plasma. Most previous studies in this area focus on the role that the dissipation of turbulent energy on microscopic kinetic scales plays in the overall heating of the plasma. However, with magnetic pumping, particles are energized by the largest-scale turbulent fluctuations, thusmore » bypassing the energy cascade. In contrast to other models, we include the pressure anisotropy term, providing a channel for the large-scale fluctuations to heat the plasma directly. A complete set of coupled differential equations describing the evolution, and energization, of the distribution function are derived, as well as an approximate closed-form solution. Numerical simulations using the VPIC kinetic code are applied to verify the model's analytical predictions. The results of the model for realistic solar wind scenario are computed, where thermal streaming of particles are important for generating a phase shift between the magnetic perturbations and the pressure anisotropy. In turn, averaged over a pump cycle, the phase shift permits mechanical work to be converted directly to heat in the plasma. Here, the results of this scenario show that magnetic pumping may account for a significant portion of the solar wind energization.« less
NASA Astrophysics Data System (ADS)
Testan, Peter R.
1987-04-01
A number of Color Hard Copy (CHC) market drivers are currently indicating strong growth in the use of CHC technologies for the business graphics marketplace. These market drivers relate to product, software, color monitors and color copiers. The use of color in business graphics allows more information to be relayed than is normally the case in a monochrome format. The communicative powers of full-color computer generated output in the business graphics application area will continue to induce end users to desire and require color in their future applications. A number of color hard copy technologies will be utilized in the presentation graphics arena. Thermal transfer, ink jet, photographic and electrophotographic technologies are all expected to be utilized in the business graphics presentation application area in the future. Since the end of 1984, the availability of color application software packages has grown significantly. Sales revenue generated by business graphics software is expected to grow at a compound annual growth rate of just over 40 percent to 1990. Increased availability of packages to allow the integration of text and graphics is expected. Currently, the latest versions of page description languages such as Postscript, Interpress and DDL all support color output. The use of color monitors will also drive the demand for color hard copy in the business graphics market place. The availability of higher resolution screens is allowing color monitors to be easily used for both text and graphics applications in the office environment. During 1987, the sales of color monitors are expected to surpass the sales of monochrome monitors. Another major color hard copy market driver will be the color copier. In order to take advantage of the communications power of computer generated color output, multiple copies are required for distribution. Product introductions of a new generation of color copiers is now underway with additional introductions expected
Dias, W S; Bertrand, D; Lyra, M L
2017-06-01
Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.
NASA Astrophysics Data System (ADS)
Dias, W. S.; Bertrand, D.; Lyra, M. L.
2017-06-01
Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d >4 .
NASA Astrophysics Data System (ADS)
Abou-zeid, Mohamed Y.; Mohamed, Mona A. A.
2017-09-01
This article is an analytic discussion for the motion of power-law nanofluid with heat transfer under the effect of viscous dissipation, radiation, and internal heat generation. The governing equations are discussed under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using homotopy perturbation method. Results for the behaviours of the axial velocity, temperature, and nanoparticles as well as the skin friction coefficient, reduced Nusselt number, and Sherwood number with other physical parameters are obtained graphically and analytically. It is found that as the power-law exponent increases, both the axial velocity and temperature increase, whereas nanoparticles decreases. These results may have applicable importance in the research discussions of nanofluid flow in channels with small diameters under the effect of different temperature distributions.
NASA Astrophysics Data System (ADS)
Reynolds, A. M.
2008-07-01
The results of numerical simulations indicate that deterministic walks with inverse-square power-law scaling are a robust emergent property of predators that use chemotaxis to locate randomly and sparsely distributed stationary prey items. It is suggested that chemotactic destructive foraging accounts for the apparent Lévy flight movement patterns of Oxyrrhis marina microzooplankton in still water containing prey items. This challenges the view that these organisms are executing an innate optimal Lévy flight searching strategy. Crucial for the emergence of inverse-square power-law scaling is the tendency of chemotaxis to occasionally cause predators to miss the nearest prey item, an occurrence which would not arise if prey were located through the employment of a reliable cognitive map or if prey location were visually cued and perfect.
Pham, A J; Schilling, M W; Yoon, Y; Kamadia, V V; Marshall, D L
2008-05-01
The objectives of this study were to characterize volatile compounds and to determine the characteristic aromas associated with impact compounds in 4 fish sauces using solid-phase micro-extraction, gas chromatography-mass spectrometry, Osme, and gas chromatography olfactometry (SPME-Osme-GCO) coupled with Stevens' Power Law. Compounds were separated using GCMS and GCO and were identified with the mass spectral database, aroma perceived at the sniffing port, retention indices, and verification of compounds by authentic standards in the GCMS and GCO. Aromas that were isolated and present in all 4 fish sauce samples at all concentrations included fishy (trimethylamine), pungent and dirty socks (combination of butanoic, pentanoic, hexanoic, and heptanoic acids), cooked rice and buttery popcorn (2,6-dimethyl pyrazine), and sweet and cotton candy (benzaldehyde). All fish sauces contained the same aromas as determined by GCO and GCMS (verified using authentic standard compounds), but the odor intensity associated with each compound or group of compounds was variable for different fish sauce samples. Stevens' Power Law exponents were also determined using this analytical technique, but exponents were not consistent for the same compounds that were found in all fish sauces. Stevens' Power Law exponents ranged from 0.14 to 0.37, 0.24 to 0.34, 0.09 to 0.21, and 0.10 to 0.35 for dirty socks, fishy, buttery popcorn, and sweet aromas, respectively. This demonstrates that there is variability in Stevens' Power Law exponents for odorants within fish sauce samples.
