LAT, The Fermi
2010-01-01
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 $\\Epeak = 3.9\\pm 0.3$\\,MeV, which is the highest yet measured, and a hard power-law component with photon index $-1.62\\pm 0.03$ that dominates the emission below $\\approx$\\,20\\,keV and above $\\approx$\\,100\\,MeV. The onset of the high-energy spectral component appears to be delayed by $\\sim$\\,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. Observ...
A Hard X-Ray Power-Law Spectral Cutoff in Centaurus X-4
DEFF Research Database (Denmark)
Chakrabarty, Deepto; Tomsick, John A.; Grefenstette, Brian W.;
2015-01-01
The low-mass X-ray binary 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 unkno...
Guo, Fan; Daughton, William; Liu, Yi-Hsin
2014-01-01
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density $\\sigma \\equiv B^2/(4 \\pi n m_ec^2) > 1$ and when the system size is sufficiently large. In the limit $\\sigma \\gg 1$, the spectral index approaches $p=1$ and most of the available energy is converted into non-thermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection.
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin
2014-01-01
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density $\\sigma \\equiv B...
A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4
Energy Technology Data Exchange (ETDEWEB)
Chakrabarty, Deepto; Nowak, Michael A. [MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Tomsick, John A.; Boggs, Steven E.; Craig, William W. [Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States); Grefenstette, Brian W.; Fürst, Felix; Harrison, Fiona A.; Rana, Vikram [Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States); Psaltis, Dimitrios [Department of Astronomy, University of Arizona, Tucson, AZ 85721 (United States); Bachetti, Matteo; Barret, Didier [Observatoire Midi-Pyrénées, Université de Toulouse III - Paul Sabatier, F-31400 Toulouse (France); Christensen, Finn E. [Division of Astrophysics, National Space Institute, Technical University of Denmark, DK-2800 Lyngby (Denmark); Hailey, Charles J. [Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027 (United States); Kaspi, Victoria M. [Department of Physics, McGill University, Montreal, PQ H3A 2T8 (Canada); Miller, Jon M. [Department of Astronomy, University of Michigan, Ann Arbor, MI 48109 (United States); Stern, Daniel [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 (United States); Wik, Daniel R.; Zhang, William W. [Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Wilms, Jörn, E-mail: deepto@mit.edu [Dr. Karl-Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Universität Erlangen-Nürnberg, D-96049 Bamberg (Germany)
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 thermal 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.
A Hard X-Ray Power-Law Spectral Cutoff in Centaurus X-4
Chakrabarty, Deepto; Grefenstette, Brian W; Psaltis, Dimitrios; Bachetti, Matteo; Barret, Didier; Boggs, Steven E; Christensen, Finn E; Craig, William W; Fuerst, Felix; Hailey, Charles J; Harrison, Fiona A; Kaspi, Victoria A; Miller, Jon M; Nowak, Michael A; Rana, Vikram; Stern, Daniel; Wik, Daniel R; Wilms, Joern; Zhang, William W
2014-01-01
The low-mass X-ray binary 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 x 10^(33) erg/s (for D=1kpc), with around 60 percent in the thermal 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. 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 an 18 keV electron temperature, which can be understood as...
Suzaku Discovery of a Hard Component Varying Independently of the Power-Law Emission in MCG-6-30-15
Noda, Hirofumi; Makishima, Kazuo; Uehara, Yuuichi; Yamada, Shin'ya; Nakazawa, Kazuhiro
2011-01-01
Focusing on hard X-ray variability, we reanalyzed Suzaku data of Type I Seyfert galaxy MCG-6-30-15 obtained in 2006. Intensity-sorted spectroscopy and a principal component analysis consistently revealed a very hard component that varies independently of the dominant power-law emission. Although the exact nature of this hard component is not yet identified, it can be modeled as a power-law with a photon index ~2 affected by a partial covering absorption, or as a thermal Comptonization emissio...
A Hard X-Ray Power-law Spectral Cutoff in Centaurus X-4
Chakrabarty, Deepto; Tomsick, John A.; Grefenstette, Brian W.; Psaltis, Dimitrios; Bachetti, Matteo; Barret, Didier; Boggs, Steven E.; Christensen, Finn E.; Craig, William W.; Fürst, Felix; Hailey, Charles J.; Harrison, Fiona A.; Kaspi, Victoria M.; Miller, Jon M.; Nowak, Michael A.; Rana, Vikram; Stern, Daniel; Wik, Daniel R.; Wilms, Jörn; Zhang, William W.
2014-12-01
The low-mass X-ray binary (LMXB) Cen X-4 is the brightest and closest (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× 1033 D^2_kpc erg s-1, with sime60% in the thermal 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 kTe = 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.
Evidence for two hard X-ray components in double power-law fits to the 1980 June 7 flare
Smith, Dean F.; Orwig, Larry E.
1988-01-01
The June 7, 1980 flare at 0312 UT was analyzed with double power-law fits on the basis of SMM hard X-ray burst spectrometer data. The flare is found to consist of seven peaks of characteristic time scale of about 8 sec followed by seven valleys which may contain significant peak components because of overlap. It is suggested that the possibility of thermal spectra for the peaks is unlikely. An investigation of the double power-law parameters through the third and fourth peaks revealed a hysteresis effect in the fourth peak. The present results have been interpreted in terms of a trap plus precipitation model.
Hard-core thinnings of germ-grain models with power-law grain sizes
Kuronen, Mikko
2012-01-01
Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ-grain model. A fundamental question is whether long-range dependence is preserved under such thinnings. To answer this question we study four natural thinnings of a Poisson germ-grain model where the grains are spheres with a regularly varying size distribution. We show that a thinning which favors large grains preserves the slow correlation decay of the original model, whereas a thinning which favors small grains does not. Our most interesting finding concerns the case where only disjoint grains are retained, which corresponds to the well-known Mat\\'ern type I thinning. In the resulting germ-grain model, typical grains have exponentially small sizes, but rather surprisingly, the long-range dependence property is still present. As a byproduct, we obtain new mechanisms for generating hom...
The Causal Connection Between Disc and Power-Law Variability in Hard State Black Hole X-Ray Binaries
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.
Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.
2013-11-01
We explore the nonequilibrium dynamics of a two-dimensional trapped Bose-Einstein condensate excited by a moving red-detuned laser potential. The trap is a combination of a general power-law potential cutoff by a hard wall box potential. The red laser potential is allowed to exit the box potential, leaving the system in a highly nonequilibrium state. This is crucial since the red laser potential squeezes the BEC trapped inside it against the hard wall-boundary at this instant, paving the way for the creation of a shock wave. Once the red laser potential has left the box potential, the Hamiltonian of the system becomes time-independent and the total energy stabilizes. Our systems are simulated by the time-dependent Gross-Ptiaevskii Equation which is numerically solved by the split-step Crank-Nicolson method in real time. It is found that the value at which the total energy stabilizes in the transient stage of the simulation is largely controlled by the initialization process. Before the red laser potential leaves the trap, when the Hamiltonian of the system is still time-dependent, oscillations in the total energy occur if the system is initialized adiabatically by application of a gradually growing and moving red laser potential. If this laser potential is not moving, yet fully present in the initialization process, these oscillations are not observed in the transient stage of the simulation. In addition, the system displays oscillations in the root-mean-square radius of the trapped cloud. The amplitudes of these radial oscillations continue even after the red laser potential leaves the box potential and are used to explore the deviation of the nonstationary states from the corresponding ground states. It is demonstrated that the geometry of the power law potential influences the amplitude of these radial oscillations, reducing them and bringing the systems closer to an equilibrium state. We then argue that by going to tighter trapping geometries, it is not
Thomas, Hoben
1981-01-01
Psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions are examined. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates given for several common estimation situations.…
Power laws in software systems
Tonelli, Roberto
2012-01-01
The main topic of my PhD has been the study of power laws in software systems within the perspective of describing software quality. My PhD research contributes to a recent stream of studies in software engineering, where the investigation of power laws in software systems has become widely popular in recent years, since they appear on an incredible variety of different software quantities and properties, like, for example, software metrics, software faults, refactoring, Java byte-code,...