2011-03-01
An e?ective Nonlinear Schr?dinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a... soliton amplitude profiles are displayed as a hyperbolic secant function and hold there profile at short distances on the order of centimeters. Dark ...spatial solitons are similar but have hyperbolic tangent type profiles. Dark spatial solitons were first observed by Jerominek in 1985 and Belanger and
Kaltenbach, Benjamin; Bucher, Andreas M; Wichmann, Julian L; Nickel, Dominik; Polkowski, Christoph; Hammerstingl, Renate; Vogl, Thomas J; Bodelle, Boris
2017-11-01
The aim of this study was to assess the feasibility of a free-breathing dynamic liver imaging technique using a prototype Cartesian T1-weighted volumetric interpolated breathhold examination (VIBE) sequence with compressed sensing and simultaneous acquisition of a navigation signal for hard-gated and motion state-resolved reconstruction. A total of 43 consecutive oncologic patients (mean age, 66 ± 11 years; 44% female) underwent free-breathing dynamic liver imaging for the evaluation of liver metastases from colorectal cancer using a prototype Cartesian VIBE sequence (field of view, 380 × 345 mm; image matrix, 320 × 218; echo time/repetition time, 1.8/3.76 milliseconds; flip angle, 10 degrees; slice thickness, 3.0 mm; acquisition time, 188 seconds) with continuous data sampling and additionally acquired self-navigation signal. Data were iteratively reconstructed using 2 different approaches: first, a hard-gated reconstruction only using data associated to the dominating motion state (CS VIBE, Compressed Sensing VIBE), and second, a motion-resolved reconstruction with 6 different motion states as additional image dimension (XD VIBE, eXtended dimension VIBE). Continuous acquired data were grouped in 16 subsequent time increments with 11.57 seconds each to resolve arterial and venous contrast phases. For image quality assessment, both CS VIBE and XD VIBE were compared with the patient's last staging dynamic liver magnetic resonance imaging including a breathhold (BH) VIBE as reference standard 4.5 ± 1.2 months before. Representative quality parameters including respiratory artifacts were evaluated for arterial and venous phase images independently, retrospectively and blindly by 3 experienced radiologists, with higher scores indicating better examination quality. To assess diagnostic accuracy, same readers evaluated the presence of metastatic lesions for XD VIBE and CS VIBE compared with reference BH examination in a second session. Compared with CS VIBE, XD VIBE
NASA Technical Reports Server (NTRS)
Ashby, G. C., Jr.
1974-01-01
Experimental data have been obtained for two series of bodies at Mach 6 and Reynolds numbers, based on model length, from 1.4 million to 9.5 million. One series consisted of axisymmetric power-law bodies geometrically constrained for constant length and base diameter with values of the exponent n of 0.25, 0.5, 0.6, 0.667, 0.75, and 1.0. The other series consisted of positively and negatively cambered bodies of polygonal cross section, each having a constant longitudinal area distribution conforming to that required for minimizing zero-lift wave drag at hypersonic speeds under the geometric constraints of given length and volume. At the highest Reynolds number, the power-law body for minimum drag is blunter (exponent n lower) than predicted by inviscid theory (n approximately 0.6 instead of n = 0.667); however, the peak value of lift-drag ratio occurs at n = 0.667. Viscous effects were present on the bodies of polygonal cross section but were less pronounced than those on the power-law bodies. The trapezoidal bodies with maximum width at the bottom were found to have the highest maximum lift-drag ratio and the lowest mimimum drag.
NASA Astrophysics Data System (ADS)
Sato, Haruo; Fehler, Michael C.
2016-10-01
The envelope broadening and the peak delay of the S-wavelet of a small earthquake with increasing travel distance are results of scattering by random velocity inhomogeneities in the earth medium. As a simple mathematical model, Sato proposed a new stochastic synthesis of the scalar wavelet envelope in 3-D von Kármán type random media when the centre wavenumber of the wavelet is in the power-law spectral range of the random velocity fluctuation. The essential idea is to split the random medium spectrum into two components using the centre wavenumber as a reference: the long-scale (low-wavenumber spectral) component produces the peak delay and the envelope broadening by multiple scattering around the forward direction; the short-scale (high-wavenumber spectral) component attenuates wave amplitude by wide angle scattering. The former is calculated by the Markov approximation based on the parabolic approximation and the latter is calculated by the Born approximation. Here, we extend the theory for the envelope synthesis of a wavelet in 2-D random media, which makes it easy to compare with finite difference (FD) simulation results. The synthetic wavelet envelope is analytically written by using the random medium parameters in the angular frequency domain. For the case that the power spectral density function of the random velocity fluctuation has a steep roll-off at large wavenumbers, the envelope broadening is small and frequency independent, and scattering attenuation is weak. For the case of a small roll-off, however, the envelope broadening is large and increases with frequency, and the scattering attenuation is strong and increases with frequency. As a preliminary study, we compare synthetic wavelet envelopes with the average of FD simulation wavelet envelopes in 50 synthesized random media, which are characterized by the RMS fractional velocity fluctuation ε = 0.05, correlation scale a = 5 km and the background wave velocity V0 = 4 km s-1. We use the radiation
NASA Astrophysics Data System (ADS)
Mir, Mehedi Faruk; Muktadir Rahman, Md.; Dwaipayan, Debnath; Sakhawat Hossain Himel, Md.
2016-04-01
Energy fluctuation of ideal Fermi gas trapped under generic power law potential U=\\sumi=1d ci \\vertxi/ai \\vert n_i has been calculated in arbitrary dimensions. Energy fluctuation is scrutinized further in the degenerate limit μ ≫ KBT with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can not only exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d = 3 but also can describe the outcome for any power law potential in arbitrary dimension.
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
NASA Astrophysics Data System (ADS)
Cuansing, Eduardo C.; Liang, Gengchiau
2011-10-01
Time-dependent nonequilibrium Green's functions are used to study electron transport properties in a device consisting of two linear chain leads and a time-dependent interlead coupling that is switched on non-adiabatically. We derive a numerically exact expression for the particle current and examine its characteristics as it evolves in time from the transient regime to the long-time steady-state regime. We find that just after switch-on, the current initially overshoots the expected long-time steady-state value, oscillates and decays as a power law, and eventually settles to a steady-state value consistent with the value calculated using the Landauer formula. The power-law parameters depend on the values of the applied bias voltage, the strength of the couplings, and the speed of the switch-on. In particular, the oscillating transient current decays away longer for lower bias voltages. Furthermore, the power-law decay nature of the current suggests an equivalent series resistor-inductor-capacitor circuit wherein all of the components have time-dependent properties. Such dynamical resistive, inductive, and capacitive influences are generic in nano-circuits where dynamical switches are incorporated. We also examine the characteristics of the dynamical current in a nano-oscillator modeled by introducing a sinusoidally modulated interlead coupling between the two leads. We find that the current does not strictly follow the sinusoidal form of the coupling. In particular, the maximum current does not occur during times when the leads are exactly aligned. Instead, the times when the maximum current occurs depend on the values of the bias potential, nearest-neighbor coupling, and the interlead coupling.
Patel, Mainak; Rangan, Aaditya
2017-08-07
Infant rats randomly cycle between the sleeping and waking states, which are tightly correlated with the activity of mutually inhibitory brainstem sleep and wake populations. Bouts of sleep and wakefulness are random; from P2-P10, sleep and wake bout lengths are exponentially distributed with increasing means, while during P10-P21, the sleep bout distribution remains exponential while the distribution of wake bouts gradually transforms to power law. The locus coeruleus (LC), via an undeciphered interaction with sleep and wake populations, has been shown experimentally to be responsible for the exponential to power law transition. Concurrently during P10-P21, the LC undergoes striking physiological changes - the LC exhibits strong global 0.3 Hz oscillations up to P10, but the oscillation frequency gradually rises and synchrony diminishes from P10-P21, with oscillations and synchrony vanishing at P21 and beyond. In this work, we construct a biologically plausible Wilson Cowan-style model consisting of the LC along with sleep and wake populations. We show that external noise and strong reciprocal inhibition can lead to switching between sleep and wake populations and exponentially distributed sleep and wake bout durations as during P2-P10, with the parameters of inhibition between the sleep and wake populations controlling mean bout lengths. Furthermore, we show that the changing physiology of the LC from P10-P21, coupled with reciprocal excitation between the LC and wake population, can explain the shift from exponential to power law of the wake bout distribution. To our knowledge, this is the first study that proposes a plausible biological mechanism, which incorporates the known changing physiology of the LC, for tying the developing sleep-wake circuit and its interaction with the LC to the transformation of sleep and wake bout dynamics from P2-P21. Copyright © 2017 Elsevier Ltd. All rights reserved.
Long-Term Variability of AGN at Hard X-Rays
NASA Technical Reports Server (NTRS)
Soldi, S.; Beckmann, V.; Baumgartner W. H.; Ponti, G.; Shrader, C. R.; Lubinski, P.; Krimm, H. A.; Mattana, F.; Tueller, J.
2013-01-01
Variability at all observed wavelengths is a distinctive property of active galactic nuclei (AGN). Hard X-rays provide us with a view of the innermost regions of AGN, mostly unbiased by absorption along the line of sight. Characterizing the intrinsic hard X-ray variability of a large AGN sample and comparing it to the results obtained at lower X-ray energies can significantly contribute to our understanding of the mechanisms underlying the high-energy radiation. Methods. Swift/BAT provides us with the unique opportunity to follow, on time scales of days to years and with a regular sampling, the 14-195 keV emission of the largest AGN sample available up to date for this kind of investigation. As a continuation of an early work on the first 9 months of BAT data, we study the amplitude of the variations, and their dependence on sub-class and on energy, for a sample of 110 radio quiet and radio loud AGN selected from the BAT 58-month survey. About 80 of the AGN in the sample are found to exhibit significant variability on months to years time scales, radio loud sources being the most variable. The amplitude of the variations and their energy dependence are incompatible with variability being driven at hard X-rays by changes of the absorption column density. In general, the variations in the 14-24 and 35-100 keV bands are well correlated, suggesting a common origin of the variability across the BAT energy band. However, radio quiet AGN display on average 10 larger variations at 14-24 keV than at 35-100 keV and a softer-when-brighter behavior for most of the Seyfert galaxies with detectable spectral variability on month time scale. In addition, sources with harder spectra are found to be more variable than softer ones. These properties are generally consistent with a variable power law continuum, in flux and shape, pivoting at energies 50 keV, to which a constant reflection component is superposed. When the same time scales are considered, the timing properties of AGN at
NASA Astrophysics Data System (ADS)
Wang, Jianhui; Ma, Yongli; He, Jizhou
2015-07-01
Based on quantum thermodynamic processes, we make a quantum-mechanical (QM) extension of the typical heat engine cycles, such as the Carnot, Brayton, Otto, Diesel cycles, etc., with no introduction of the concept of temperature. When these QM engine cycles are implemented by an ideal gas confined in an arbitrary power-law trap, a relation between the quantum adiabatic exponent and trap exponent is found. The differences and similarities between the efficiency of a given QM engine cycle and its classical counterpart are revealed and discussed.