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. PMID:21946780
Kaizoji, T
2006-01-01
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) \\sim x^{-\\alpha} $, with an exponent that moves in the range of $ 1.09 < \\alpha < 1.27 $. Furthermore, we found that as the power-law exponents $ \\alpha $ approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst. PACS: 89.65.Gh
Lande, D V
2010-01-01
In the practical work of websites popularization, analysis of their efficiency and downloading it is of key importance to take into account web-ratings data. The main indicators of website traffic include the number of unique hosts from which the analyzed website was addressed and the number of granted web pages (hits) per unit time (for example, day, month or year). Of certain interest is the ratio between the number of hits (S) and hosts (H). In practice there is even used such a concept as "average number of viewed pages" (S/H), which on default supposes a linear dependence of S on H. What actually happens is that linear dependence is observed only as a partial case of power dependence, and not always. Another new power law has been discovered on the Internet, in particular, on the WWW.
Automated image enhancement using power law transformations
Indian Academy of Sciences (India)
S P Vimal; P K Thiruvikraman
2012-12-01
We propose a scheme for automating power law transformations which are used for image enhancement. The scheme we propose does not require the user to choose the exponent in the power law transformation. This method works well for images having poor contrast, especially to those images in which the peaks corresponding to the background and the foreground are not widely separated.
Modelling power-law spread of infectious diseases
Meyer, Sebastian
2013-01-01
Short-time human travel behaviour can be well described by a power law with respect to distance. We incorporate this information in space-time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a space-time point process model for individual point-referenced data, and a multivariate time series model for aggregated count data. In both frameworks, the power-law spread is embedded into the epidemic component and its decay parameter is estimated simultaneously with all other unknown parameters using (penalised) likelihood inference. The performance of the new approach is investigated by a re-analysis of individual cases of invasive meningococcal disease in Germany (2002-2008), and count data on influenza in 140 administrative districts of Southern Germany (2001-2008). In both applications, the power-law formulations substantially ...
Power Law Decay in High Intensity Turbulence
Koster, Timothy; Puga, Alejandro; Nguyen, Baolong; Larue, John
2015-11-01
In the study reported herein, the region where the power decay law is applicable for active grid generated turbulence is found by an iterative approach which determines the largest range where the ratio of the dissipation from the power law and the dissipation from the temporal velocity derivative are unity. The square of the Taylor microscale, as noted by Batchelor (1953), is linearly related to downstream distance relative to the virtual origin and can be used in a straightforward manner to find the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for various mean velocities to show the decay exponent as a function of the Taylor Reynolds number.
Power law models of stock indices
Tse, Man Kit
Viewing the stock market as a self-organized system, Sornette and Johansen introduced physics-based models to study the dynamics of stock market crashes from the perspective of complex systems. This involved modeling stock market Indices using a mathematical power law exhibiting log-periodicity as the system approaches a market crash, which acts like a critical point in a thermodynamic system. In this dissertation, I aim to investigate stock indices to determine whether or not they exhibit log-periodic oscillations, according to the models proposed by Sornette, as they approach a crash. In addition to analyzing stock market crashes in the frequency domain using the discrete Fourier transform and the Lomb-Scargle periodogram, I perform a detailed analysis of the stock market crash models through parameter estimation and model testing. I find that the probability landscapes have a complex topography and that there is very little evidence that these phase transition-based models accurately describe stock market crashes.
Power-Law Tails from Dynamical Comptonization in Converging Flows
Turolla, Roberto; Zane, Silvia; Titarchuk, Lev
2002-09-01
The effects of bulk motion Comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semianalytical, diffusion approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates when photon diffusion holds. Our semianalytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method, we find that although the power-law tail at extremely large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Γ=3 at large accretion rates, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft seed photons when the accretion rate is either quite low (~10). On the other hand, the spatial distribution of source photons controls the photon index at intermediate accretion rates, when Γ switches from the first to the second mode. Our analysis confirms that a hard tail with photon index Γ<3 is produced by the upscattering of primary photons onto infalling electrons if the central object is a black hole.
Anisotropic Power Law Inflation from Rolling Tachyons
Bhowmick, Samrat
2011-01-01
We provide an explicit solution representing an anisotropic power law inflation within the framework of rolling tachyon model. This is generated by allowing a non-minimal coupling between the tachyon and the world-volume gauge field on non-BPS D3 brane.
Instabilities in power law gradient hardening materials
DEFF Research Database (Denmark)
Niordson, Christian Frithiof; Tvergaard, Viggo
2005-01-01
Tension and compression instabilities are investigated for specimens with dimensions in the micron range. A finite strain generalization of a higher order strain gradient plasticity theory is implemented in a finite element scheme capable of modeling power law hardening materials. Effects...
Power Laws, Scale-Free Networks and Genome Biology
Koonin, Eugene V; Karev, Georgy P
2006-01-01
Power Laws, Scale-free Networks and Genome Biology deals with crucial aspects of the theoretical foundations of systems biology, namely power law distributions and scale-free networks which have emerged as the hallmarks of biological organization in the post-genomic era. The chapters in the book not only describe the interesting mathematical properties of biological networks but moves beyond phenomenology, toward models of evolution capable of explaining the emergence of these features. The collection of chapters, contributed by both physicists and biologists, strives to address the problems in this field in a rigorous but not excessively mathematical manner and to represent different viewpoints, which is crucial in this emerging discipline. Each chapter includes, in addition to technical descriptions of properties of biological networks and evolutionary models, a more general and accessible introduction to the respective problems. Most chapters emphasize the potential of theoretical systems biology for disco...
Zipf's law, power laws, and maximum entropy
Visser, Matt
2012-01-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to economics to linguistics to zoology, and even warfare. A recent model of random group formation [RGF] attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present article I argue that the cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.
Zipf's law, power laws and maximum entropy
Visser, Matt
2013-04-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.
Fractal power law in literary English
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.
Power-law Tails from Dynamical Comptonization in Converging Flows
Turolla, R; Titarchuk, L G; Turolla, Roberto; Zane, Silvia; Titarchuk, Lev
2002-01-01
The effects of bulk motion comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semi-analytical, diffusion-approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates, when photon diffusion holds. Our semi-analytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method we find that, although the power-law tail at really large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Gamma=3 at large accretion rate, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft ...
Beyond the power law: Uncovering stylized facts in interbank networks
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 Analysis of Financial Index Dynamics
Directory of Open Access Journals (Sweden)
J. Tenreiro Machado
2012-01-01
Full Text Available Power law (PL and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices (DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.