NASA Astrophysics Data System (ADS)
Ye, Zhuo-Lin; Li, Wei-Sheng; Lai, Yi-Ming; He, Ji-Zhou; Wang, Jian-Hui
2015-12-01
We propose a quantum-mechanical Brayton engine model that works between two superposed states, employing a single particle confined in an arbitrary power-law trap as the working substance. Applying the superposition principle, we obtain the explicit expressions of the power and efficiency, and find that the efficiency at maximum power is bounded from above by the function: η+ = θ/(θ + 1), with θ being a potential-dependent exponent. Supported by the National Natural Science Foundation of China under Grant Nos. 11505091, 11265010, and 11365015, and the Jiangxi Provincial Natural Science Foundation under Grant No. 20132BAB212009
NASA Astrophysics Data System (ADS)
Chitra, M.; Karthikeyan, D.
2018-04-01
A mathematical model of non-Newtonian blood flow through a stenosed artery is considered. The steadynon-Newtonian model is chosen characterized by the generalized power-law model and Herschel-Bulkley model incorporating the effect of slip velocity due to steanosed artery with permeable wall. The effects of slip velocity for non-Newtonian nature of blood on velocity, flow rate and wall shear stress of the stenosed artery with permeable wall are solved analytically. The effects of various parameters such as slip parameter (λ), power index (m) and different thickness of the stenosis (δ) on velocity, volumetric flow rate and wall shear stress are discussed through graphs.
Transport coefficients for dense hard-disk systems.
García-Rojo, Ramón; Luding, Stefan; Brey, J Javier
2006-12-01
A study of the transport coefficients of a system of elastic hard disks based on the use of Helfand-Einstein expressions is reported. The self-diffusion, the viscosity, and the heat conductivity are examined with averaging techniques especially appropriate for event-driven molecular dynamics algorithms with periodic boundary conditions. The density and size dependence of the results are analyzed, and comparison with the predictions from Enskog's theory is carried out. In particular, the behavior of the transport coefficients in the vicinity of the fluid-solid transition is investigated and a striking power law divergence of the viscosity with density is obtained in this region, while all other examined transport coefficients show a drop in that density range in relation to the Enskog's prediction. Finally, the deviations are related to shear band instabilities and the concept of dilatancy.
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
2013-10-01
A statistical description of the all-particle cosmic-ray spectrum is given in the 10^{14}\\ \\text{eV} to 10^{20}\\ \\text{eV} interval. The high-energy cosmic-ray flux is modeled as an ultra-relativistic multi-component plasma, whose components constitute a mixture of nearly ideal but nonthermal gases of low density and high temperature. Each plasma component is described by an ultra-relativistic power-law density manifested as spectral peak in the wideband fit. The “knee” and “ankle” features of the high- and ultra-high-energy spectrum turn out to be the global and local extrema of the double-logarithmic E3-scaled flux representation in which the spectral fit is performed. The all-particle spectrum is covered by recent data sets from several air shower arrays, and can be modeled as three-component plasma in the indicated energy range extending over six decades. The temperature, specific number density, internal energy and entropy of each plasma component are extracted from the partial fluxes in the broadband fit. The grand partition function and the extensive entropy functional of a non-equilibrated gas mixture with power-law components are derived in phase space by ensemble averaging.
NASA Astrophysics Data System (ADS)
Schneider, Peter; Sluse, Dominique
2013-11-01
The light travel time differences in strong gravitational lensing systems allows an independent determination of the Hubble constant. This method has been successfully applied to several lens systems. The formally most precise measurements are, however, in tension with the recent determination of H0 from the Planck satellite for a spatially flat six-parameters ΛCDM cosmology. We reconsider the uncertainties of the method, concerning the mass profile of the lens galaxies, and show that the formal precision relies on the assumption that the mass profile is a perfect power law. Simple analytical arguments and numerical experiments reveal that mass-sheet like transformations yield significant freedom in choosing the mass profile, even when exquisite Einstein rings are observed. Furthermore, the characterization of the environment of the lens does not break that degeneracy which is not physically linked to extrinsic convergence. We present an illustrative example where the multiple imaging properties of a composite (baryons + dark matter) lens can be extremely well reproduced by a power-law model having the same velocity dispersion, but with predictions for the Hubble constant that deviate by ~20%. Hence we conclude that the impact of degeneracies between parametrized models have been underestimated in current H0 measurements from lensing, and need to be carefully reconsidered.
NASA Astrophysics Data System (ADS)
Varotsos, C. A.; Efstathiou, M. N.
2018-03-01
In this paper we investigate the evolution of the energy emitted by CO2 and NO from the Earth's thermosphere on a global scale using both observational and empirically derived data. In the beginning, we analyze the daily power observations of CO2 and NO received from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) equipment on the NASA Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite for the entire period 2002-2016. We then perform the same analysis on the empirical daily power emitted by CO2 and NO that were derived recently from the infrared energy budget of the thermosphere during 1947-2016. The tool used for the analysis of the observational and empirical datasets is the detrended fluctuation analysis, in order to investigate whether the power emitted by CO2 and by NO from the thermosphere exhibits power-law behavior. The results obtained from both observational and empirical data do not support the establishment of the power-law behavior. This conclusion reveals that the empirically derived data are characterized by the same intrinsic properties as those of the observational ones, thus enhancing the validity of their reliability.
Bhattacharjee, Saikat; Mondal, Mrinmoy; De, Sirshendu
2017-05-01
Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye-Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential -73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
NASA Astrophysics Data System (ADS)
Iwamatsu, Masao
2017-10-01
The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle θ of a droplet obeys a power-law decay θ ˜t-α except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent α of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.
NASA Astrophysics Data System (ADS)
Wang, X.; Wu, H.; Tu, C. Y.; Wang, L.; He, J.; Tian, H.
2017-12-01
Sunward-propagating Alfvénic fluctuations with a power-law spectrum (SAFP) have been recently reported to be a significant physical phenomenon in the solar wind. However, some characteristics of these SAFPs are still unknown. Here we develop a new method for identifying SAFPs. In this method, we can identify all SAFPs with any value of θRB (angle between the global magnetic field and the radial direction). We find 508 SAFPs using the WIND spacecraft observation from 1995 to 2014. We also find that SAFP occurs more frequently when θRB equals 90°. The spectral index with an average -1.77 changes continuously from -2.18 for the parallel to -1.71 for the perpendicular. SAFPs occur more at the maximum and tend to be observed in the slow solar wind especially at solar minimum. We also apply the new method to identify anti-sunward-propagating Alfvénic fluctuations with a power-law spectrum (AFP) for comparison. The number of SAFPs is much less than AFPs, and the cases with local bending account for about half of all observed cases. SAFPs have a preference for negative σc and ASFs for positive. The statistical results demonstrate that SAFP has a steeper and weaker power spectrum and present a weaker power anisotropy than that of AFP. These new results may reveal new insight into the physical mechanism of the SAFP generation.
NASA Technical Reports Server (NTRS)
Bigger, J. T. Jr; Steinman, R. C.; Rolnitzky, L. M.; Fleiss, J. L.; Albrecht, P.; Cohen, R. J.
1996-01-01
BACKGROUND. The purposes of the present study were (1) to establish normal values for the regression of log(power) on log(frequency) for, RR-interval fluctuations in healthy middle-aged persons, (2) to determine the effects of myocardial infarction on the regression of log(power) on log(frequency), (3) to determine the effect of cardiac denervation on the regression of log(power) on log(frequency), and (4) to assess the ability of power law regression parameters to predict death after myocardial infarction. METHODS AND RESULTS. We studied three groups: (1) 715 patients with recent myocardial infarction; (2) 274 healthy persons age and sex matched to the infarct sample; and (3) 19 patients with heart transplants. Twenty-four-hour RR-interval power spectra were computed using fast Fourier transforms and log(power) was regressed on log(frequency) between 10(-4) and 10(-2) Hz. There was a power law relation between log(power) and log(frequency). That is, the function described a descending straight line that had a slope of approximately -1 in healthy subjects. For the myocardial infarction group, the regression line for log(power) on log(frequency) was shifted downward and had a steeper negative slope (-1.15). The transplant (denervated) group showed a larger downward shift in the regression line and a much steeper negative slope (-2.08). The correlation between traditional power spectral bands and slope was weak, and that with log(power) at 10(-4) Hz was only moderate. Slope and log(power) at 10(-4) Hz were used to predict mortality and were compared with the predictive value of traditional power spectral bands. Slope and log(power) at 10(-4) Hz were excellent predictors of all-cause mortality or arrhythmic death. To optimize the prediction of death, we calculated a log(power) intercept that was uncorrelated with the slope of the power law regression line. We found that the combination of slope and zero-correlation log(power) was an outstanding predictor, with a
Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.
2013-01-10
We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlomore » sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling
NASA Astrophysics Data System (ADS)
Weisz, Daniel R.; Fouesneau, Morgan; Hogg, David W.; Rix, Hans-Walter; Dolphin, Andrew E.; Dalcanton, Julianne J.; Foreman-Mackey, Daniel T.; Lang, Dustin; Johnson, L. Clifton; Beerman, Lori C.; Bell, Eric F.; Gordon, Karl D.; Gouliermis, Dimitrios; Kalirai, Jason S.; Skillman, Evan D.; Williams, Benjamin F.
2013-01-01
We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M >~ 1 M ⊙). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, α, are unbiased and that the uncertainty, Δα, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on α, and provide an analytic approximation for Δα as a function of the observed number of stars and mass range. Comparison with literature studies shows that ~3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield langαrang = 2.46, with a 1σ dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF
NASA Astrophysics Data System (ADS)
Olajuwon, B. I.; Oyelakin, I. S.
2012-12-01
The paper investigates convection heat and mass transfer in power law fluid flow with non relaxation time past a vertical porous plate in presence of a chemical reaction, heat generation, thermo diffu- sion and thermal diffusion. The non - linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration profiles for pseudo plastic fluids and for different values of parameters governing the prob- lem. The skin friction, heat transfer and mass transfer rates are presented numerically in tabular form. The results show that these parameters have significant effects on the flow, heat transfer and mass transfer.
NASA Astrophysics Data System (ADS)
Bahauddin, Shah Mohammad; Mehedi Faruk, Mir
2016-09-01
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.
NASA Technical Reports Server (NTRS)
Ashby, G. C., Jr.; Harris, J. E.
1974-01-01
Wave and skin-friction drag have been numerically calculated for a series of power-law bodies at a Mach number of 6 and Reynolds numbers, based on body length, from 1.5 million to 9.5 million. Pressure distributions were computed on the nose by the inverse method and on the body by the method of characteristics. These pressure distributions and the measured locations of boundary-layer transition were used in a nonsimilar-boundary-layer program to determine viscous effects. A coupled iterative approach between the boundary-layer and pressure-distribution programs was used to account for boundary-layer displacement-thickness effects. The calculated-drag coefficients compared well with previously obtained experimental data.
NASA Astrophysics Data System (ADS)
Zimmerman, R. W.; Leung, C. T.