Study on local resistance of non-Newtonian power law fluid in elbow pipes
Zhang, Hao; Xu, Tiantian; Zhang, Xinxin; Wang, Yuxiang; Wang, Yuancheng; Liu, Xueting
2016-06-01
This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved 90° bend pipe with circular cross-sections, which are widely used in industrial applications. By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained. To explore the change rule the experiment is carried out by changing the Reynolds number, the wall roughness and different diameter ratio of elbow pipe. The variation of the local resistance coefficient with the Reynolds number, the diameter ratio and the wall roughness is presented comprehensively in the paper. The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid; the wall roughness has a significant impact on the local resistance coefficient. As the pipe wall roughness increasing, the coefficient of local resistance force will increase. The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow, which increases the kinetic energy dissipation of the main flow. This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.
Study on Local Resistance of non-Newtonian Power Law Fluid in Elbow Pipes
Institute of Scientific and Technical Information of China (English)
ZHANG Hao; XU Tiantian; ZHANG Xinxin; WANG Yuxiang; WANG Yuancheng; LIU Xueting
2016-01-01
This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved 90° bend pipe with circnlar cross-soctions,which are widely used in industrial applications.By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained.To explore the change rule the experiment is carried out by changing the Reynolds number,the wall roughness and different diameter ratio of elbow pipe.The variation of the local resistance coefficient with the Reynolds number,the diameter ratio and the wall roughness is presented comprehensively in the paper.The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid;the wall roughness has a significant impact on the local resistance coefficient.As the pipe wall roughness increasing,the coefficient of local resistance force will increase.The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow,which increases the kinetic energy dissipation of the main flow.This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.
Influence of probiotic cultures addition on the properties of semi-hard ewe’s cheese
Directory of Open Access Journals (Sweden)
Blaženka Kos
2011-12-01
Full Text Available Addition of probiotic bacteria into fermented milk beverages has been the subject of many studies, however, addition of these bacteria into cheeses, especially the ones made from ewe’s milk, has not been thoroughly investigated. Therefore, the aim of this study was to produce probiotic semi-hard ewe’s cheese with addition of probiotic strain Bifidobacterium animalis subsp. lactis BB-12 and Lactobacillus acidophilus LA-5. Cheese ripening occurred during 45 days at 13 °C and 85 % of relative humidity. During that period, chemical parameters were determined and microbiological analysis of manufactured probiotic cheeses was performed. Addition of probiotic cultures did not significantly influence the chemical properties and microbiological quality of produced cheeses in comparison with the control cheeses without addition of probiotic cultures. Number of live probiotic bacteria remained at about 106-107 CFU/g of probiotic cheeses during 45 days of ripening, which was confirmed by RAPD method. Sensory properties of probiotic semi-hard ewe’s cheese with Bifidobacterium animalis subsp. lactis BB-12 were similar to those obtained for cheeses without addition of probiotic, while addition of Lactobacillus acidophilus LA-5 improved the taste of cheeses. Obtained results demonstrated that semi-hard ewe’s cheese can be an effective matrix for addition of probiotic cultures Bifidobacterium animalis subsp. lactis BB-12 and Lactobacillus acidophilus LA-5.
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.
Universal power law governing pedestrian interactions
Karamouzas, Ioannis; Guy, Stephen J
2014-01-01
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 in 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.
Power Laws and Fragility in Flow Networks
Shore, Jesse; 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.
Power-Law Persistence in the Atmosphere: Analysis and Applications
Bunde, A; Govindan, R; Havlin, S; Koscielny-Bunde, E; Rybski, D; Vjushin, D; Bunde, Armin; Eichner, Jan F.; Govindan, Rathinaswamy; Havlin, Shlomo; Koscielny-Bunde, Eva; Rybski, Diego; Vjushin, Dmitry
2003-01-01
We review recent results on the appearance of long-term persistence in climatic records and their relevance for the evaluation of global climate models and rare events. The persistence can be characterized, for example, by the correlation C(s) of temperature variations separated by s days. We show that, contrary to previous expectations, C(s) decays for large s as a power law, C(s) ~ s^(-gamma). For continental stations, the exponent gamma is always close to 0.7, while for stations on islands gamma is about 0.4. In contrast to the temperature fluctuations, the fluctuations of the rainfall usually cannot be characterized by long-term power-law correlations but rather by pronounced short-term correlations. The universal persistence law for the temperature fluctuations on continental stations represents an ideal (and uncomfortable) test-bed for the state of-the-art global climate models and allows us to evaluate their performance. In addition, the presence of long-term correlations leads to a novel approach for ...
Discrete power law with exponential cutoff and Lotka's Law
Smolinsky, Lawrence
2015-01-01
The first bibliometric law appeared in Alfred J. Lotka's 1926 examination of author productivity in chemistry and physics. The result is that the productivity distribution is thought to be described by a power law. In this paper, Lotka's original data on author productivity in chemistry is reconsidered by comparing the fit of the data to both a discrete power law and a discrete power law with exponential cutoff.
Cota, Wesley F C; Ódor, Géza
2015-01-01
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 non-fluctuating (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 $\\lambda_1<\\lambda<\\lambda_2$, suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudo thresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at $\\lambda_2$. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths...
A Generalization of the Power Law Distribution with Nonlinear Exponent
Prieto, Faustino; Sarabia, José María
2016-01-01
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 nonlinear function which depends on data and two parameters. Then, we provide some basic prope...
Power law scaling in synchronization of brain signals depends on cognitive load
Directory of Open Access Journals (Sweden)
Jose Luis ePerez Velazquez
2014-05-01
Full Text Available 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 behaviours.
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.
The Flow of Power-Law Fluids in Axisymmetric Corrugated Tubes
Sochi, Taha
2010-01-01
In this article we present an analytical method for deriving the relationship between the pressure drop and flow rate in laminar flow regimes, and apply it to the flow of power-law fluids through axially-symmetric corrugated tubes. The method, which is general with regards to fluid and tube shape within certain restrictions, can also be used as a foundation for numerical integration where analytical expressions are hard to obtain due to mathematical or practical complexities. Five converging-...
A Universal Power Law Governing Pedestrian Interactions
Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.
2015-03-01
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 in 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. Work at Argonne National Laboratory is supported by the U.S. Department of Energy, under Contract No. DE-AC02-06CH11357. Work at the University of Minnesota is supported by MnDRIVE Initiative on Robotics, Sensors, and Advanced Manufacturing.
Anisotropic power-law k-inflation
Ohashi, Junko; Tsujikawa, Shinji
2013-01-01
It is known that power-law k-inflation can be realized for the Lagrangian $P=Xg(Y)$, where $X=-(\\partial \\phi)^2/2$ is the kinetic energy of a scalar field $\\phi$ and $g$ is an arbitrary function in terms of $Y=Xe^{\\lambda \\phi/M_{pl}}$ ($\\lambda$ is a constant and $M_{pl}$ is the reduced Planck mass). In the presence of a vector field coupled to the inflaton with an exponential coupling $f(\\phi) \\propto e^{\\mu \\phi/M_{pl}}$, we show that the models with the Lagrangian $P=Xg(Y)$ generally give rise to anisotropic inflationary solutions with $\\Sigma/H=constant$, where $\\Sigma$ is an anisotropic shear and $H$ is an isotropic expansion rate. Provided these anisotropic solutions exist in the regime where the ratio $\\Sigma/H$ is much smaller than 1, they are stable attractors irrespective of the forms of $g(Y)$. We apply our results to concrete models of k-inflation such as the generalized dilatonic ghost condensate/the DBI model and we numerically show that the solutions with different initial conditions converge...
Persistence of locality in systems with power-law interactions
Gong, Zhe-Xuan; Michalakis, Spyridon; Gorshkov, Alexey V
2014-01-01
Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\\alpha}$ interactions with $\\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but $qualitatively~reproduce$ the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems.
Natural orbit approximations in single power-law potentials
Struck, Curtis
2014-01-01
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to improve accuracy, especially for nearly radial orbits. 1) It is found that moderately improved orbital fits can be achieved with higher order perturbation expansions (in eccentricity), with the addition of `harmonic' terms to the solution. 2) Alternately, a matching of the extreme radial excursions of an orbit can be imposed, and a more accurate estimate of the eccentricity parameter is obtained. However, the error in the precession frequency is usually increased. 3) A correction function of small magnitude corrects the frequency problem. With this correction, even first order approximations yield excellent fits at quite high eccentricity over a range of potential indices that includes flat and falling rotation curve cases. 4) Adding a first harmonic term to fit the breadt...
Dexter, Jason; Blaes, Omer
2014-03-01
We propose a new model of the steep power-law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, the inner radii of radiation pressure dominated accretion discs are expected to (i) become effectively optically thin and (ii) produce significant luminosities. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energies. These spectra sum together to form a steep power-law tail to the spectrum. A given photon energy on this tail corresponds to a narrow range in radius, so that local vertical oscillations of the disc naturally produce high-quality high-frequency quasi-periodic oscillations (HFQPOs) in the hard X-ray band. The two lowest order modes have a robust frequency ratio of sqrt{7/3}˜eq 1.53. This model explains the appearance of steep power-law spectra and HFQPOs at high luminosity, the 3:2 HFQPO frequency ratios, and their association with the power-law spectral component. We predict an increase in QPO quality factor when the power spectrum is restricted to a narrower photon energy band, and an increase in HFQPO frequency at higher X-ray energies or lower luminosities. Future X-ray telescopes could detect additional HFQPOs from higher order modes. We demonstrate how this model could be used to measure black hole spin from HFQPOs, and qualitatively estimate the spin of GRO J1655-40 as a/M ˜ 0.4-0.7.
The Power-law Tail Exponent of Income Distributions
Clementi, F; Gallegati, M
2006-01-01
In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimising the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data for Australia and Italy.
Power-law distribution of pressure fluctuations in multiphase flow
Gheorghiu, S.; J.R. van Ommen; Coppens, M.-O.
2003-01-01
The power-law distribution of pressure fluctuation in multiphase flow was discussed. It was found that the probability density function exhibited a power-law drop-off and was well represented by a Tsallis distribution. The analysis showed that the Tsallis statistics arised as a result of bubble polydispersity, rather than system nonextensivity.
Power laws in the information production process Lotkaian informetrics
Egghe, Leo
2005-01-01
Explains many informetric regularities, only based on a decreasing power law as size-frequency function, that is Lotka''s law. This book revives the historical formulation of Alfred Lotka and shows the power of this power law, both in classical aspects of informetrics as well as in applications such as social networks and others.
Reconciling power laws in microscopic and macroscopic neural recordings
Pettersen, Klas H; Tetzlaff, Tom; Einevoll, Gaute T
2013-01-01
Power laws, characterized by quantities following 1/x^\\alpha{} distributions, are commonly reported when observing nature or society, and the question of their origin has for a long time intrigued physicists. Power laws have also been observed in neural recordings, both at the macroscopic and microscopic levels: at the macroscopic level, the power spectral density (PSD) of the electroencephalogram (EEG) has been seen to follow 1/f^\\alpha{} distributions; at the microscopic level similar power laws have been observed in single-neuron recordings of the neuronal soma potential and soma current, yet with different values of the power-law exponent \\alpha. In this theoretical study we find that these observed macroscopic and microscopic power laws may, despite the widely different spatial scales and different exponents, have the same source. By a combination of simulation on a biophysical detailed, pyramidal neuron model and analytical investigations of a simplified ball and stick neuron, we find that the transfer ...
Visiting Power Laws in Cyber-Physical Networking Systems
Directory of Open Access Journals (Sweden)
Ming Li
2012-01-01
Full Text Available Cyber-physical networking systems (CPNSs are made up of various physical systems that are heterogeneous in nature. Therefore, exploring universalities in CPNSs for either data or systems is desired in its fundamental theory. This paper is in the aspect of data, aiming at addressing that power laws may yet be a universality of data in CPNSs. The contributions of this paper are in triple folds. First, we provide a short tutorial about power laws. Then, we address the power laws related to some physical systems. Finally, we discuss that power-law-type data may be governed by stochastically differential equations of fractional order. As a side product, we present the point of view that the upper bound of data flow at large-time scaling and the small one also follows power laws.
Resurrecting power law inflation in the light of Planck results
International Nuclear Information System (INIS)
It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter fNLequil are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our model is structurally similar to that of a canonical scalar field and has a power law form for the kinetic term. A simple extension of our model resolves the graceful exit problem which usually afflicts models of power law inflation
Power-law defect energy in a single-crystal gradient plasticity framework: a computational study
Bayerschen, E.; Böhlke, T.
2016-07-01
A single-crystal gradient plasticity model is presented that includes a power-law type defect energy depending on the gradient of an equivalent plastic strain. Numerical regularization for the case of vanishing gradients is employed in the finite element discretization of the theory. Three exemplary choices of the defect energy exponent are compared in finite element simulations of elastic-plastic tricrystals under tensile loading. The influence of the power-law exponent is discussed related to the distribution of gradients and in regard to size effects. In addition, an analytical solution is presented for the single slip case supporting the numerical results. The influence of the power-law exponent is contrasted to the influence of the normalization constant.
Modified power law equations for vertical wind profiles. [in investigation of windpower plant siting
Spera, D. A.; Richards, T. R.
1979-01-01
In an investigation of windpower plant siting, equations are presented and evaluated for a wind profile model which incorporates both roughness and wind speed effects, while retaining the basic simplicity of the Hellman power law. These equations recognize the statistical nature of wind profiles and are compatible with existing analytical models and recent wind profile data. Predictions of energy output based on the proposed profile equations are 10% to 20% higher than those made with the 1/7 power law. In addition, correlation between calculated and observed blade loads is significantly better at higher wind speeds when the proposed wind profile model is used than when a constant power model is used.
Magnetic characterization of HSLA steel by power-law decay exponents of Barkhausen emission signal
Energy Technology Data Exchange (ETDEWEB)
Tarafder, M. [National Metallurgical Laboratory, Mathematical Modelling and Simulation Division, Jamshedpur 831 007 (India)], E-mail: mt@nmlindia.org; Chattoraj, I. [National Metallurgical Laboratory, Mathematical Modelling and Simulation Division, Jamshedpur 831 007 (India); Nasipuri, M. [Jadavpur University, Kolkata 700032 (India); Mitra, A. [National Metallurgical Laboratory, Mathematical Modelling and Simulation Division, Jamshedpur 831 007 (India)
2009-04-15
The general trend of magnetic behaviour of materials is that the mechanically hard materials are also magnetically hard. However for the high strength low alloy (HSLA) steel tempered at various aging temperatures, the correlation was reported as negative. The anomaly could not be explained by the magnetic parameters like RMS voltage calculated from the Barkhausen emission signal and the coercivity from the magnetic hysteresis loop. This paper reports another magnetic parameter known as power-law decay exponent which shows excellent correlation with the mechanical properties and thus explains the progressive evolution of the microstructural constituents in HSLA steel.