2009-12-01
Most oil and gas reservoirs, as well as most potential sites for nuclear waste disposal, are naturally fractured. In these sites, the network of fractures will provide the main path for fluid to flow through the rock mass. In many cases, the fracture density is so high as to make it impractical to model it with a discrete fracture network (DFN) approach. For such rock masses, it would be useful to have recourse to analytical, or semi-analytical, methods to estimate the macroscopic hydraulic conductivity of the fracture network. We have investigated single-phase fluid flow through generated stochastically two-dimensional fracture networks. The centers and orientations of the fractures are uniformly distributed, whereas their lengths follow a lognormal distribution. The aperture of each fracture is correlated with its length, either through direct proportionality, or through a nonlinear relationship. The discrete fracture network flow and transport simulator NAPSAC, developed by Serco (Didcot, UK), is used to establish the “true” macroscopic hydraulic conductivity of the network. We then attempt to match this value by starting with the individual fracture conductances, and using various upscaling methods. Kirkpatrick’s effective medium approximation, which works well for pore networks on a core scale, generally underestimates the conductivity of the fracture networks. We attribute this to the fact that the conductances of individual fracture segments (between adjacent intersections with other fractures) are correlated with each other, whereas Kirkpatrick’s approximation assumes no correlation. The power-law averaging approach proposed by Desbarats for porous media is able to match the numerical value, using power-law exponents that generally lie between 0 (geometric mean) and 1 (harmonic mean). The appropriate exponent can be correlated with statistical parameters that characterize the fracture density.
Sugimori, Michiya; Hayakawa, Yumiko; Koh, Masaki; Hayashi, Tomohide; Tamura, Ryoi; Kuroda, Satoshi
2018-01-01
Glioblastoma resists chemoradiotherapy, then, recurs to be a fatal space-occupying lesion. The recurrence is caused by re-growing cell populations such as glioma stem cells (GSCs), suggesting that GSC populations should be targeted. This study addressed whether a novel anti-cancer drug, OTS964, an inhibitor for T-LAK cell originated protein kinase (TOPK), is effective in reducing the size of the heterogeneous GSC populations, a power-law coded heterogeneous GSC populations consisting of glioma sphere (GS) clones, by detailing quantitative growth properties. We found that OTS964 killed GS clones while suppressing the growth of surviving GS clones, thus identifying clone-eliminating and growth-disturbing efficacies of OTS964. The efficacies led to a significant size reduction in GS populations in a dose-dependent manner. The surviving GS clones reconstructed GS populations in the following generations; the recovery of GS populations fits a recurrence after the chemotherapy. The recovering GS clones resisted the clone-eliminating effect of OTS964 in sequential exposure during the growth recovery. However, surprisingly, the resistant properties of the recovered-GS clones had been plastically canceled during self-renewal, and then the GS clones had become re-sensitive to OTS964. Thus, OTS964 targets GSCs to eliminate them or suppress their growth, resulting in shrinkage of the power-law coded GSC populations. We propose a therapy focusing on long-term control in recurrence of glioblastoma via reducing the size of the GSC populations by OTS964. PMID:29423027
Sugimori, Michiya; Hayakawa, Yumiko; Koh, Masaki; Hayashi, Tomohide; Tamura, Ryoi; Kuroda, Satoshi
2018-01-09
Glioblastoma resists chemoradiotherapy, then, recurs to be a fatal space-occupying lesion. The recurrence is caused by re-growing cell populations such as glioma stem cells (GSCs), suggesting that GSC populations should be targeted. This study addressed whether a novel anti-cancer drug, OTS964, an inhibitor for T-LAK cell originated protein kinase (TOPK), is effective in reducing the size of the heterogeneous GSC populations, a power-law coded heterogeneous GSC populations consisting of glioma sphere (GS) clones, by detailing quantitative growth properties. We found that OTS964 killed GS clones while suppressing the growth of surviving GS clones, thus identifying clone-eliminating and growth-disturbing efficacies of OTS964. The efficacies led to a significant size reduction in GS populations in a dose-dependent manner. The surviving GS clones reconstructed GS populations in the following generations; the recovery of GS populations fits a recurrence after the chemotherapy. The recovering GS clones resisted the clone-eliminating effect of OTS964 in sequential exposure during the growth recovery. However, surprisingly, the resistant properties of the recovered-GS clones had been plastically canceled during self-renewal, and then the GS clones had become re-sensitive to OTS964. Thus, OTS964 targets GSCs to eliminate them or suppress their growth, resulting in shrinkage of the power-law coded GSC populations. We propose a therapy focusing on long-term control in recurrence of glioblastoma via reducing the size of the GSC populations by OTS964.
NASA Astrophysics Data System (ADS)
Kristensen, Erik; Delefosse, Matthieu; Quintana, Cintia O.; Banta, Gary T.; Petersen, Hans Christian; Jørgensen, Bent
2013-03-01
The lack of a common statistical approach describing the distribution and dispersion pattern of marine benthic animals has often hampered the comparability among studies. The purpose of this study is therefore to apply an alternative approach, Taylor's power law, to data on spatial and temporal distribution of 9 dominating benthic invertebrate species from two study areas, the estuaries Odense Fjord and Roskilde Fjord, Denmark. The slope (b) obtained from the power relationship of sample variance (s2) versus mean (μ) appears to be species-specific and independent of location and time. It ranges from a low of ~ 1 for large-bodied (> 1 mg AFDW) species (e.g. Marenzelleria viridis, Nereis diversicolor) to a high of 1.6-1.9 for small-bodied (< 1 mg AFDW) species (e.g. Pygospio elegans and Tubificoides benedii). Accordingly, b is apparently a valuable species-specific dispersion index based on biological factors such as behavior and intraspecific interactions. Thus, at the examined spatial scale, the more intense intraspecific interactions (e.g. territoriality) cause less aggregated distribution patterns among large- than small-bodied invertebrates. The species-specific interactions seem sufficiently strong to override environmental influences (e.g. water depth and sediment type). The strong linear relationship between the slope b and intercept log(a) from the power relationship is remarkably similar for all surveys providing a common slope of - 1.63 with the present sampling approach. We suggest that this relationship is an inherent characteristic of Taylor's power law, and that b as a dispersion index may be biased by e.g. sampling errors when this relationship is weak. The correlation strength between b and log(a) could therefore be envisioned as a data quality check.