Magnetic characterization of HSLA steel by power-law decay exponents of Barkhausen emission signal
Tarafder, M.; Chattoraj, I.; Nasipuri, M.; Mitra, A.
2009-04-01
The general trend of magnetic behaviour of materials is that the mechanically hard materials are also magnetically hard. However for the high strength low alloy (HSLA) steel tempered at various aging temperatures, the correlation was reported as negative. The anomaly could not be explained by the magnetic parameters like RMS voltage calculated from the Barkhausen emission signal and the coercivity from the magnetic hysteresis loop. This paper reports another magnetic parameter known as power-law decay exponent which shows excellent correlation with the mechanical properties and thus explains the progressive evolution of the microstructural constituents in HSLA steel.
Statistical analyses support power law distributions found in neuronal avalanches.
Directory of Open Access Journals (Sweden)
Andreas Klaus
Full Text Available The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii model parameter estimation to determine the specific exponent of the power law, and (iii comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect. This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Power-Law Entropy Corrected Holographic Dark Energy Model
Sheykhi, Ahmad(Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz, 71454, Iran); Jamil, Mubasher
2010-01-01
Among various scenarios to explain the acceleration of the universe expansion, the holographic dark energy (HDE) model has got a lot of enthusiasm recently. In the derivation of holographic energy density, the area relation of the black hole entropy plays a crucial role. Indeed, the power-law corrections to entropy appear in dealing with the entanglement of quantum fields in and out the horizon. Inspired by the power-law corrected entropy, we propose the so-called "power-law entropy-corrected...
Helmholtz solitons in power-law optical materials
International Nuclear Information System (INIS)
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified
Microcanonical Foundation for Systems with Power-Law Distributions
Abe, Sumiyoshi; Rajagopal, and A. K.
2000-01-01
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can also be derived.
Power-Law Entropy Corrected Holographic Dark Energy
Sheykhi, Ahmad
2010-01-01
Among various scenarios to explain the acceleration of the universe expansion, the holographic dark energy (HDE) model has got a lot of enthusiasm recently. In the derivation of holographic energy density, the area relation of the black hole entropy plays a crucial role. Indeed, the power-law corrections to entropy appear in dealing with the entanglement of quantum fields in and out the horizon. Inspired by the power-law corrected entropy, we propose the so-called "power-law entropy-corrected holographic dark energy" (PLECHDE) in this Letter. We investigate the cosmological implications of this model and calculate some relevant cosmological parameters and their evolution. We also briefly study the so-called "power-law entropy-corrected agegraphic dark energy" (PLECADE).
Power-Law entropy corrected holographic dark energy model
Sheykhi, Ahmad; Jamil, Mubasher
2011-10-01
Among various scenarios to explain the acceleration of the universe expansion, the holographic dark energy (HDE) model has got a lot of enthusiasm recently. In the derivation of holographic energy density, the area relation of the black hole entropy plays a crucial role. Indeed, the power-law corrections to entropy appear in dealing with the entanglement of quantum fields in and out the horizon. Inspired by the power-law corrected entropy, we propose the so-called "power-law entropy-corrected holographic dark energy" (PLECHDE) in this Letter. We investigate the cosmological implications of this model and calculate some relevant cosmological parameters and their evolution. We also briefly study the so-called "power-law entropy-corrected agegraphic dark energy" (PLECADE).
POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS
Institute of Scientific and Technical Information of China (English)
ZhangWe
2003-01-01
The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields. For the requirement of later derivation, the HRR singular fields and the high-order asymptotic fields are first examined. That they are essentially the isotropic, incompressible, power law type nonlinear elastic crack-tip fields is illustrated. After a concise review of the elasticity recovery correspondence principle for solving the nonlinear viscoelastic problems, the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed. The solution of the crack-tip stress, strain fields for the power law type nonlinear viscoelastic materials, especially for the modified polypropylene, is obtained.
Punctuated equilibrium and power law in economic dynamics
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.
Optimal approximations of power-laws with exponentials
Thierry Bochud; Damien Challet
2006-01-01
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
Power-law distributions in binned empirical data
Virkar, Yogesh
2012-01-01
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities, and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for developing an understanding of complex systems. However, statistical evidence for or against the power-law hypothesis is complicated by large fluctuations in the empirical distribution's tail, and these are worsened when information is lost from binning the data. We adapt the statistically principled framework for testing the power-law hypothesis, developed by Clauset, Shalizi and Newman, to the case of binned data. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov-Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. We evaluate the effectiveness of these methods on synthetic binned data with known structure and apply them to twelve real-world binned data...
Wind Velocity Vertical Extrapolation by Extended Power Law
Zekai Şen; Abdüsselam Altunkaynak; Tarkan Erdik
2012-01-01
Wind energy gains more attention day by day as one of the clean renewable energy resources. We predicted wind speed vertical extrapolation by using extended power law. In this study, an extended vertical wind velocity extrapolation formulation is derived on the basis of perturbation theory by considering power law and Weibull wind speed probability distribution function. In the proposed methodology not only the mean values of the wind speeds at different elevations but also their standard dev...
Power-laws and spectral analysis of the Internet topology
Subedi, Laxmi
2010-01-01
In this thesis, we present the analysis on power-laws and spectral properties of the Internet topology at AS level based on Border Gateway Protocol (BGP) routing datasets collected from two repositories (Route Views and RIPE) over the period of five years. Analysis of collected datasets revealed that the two datasets have similar historical trends in the development of the Internet. Furthermore, the power-law exponents have not substantially changed over time while spectral analysis revealed ...
Electric field in media with power-law spatial dispersion
Tarasov, Vasily E.
2016-04-01
In this paper, we consider electric fields in media with power-law spatial dispersion (PLSD). Spatial dispersion means that the absolute permittivity of the media depends on the wave vector. Power-law type of this dispersion is described by derivatives and integrals of non-integer orders. We consider electric fields of point charge and dipole in media with PLSD, infinite charged wire, uniformly charged disk, capacitance of spherical capacitor and multipole expansion for PLSD-media.
Power laws in citation distributions: Evidence from Scopus
Brzezinski, Michal
2014-01-01
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 mo...
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.
Zhang, G; Torquato, S
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space R^{d} has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g(2)(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.
Zhang, G; Torquato, S
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space R^{d} has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g(2)(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average
Power-law cross-correlations estimation under heavy tails
Kristoufek, Ladislav
2016-11-01
We examine the performance of six estimators of the power-law cross-correlations-the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator-under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the α-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.
Statistical tests for power-law cross-correlated processes
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.
Statistical tests for power-law cross-correlated processes.
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, ρ(DCCA)(T,n), where T is the total length of the time series and n the window size. For ρ(DCCA)(T,n), we numerically calculated the Cauchy inequality -1 ≤ ρ(DCCA)(T,n) ≤ 1. Here we derive -1 ≤ ρ DCCA)(T,n) ≤ 1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ρ(DCCA) 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 ρ(DCCA)(T,n) tends with increasing T to 1/T. Using ρ(DCCA)(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. PMID:22304166
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. PMID:26764792
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 complete data frame work for fitting power law distributions
Gillespie, Colin S
2014-01-01
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed distributions requires care, especially since the power law behaviour may only be present in the distributional tail. Current state of the art methods for fitting these models rely on estimating the cut-off parameter $x_{\\min}$. This results in the majority of collected data being discarded. This paper provides an alternative, principled approached for fitting heavy tailed distributions. By directly modelling the deviation from the power law distribution, we can fit and compare a variety of competing models in a single unified framework.
Power-law hereditariness of hierarchical fractal bones.
Deseri, Luca; Di Paola, Mario; Zingales, Massimiliano; Pollaci, Pietro
2013-12-01
In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law. PMID:23836622
Power laws statistics of cliff failures, scaling and percolation
Baldassarri, Andrea
2014-01-01
The size of large cliff failures may be described in several ways, for instance considering the horizontal eroded area at the cliff top and the maximum local retreat of the coastline. Field studies suggest that, for large failures, the frequencies of these two quantities decrease as power laws of the respective magnitudes, defining two different decay exponents. Moreover, the horizontal area increases as a power law of the maximum local retreat, identifying a third exponent. Such observation suggests that the geometry of cliff failures are statistically similar for different magnitudes. Power laws are familiar in the physics of critical systems. The corresponding exponents satisfy precise relations and are proven to be universal features, common to very different systems. Following the approach typical of statistical physics, we propose a "scaling hypothesis" resulting in a relation between the three above exponents: there is a precise, mathematical relation between the distributions of magnitudes of erosion ...
Afterglow Light Curves and Broken Power Laws: A Statistical Study
J'ohannesson, G; Gudmundsson, E H; J\\'ohannesson, Gudlaugur; Bj\\"ornsson, Gunnlaugur; Gudmundsson, Einar H.
2006-01-01
In gamma-ray burst research it is quite common to fit the afterglow light curves with a broken power law to interpret the data. We apply this method to a computer simulated population of afterglows and find systematic differences between the known model parameters of the population and the ones derived from the power law fits. In general, the slope of the electron energy distribution is overestimated from the pre-break light curve slope while being underestimated from the post-break slope. We also find that the jet opening angle derived from the fits is overestimated in narrow jets and underestimated in wider ones. Results from fitting afterglow light curves with broken power laws must therefore be interpreted with caution since the uncertainties in the derived parameters might be larger than estimated from the fit. This may have implications for Hubble diagrams constructed using gamma-ray burst data.
Power-law relations in random networks with communities
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.
2016-07-01
Most random graph models are locally tree-like—do not contain short cycles—rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ . In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ =γ -1 .
Characterizing and Predicting the Robustness of Power-law Networks
LaRocca, Sarah
2013-01-01
Power-law networks such as the Internet, terrorist cells, species relationships, and cellular metabolic interactions are susceptible to node failures, yet maintaining network connectivity is essential for network functionality. Disconnection of the network leads to fragmentation and, in some cases, collapse of the underlying system. However, the influences of the topology of networks on their ability to withstand node failures are poorly understood. Based on a study of the response of 2,000 power-law networks to node failures, we find that networks with higher nodal degree and clustering coefficient, lower betweenness centrality, and lower variability in path length and clustering coefficient maintain their cohesion better during such events. We also find that network robustness, i.e., the ability to withstand node failures, can be accurately predicted a priori for power-law networks across many fields. These results provide a basis for designing new, more robust networks, improving the robustness of existing...
Robust Statistical Detection of Power-Law Cross-Correlation
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-06-01
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.
Between disorder and order: A case study of power law
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.
Logarithmic Correlations For Turbulent Pipe Flow Of Power Law Fluids
Trinh, K T
2010-01-01
This paper uses the estimates of phase-locked parameters at the onset of bursting presented in a companion paper to derive logarithmic correlations for turbulent friction factor losses in time-independent power law fluids. Two different techniques for analysis were used. They gave logarithmic correlations with different coefficients. But both correlations predicted 264 data points of friction factors published in the literature with a standard error of 1.3%. The derivations show how modern understanding of coherent structures embedded in turbulent flow fields can be used to derive engineering correlations for head losses. Key words: Friction factor, turbulent, logarithmic correlations, power law, non-Newtonian
Power-law distribution in Japanese racetrack betting
Ichinomiya, Takashi
2006-01-01
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 $P_o(x)$ indicates a clear power law $P_o(x)\\propto 1/x$, where $x$ represents the final odds. This power law ca...
Universal power law behaviors in genomic sequences and evolutionary models
Martignetti, L
2007-01-01
We study the length distribution of a particular class of DNA sequences known as 5'UTR exons. These exons belong to the messanger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that both in mouse and in human these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model which may explain this finding. We conjecture that this power law behaviour could indeed be a general feature of higher eukaryotes.
Natural orbit approximations in single power-law potentials
Struck, Curtis
2015-01-01
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here, I explore several extensions of these approximations to improve accuracy, especially for nearly radial orbits. (1) It is found that moderately improved orbital fits can be achieved with higher order perturbation expansions (in eccentricity), with the addition of `harmonic' terms to the solution. (2) Alternately, a matching of the extreme radial excursions of an orbit can be imposed, and a more accurate estimate of the eccentricity parameter is obtained. However, the error in the precession frequency is usually increased. (3) A correction function of small magnitude corrects the frequency problem. With this correction, even first-order approximations yield excellent fits at quite high eccentricity over a range of potential indices that includes flat and falling rotation-curve cases. (4) Adding a first harmonic term to fit the breadth of the orbital loops, and determining the fundamental and harmonic coefficients by matching to three orbital positions further improves the fit. With a couple of additional small corrections, one obtains excellent fits to orbits with radial ranges of more than a thousand for some potentials. These simple corrections to the basic p-ellipse are basically in the form of several successive approximations, and can provide high accuracy. They suggest new results including that the apsidal precession rate scales approximately as log(1 - e) at very high eccentricities e. New insights are also provided on the occurrence of periodic orbits in various potentials, especially at high eccentricity.
Thresholded Power Law Size Distributions of Instabilities in Astrophysics
Aschwanden, Markus J
2015-01-01
Power law-like size distributions are ubiquitous in astrophysical instabilities. There are at least four natural effects that cause deviations from ideal power law size distributions, which we model here in a generalized way: (1) a physical threshold of an instability; (2) incomplete sampling of the smallest events below a threshold $x_0$; (3) contamination by an event-unrelated background $x_b$; and (4) truncation effects at the largest events due to a finite system size. These effects can be modeled in simplest terms with a "thresholded power law" distribution function (also called generalized Pareto [type II] or Lomax distribution), $N(x) dx \\propto (x+x_0)^{-a} dx$, where $x_0 > 0$ is positive for a threshold effect, while $x_0 < 0$ is negative for background contamination. We analytically derive the functional shape of this thresholded power law distribution function from an exponential-growth evolution model, which produces avalanches only when a disturbance exceeds a critical threshold $x_0$. We app...