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.
Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles
Effenberger, Frederic; Costa, Fatima Rubio da; Petrosian, Vahé
2017-02-01
Flares close to the solar limb, where the footpoints are occulted, can reveal the spectrum and structure of the coronal looptop source in X-rays. We aim at studying the properties of the corresponding energetic electrons near their acceleration site, without footpoint contamination. To this end, a statistical study of partially occulted flares observed with Reuven Ramaty High-Energy Solar Spectroscopic Imager is presented here, covering a large part of solar cycles 23 and 24. We perform detailed spectra, imaging, and light curve analyses for 116 flares and include contextual observations from SDO and STEREO when available, providing further insights into flaremore » emission that were previously not accessible. We find that most spectra are fitted well with a thermal component plus a broken power-law, non-thermal component. A thin-target kappa distribution model gives satisfactory fits after the addition of a thermal component. X-ray imaging reveals small spatial separation between the thermal and non-thermal components, except for a few flares with a richer coronal source structure. A comprehensive light curve analysis shows a very good correlation between the derivative of the soft X-ray flux (from GOES ) and the hard X-rays for a substantial number of flares, indicative of the Neupert effect. The results confirm that non-thermal particles are accelerated in the corona and estimated timescales support the validity of a thin-target scenario with similar magnitudes of thermal and non-thermal energy fluxes.« less
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.
Correlating particle hardness with powder compaction performance.
Cao, Xiaoping; Morganti, Mikayla; Hancock, Bruno C; Masterson, Victoria M
2010-10-01
Assessing particle mechanical properties of pharmaceutical materials quickly and with little material can be very important to early stages of pharmaceutical research. In this study, a wide range of pharmaceutical materials were studied using atomic force microscopy (AFM) nanoindentation. A significant amount of particle hardness and elastic modulus data were provided. Moreover, powder compact mechanical properties of these materials were investigated in order to build correlation between the particle hardness and powder compaction performance. It was found that the materials with very low or high particle hardness most likely exhibit poor compaction performance while the materials with medium particle hardness usually have good compaction behavior. Additionally, the results from this study enriched Hiestand's special case concept on particle hardness and powder compaction performance. This study suggests that the use of AFM nanoindentation can help to screen mechanical properties of pharmaceutical materials at early development stages of pharmaceutical research.
NASA Astrophysics Data System (ADS)
Liang, Xuecheng
Dynamic hardness (Pd) of 22 different pure metals and alloys having a wide range of elastic modulus, static hardness, and crystal structure were measured in a gas pulse system. The indentation contact diameter with an indenting sphere and the radius (r2) of curvature of the indentation were determined by the curve fitting of the indentation profile data. r 2 measured by the profilometer was compared with that calculated from Hertz equation in both dynamic and static conditions. The results indicated that the curvature change due to elastic recovery after unloading is approximately proportional to the parameters predicted by Hertz equation. However, r 2 is less than the radius of indenting sphere in many cases which is contradictory to Hertz analysis. This discrepancy is believed due to the difference between Hertzian and actual stress distributions underneath the indentation. Factors which influence indentation elastic recovery were also discussed. It was found that Tabor dynamic hardness formula always gives a lower value than that directly from dynamic hardness definition DeltaE/V because of errors mainly from Tabor's rebound equation and the assumption that dynamic hardness at the beginning of rebound process (Pr) is equal to kinetic energy change of an impact sphere over the formed crater volume (Pd) in the derivation process for Tabor's dynamic hardness formula. Experimental results also suggested that dynamic to static hardness ratio of a material is primarily determined by its crystal structure and static hardness. The effects of strain rate and temperature rise on this ratio were discussed. A vacuum rotating arm apparatus was built to measure Pd at 70, 127, and 381 mum sphere sizes, these results exhibited that Pd is highly depended on the sphere size due to the strain rate effects. P d was also used to substitute for static hardness to correlate with abrasion and erosion resistance of metals and alloys. The particle size effects observed in erosion were
Inhomogeneous hard homonuclear molecules
NASA Astrophysics Data System (ADS)
Quintana, Jacqueline
A review is given of some features of theories for inhomogeneous fluids of nonspherical molecules that take as input the direct correlation function of the corresponding homogeneous system. Two different methods are described for defining the structure of hard homonuclear molecules close to a hard planar wall. A spherical harmonics expanison (SHE) within the integral equation (IE) method is presented and, for comparison, a version of density functional theory for orientable hard bodies. In both cases the Pynn-Lado model is employed and a comparison is made with Monte Carlo data. The results indicate that for hard molecules the IE approach does not always capture the effects of orientation due to the characteristics of the SHE for the step function. This disadvantage is particularly true in the case of the orientationally averaged density profile.
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.
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.
Hard X-ray imaging of the Galactic black hole candidate GX 339 - 4
NASA Technical Reports Server (NTRS)
Covault, C. E.; Grindlay, J. E.; Manandhar, R. P.