Unobserved heterogeneity in the power law nonhomogeneous Poisson process
International Nuclear Information System (INIS)
A study of possible consequences of heterogeneity in the failure intensity of repairable systems is presented. The basic model studied is the nonhomogeneous Poisson process with power law intensity function. When several similar systems are under observation, the assumption that the corresponding processes are independent and identically distributed is often questionable. In practice there may be an unobserved heterogeneity among the systems. The heterogeneity is modeled by introduction of unobserved gamma distributed frailties. The relevant likelihood function is derived, and maximum likelihood estimation is illustrated. In a simulation study we then compare results when using a power law model without taking into account heterogeneity, with the corresponding results obtained when the heterogeneity is accounted for. A motivating data example is also given. - Highlights: • Consequences of overlooking heterogeneity in similar repairable systems are studied. • Likelihood functions are established for power law NHPP w/ and w/o heterogeneity. • ML estimators for parameters of power law NHPP with heterogeneity are derived. • A simulation study shows the effects of heterogeneity and its ignorance in models
Power-law relations in random networks with communities
Stegehuis, Clara; van Leeuwaarden, Johan S H
2016-01-01
Most random graph models are locally tree-like - do not contain short cycles - which makes them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Furthermore, viewing real-world networks as realizations of the HCM reveals two previously unobserved power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. Many real-world networks have both a community structure and a power-law degree distribution. We relate the power-law exponent $\\tau$ of the degree distribution with the power-law exponent of the community size distribution $\\gamma$. In the special case of dense communities, this relation takes ...
Power Laws and Gaussians for Stock Market Fluctuations
Tuncay, C; Tuncay, Caglar; Stauffer, Dietrich
2006-01-01
The daily volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well long-term trends. We also model the transition to a Gaussian distribution for longer time intervals, like months instead of days.
Relation between dark matter density and temperature with power law
International Nuclear Information System (INIS)
In this paper, we consider the relation between temperature and density of dark matter. The temperature of dark matter for power-law form density is obtained by using Jeans equation. Then, we compare our result with a mass model and obtain the permissible limit of r.
On the flow of power-law fluids
Kolář, V. (Václav)
2011-01-01
An update on generalized similarity transformation applied to the flow of power-law fluids is presented. The paper surveys both steady and unsteady flow problems: (i) wall jets and (ii) unsteady liquid-film stretching. The latter case assumes that the flow field is similar in time and space. Some practical issues are addressed.
The power laws of nanoscale forces under ambient conditions.
Lai, Chia-Yun; Olukan, Tuza; Santos, Sergio; Al Ghaferi, Amal; Chiesa, Matteo
2015-12-25
We report a power law derived from experimental atomic force microscopy (AFM) data suggesting a nano to mesoscale transition in force-distance dependencies. Our results are in relative agreement with the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only. PMID:26486193
Back-reaction effect in power-law inflation
Bellini, M
2004-01-01
I consider a power-law inflationary model taking into account back-reaction effects. The interesting result is that the spectrum for the scalar field fluctuations does not depends on the expansion rate of the universe $p$ and that it result to be scale invariant for cosmological scales. However, the amplitude for these fluctuations depends on $p$.
Power-law Distributions in Information Science - Making the Case for Logarithmic Binning
Milojević, Staša
2010-01-01
We suggest partial logarithmic binning as the method of choice for uncovering the nature of many distributions encountered in information science (IS). Logarithmic binning retrieves information and trends "not visible" in noisy power-law tails. We also argue that obtaining the exponent from logarithmically binned data using a simple least square method is in some cases warranted in addition to methods such as the maximum likelihood. We also show why often used cumulative distributions can make it difficult to distinguish noise from genuine features, and make it difficult to obtain an accurate power-law exponent of the underlying distribution. The treatment is non-technical, aimed at IS researchers with little or no background in mathematics.
Energy Technology Data Exchange (ETDEWEB)
Qu, Jun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Zhou, Yan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Leonard, Donovan N [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Meyer, III, Harry M [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Luo, Huimin [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-03-01
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.
Power law cosmology model comparison with CMB scale information
Tutusaus, Isaac; Blanchard, Alain; Dupays, Arnaud; Zolnierowski, Yves; Cohen-Tanugi, Johann; Ealet, Anne; Escoffier, Stéphanie; Fèvre, Olivier Le; Ilić, Stéphane; Piazza, Federico; Pisani, Alice; Plaszczynski, Stéphane; Sakr, Ziad; Salvatelli, Valentina; Schücker, Thomas; Tilquin, André; Virey, Jean-Marc
2016-01-01
Despite the ability of the cosmological concordance model ($\\Lambda$CDM) to describe the cosmological observations exceedingly well, power law expansion of the Universe scale radius 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 $\\Lambda$CDM and power law expansion models with $n \\sim 1.5$, 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 is well known to provide the most stringent constraints on standard cosmological models, in particular through the position of the first peak of the temperature ...
Robustness of Power-law Behavior in Cascading Failure Models
Sloothaak, F; Zwart, A P
2016-01-01
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially meet the load demands imposed on the network. Every single line failure changes the load distribution in the surviving network, possibly causing further lines to become overloaded and trip as well. An initial single line failure can therefore potentially trigger massive cascading effects, and in this paper we measure the risk of such cascading events by the probability that the number of failed lines exceeds a certain large threshold. Under particular critical conditions, the exceedance probability follows a power-law distribution, implying a significant risk of severe failures. We examine the robustness of the power-law behavior by exploring under which assumptions this behavior prevails.
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 . 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.
Wind Velocity Vertical Extrapolation by Extended Power Law
Directory of Open Access Journals (Sweden)
Zekai Şen
2012-01-01
Full Text Available Wind energy gains more attention day by day as one of the clean renewable energy resources. We predicted wind speed vertical extrapolation by using extended power law. In this study, an extended vertical wind velocity extrapolation formulation is derived on the basis of perturbation theory by considering power law and Weibull wind speed probability distribution function. In the proposed methodology not only the mean values of the wind speeds at different elevations but also their standard deviations and the cross-correlation coefficient between different elevations are taken into consideration. The application of the presented methodology is performed for wind speed measurements at Karaburun/Istanbul, Turkey. At this location, hourly wind speed measurements are available for three different heights above the earth surface.
Power-law distribution in Japanese racetrack betting
Ichinomiya, T
2006-01-01
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 $P_o(x)$ indicates a clear power law $P_o(x)\\propto 1/x$, where $x$ represents the final odds. This power law can be explained on the basis of the assumption that that every bettor bets his money on the horse that appears to be the strongest in a race.
Effects of Sorghum Flour Addition on Chemical and Rheological Properties of Hard White Winter Wheat
Ranya F. Abdelghafor; Abdelmoneim I. Mustafa; Amir M.H. brahim; Yuanhong R. Chen; Padmanaban G. Krishnan
2013-01-01
This study was carried out to investigate the chemical and rheological properties of different blends prepared using hard white winter wheat (HWWW; Triticum aestivum Desf.) and whole or decorticated sorghum (Sorghum bicolor). Whole and decorticated sorghum were used to replace 5, 10, 15 and 20% of wheat flour. Wheat samples had higher protein, moisture and calcium values and lower fat, ash, carbohydrates, iron and phosphorous values compared to whole and decorticated sorghum flours. Decortica...