1992-01-01
Imaging and spectral observations in the energy range 25-250 keV of the black hole candidate GX 339 - 4 have been obtained with the Energetic X-ray Imaging Telescope Experiment. Observations were made during a balloon flight from Alice Springs, Australia on UT 1989 May 8-10. A single source of nearly 6-sigma significance is detected near the center of the 3.4-deg field of view with a position consistent with GX 339 - 4. This is the first imaging observation of GX 339 - 4 at hard X-ray energies. This result confirms previously reported results from nonimaging experiments showing significant hard X-ray flux up to greater than about 60 keV, with a power-law spectral fit similar to the other black hole candidates such as Cygnus X - 1. The source may have been in an outburst state similar to that recently detected with BATSE on GRO.
NASA Astrophysics Data System (ADS)
Mendoza-Ponce, A.; Perez Lopez, R.; Guardiola-Albert, C.; Garduño-Monroy, V. H.; Figueroa-Soto, Á.
2017-12-01
The Trans Mexican Volcanic Belt (TMVB) is related to the convergence between the Cocos and Rivera plates beneath the North American plate by the Middle America Trench (MAT). Moreover, there is also intraplate faulting within the TMVB, which is responsible of important earthquakes like the Acambay in 1912 (Mw 7.0) and Maravatío in 1979 (Mb 5.3). In this tectonic scheme, monogenetic volcanoes, active faulting and earthquakes configure a complex tectonic frame where different spatial anisotropy featured this activity. This complexity can be characterized by the power-law of the frequency-size distribution of the monogenetic volcanoes, the faults and the earthquakes. This power-law is determined by the b-value of the Gutenberg-Richter law in case of the earthquakes. The novelty of this work is the application of geostatistics techniques (variograms) for the analysis of spatial distribution of the b-values obtained from the size distribution of the basal diameter for monogenetic volcanoes in the Michoacán-Guanajuato Volcanic Field (bmv), surface area for faults in the Morelia-Acambay fault system (bf) and the seismicity in the Central TMVB (beq). Therefore, the anisotropy in each case was compared and a geometric tectonic model was proposed. The evaluation of the spatial distribution of the b-value maps gives us a general interpretation of the tectonic stress field and the seismic hazard in the zone. Hence, the beq-value map for the seismic catalog shows anomalously low and high values, reveling two different processes, one related to a typical tectonic rupture (low b-values) and the other one related to hydraulic fracturing (high b-values). The resulting bmv-map for the diameter basal cones indicates us the locations of the ages of the monogenetic volcanoes, giving important information about the volcanic hazard. High bmv-values are correlated with the presence of young cinder cones and an increasing probability of a new volcano. For the Morelia-Acambay fault system
NASA Astrophysics Data System (ADS)
Teixeira, Sebastião Braz
2006-06-01
The coast of the Central Algarve, Portugal, is dominated by sea-cliffs, cut on Miocene calcarenites; here, the main coastal geologic hazards result from the conflict between human occupation and sea-cliff recession. The evolution of this rocky coast occurs through an intermittent and discontinuous series of slope mass movements, along a 46 km cliff front. For the last 30 years, the increase of tourism occupation has amplified the risks to both people and buildings. In the last decade we have seen several accidents caused by cliff failure, which killed or wounded people and destroyed several buildings. The definition of buffer zones limited by hazard lines parallel to the cliff edge, where land use is restricted, is a widely used and effective preventive measure for mitigating risk. Rocky coasts typically show a slow cliff evolution. The process of gathering statistically significant field inventories of mass movements is, thus, very long. Although mass movement catalogues provide fundamental information on sea cliff evolution patterns and are an outstanding tool in hazard assessment, published data sets are still rare. In this work, we use two inventories of mass movement width, recorded on sea cliffs cut on Miocene calcarenites: a nine year long continuous field inventory (1995-2004) with 140 recorded events, and a 44 year long catalogue based on comparative analysis of aerial photographs (1947-1991), that includes 177 events. The cumulative frequency-width distributions of both data sets fit, above a critical width value corresponding to the threshold of full completeness of the inventories, to power-law distributions. The knowledge of the limits of the catalogues enabled the construction of a 53 year long record inventory over the range of mean width ⩾3 m ( n=167 events) and maximum width ⩾4 m ( n=155 events). The data assembled corresponds to a partial series and was converted to a return period-size distribution. Both return period-width distributions
TRACING THE REVERBERATION LAG IN THE HARD STATE OF BLACK HOLE X-RAY BINARIES
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
Crystallization and dynamical arrest of attractive hard spheres.
Babu, Sujin; Gimel, Jean-Christophe; Nicolai, Taco
2009-02-14
Crystallization of hard spheres interacting with a square well potential was investigated by numerical simulations using so-called Brownian cluster dynamics. The phase diagram was determined over a broad range of volume fractions. The crystallization rate was studied as a function of the interaction strength expressed in terms of the second virial coefficient. For volume fractions below about 0.3 the rate was found to increase abruptly with increasing attraction at the binodal of the metastable liquid-liquid phase separation. The rate increased until a maximum was reached after which it decreased with a power law dependence on the second virial coefficient. Above a critical percolation concentration, a transient system spanning network of connected particles was formed. Crystals were formed initially as part of the network, but eventually crystallization led to the breakup of the network. The lifetime of the transient gels increased very rapidly over a small range of interaction energies. Weak attraction destabilized the so-called repulsive crystals formed in pure hard sphere systems and shifted the coexistence line to higher volume fractions. Stronger attraction led to the formation of a denser, so-called attractive, crystalline phase. Nucleation of attractive crystals in the repulsive crystalline phase was observed close to the transition.