Weak power law rheology of soft glassy and gelled materials
Patricio, Pedro
2015-01-01
We make a parallel excursion to the generalised Maxwell and Kelvin-Voigt models to find which general conditions may lead to the weak power law behaviours of the elastic and viscous moduli, $G'(w)\\sim G''(w)\\sim w^\\alpha$, with $0 y\\approx \\alpha$ and $y> x\\approx \\alpha$ for respectively the generalised Maxwell and Kelvin-Voigt models. Beyond this region, we find very different and interesting exponents.
Power-law cosmology, SN Ia, and BAO
International Nuclear Information System (INIS)
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime a(t) ∼ tβ with β close to 3/2 in a spatially flat universe is a good fit to these data
Characterizing and predicting the robustness of power-law networks
International Nuclear Information System (INIS)
Power-law networks such as the Internet, terrorist cells, species relationships, and cellular metabolic interactions are susceptible to node failures, yet maintaining network connectivity is essential for network functionality. Disconnection of the network leads to fragmentation and, in some cases, collapse of the underlying system. However, the influences of the topology of networks on their ability to withstand node failures are poorly understood. Based on a study of the response of 2000 randomly-generated power-law networks to node failures, we find that networks with higher nodal degree and clustering coefficient, lower betweenness centrality, and lower variability in path length and clustering coefficient maintain their cohesion better during such events. We also find that network robustness, i.e., the ability to withstand node failures, can be accurately predicted a priori for power-law networks across many fields. These results provide a basis for designing new, more robust networks, improving the robustness of existing networks such as the Internet and cellular metabolic pathways, and efficiently degrading networks such as terrorist cells. - Highlights: • Examine relationship between network topology and robustness to failures. • Relationship is statistically significant for scale-free networks. • Use statistical models to estimate robustness to failures for real-world networks
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
Econophysical anchoring of unimodal power-law distributions
Eliazar, Iddo I.; Cohen, Morrel H.
2013-09-01
The sciences are abundant with size distributions whose densities have a unimodal shape and power-law tails both at zero and at infinity. The quintessential examples of such unimodal and power-law (UPL) distributions are the sizes of income and wealth in human societies. While the tails of UPL distributions are precisely quantified by their corresponding power-law exponents, their bulks are only qualitatively characterized as unimodal. Consequently, different statistical models of UPL distributions exist, the most popular considering lognormal bulks. In this paper we present a general econophysical framework for UPL distributions termed ‘the anchoring method’. This method: (i) universally approximates UPL distributions via three ‘anchors’ set at zero, at infinity, and at an intermediate point between zero and infinity (e.g. the mode); (ii) is highly versatile and broadly applicable; (iii) encompasses the existing statistical models of UPL distributions as special cases; (iv) facilitates the introduction of new statistical models of UPL distributions and (v) yields a socioeconophysical analysis of UPL distributions.
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. PMID:26774613
Scaling range of power laws that originate from fluctuation analysis
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.
Power-law deformation of Wishart-Laguerre ensembles of random matrices
Akemann, G
2008-01-01
We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size NxM for all three beta, in terms of the orthogonal polynomials of the standard Wishart-Laguerre ensembles. For large-N in a certain double scaling limit we obtain a generalised Marcenko-Pastur distribution on the macroscopic scale, and a generalised Bessel-law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power-law tails, where the microscopic limit depends on beta and the difference M-N. In the limit where our parameter governing the power-law goes to infinity we recover the correlations of the Wishart-Laguerre ensembles. To illustrate these findings the generalised Marcenko-Pastur distribut...
Simple inflationary quintessential model. II. Power law potentials
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
Universal Power Law for Relationship between Rainfall Kinetic Energy and Rainfall Intensity
Seung Sook Shin; Sang Deog Park; Byoung Koo Choi
2016-01-01
Rainfall kinetic energy has been linked to linear, exponential, logarithmic, and power-law functions using rainfall intensity as an independent variable. The power law is the most suitable mathematical expression used to relate rainfall kinetic energy and rainfall intensity. In evaluating the rainfall kinetic energy, the empirical power laws have shown a larger deviation than other functions. In this study, universal power law between rainfall kinetic energy and rainfall intensity was propose...
Size-frequency and rank-frequency relations,power laws and exponentials: a unified approach
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Power laws, such as Zipf's law, and exponential relations, leading to straight lines in logarithmic or semi-logarithmic scales, are presented in a unified setting. It is shown that the class of size-frequency power laws is larger than the class of rank-frequency power laws. Their ubiquity in all fields of science is illustrated.
Power-Law Tail in the Chinese Wealth Distribution
Institute of Scientific and Technical Information of China (English)
DING Ning; WANG You-Gui
2007-01-01
@@ We analyse the data from the recently published lists of the richest Chinese from the year 2003 to 2005. The results confirm that in these years the wealth is distributed according to a power law with exponents between 1.758 and 2.285 in the high end. The power distribution is found to be quite robust although the persons in the list change drastically and the wealth increases rapidly. The relation between the wealth and the absolute change of wealth rejects the notion that the wealth evolution is a multiplicative stochastic process.
Adhesion of nanoscale asperities with power-law profiles
Grierson, David S.; Liu, Jingjing; Carpick, Robert W.; Turner, Kevin T.
2013-02-01
The behavior of single-asperity micro- and nanoscale contacts in which adhesion is present is important for the performance of many small-scale mechanical systems and processes, such as atomic force microscopy (AFM). When analyzing such problems, the bodies in contact are often assumed to have paraboloidal shapes, thus allowing the application of the familiar Johnson-Kendall-Roberts (JKR), Derjaguin-Müller-Toporov (DMT), or Maugis-Dugdale (M-D) adhesive contact models. However, in many situations the asperities do not have paraboloidal shapes and, instead, have geometries that may be better described by a power-law function. An M-D-n analytical model has recently been developed to extend the M-D model to asperities with power-law profiles. We use a combination of M-D-n analytical modeling, finite element (FE) analysis, and experimental measurements to investigate the behavior of nanoscale adhesive contacts with non-paraboloidal geometries. Specifically, we examine the relationship between pull-off force, work of adhesion, and range of adhesion for asperities with power-law-shaped geometries. FE analysis is used to validate the M-D-n model and examine the effect of the shape of the adhesive interaction potential on the pull-off force. In the experiments, the extended M-D model is applied to analyze pull-off force measurements made on nanoscale tips that are engineered via gradual wear to have power-law shapes. The experimental and modeling results demonstrate that the range of the adhesive interaction is a crucial parameter when quantifying the adhesion of non-paraboloidal tips, quite different than the familiar paraboloidal case. The application of the M-D-n model to the experimental results yields an unusually large adhesion range of 4-5 nm, a finding we attribute to either the presence of long-range van der Waals forces or deviations from continuum theory due to atomic-scale roughness of the tips. Finally, an adhesion map to aid in analysis of pull-off force
Analytical Limit Distributions from Random Power-Law Interactions
Zaid, Irwin; Mizuno, Daisuke
2016-07-01
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
Failure analysis on China power grid based on power law
Institute of Scientific and Technical Information of China (English)
Xiaofeng WENG; Yiguang HONG; Ancheng XUE; Shengwei MEI
2006-01-01
This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance (SWV) and rescaled rangestatistics (R/S), this paper studies the blackout data in China power system during 1988-1997. The result of analysis shows that the blackout data of 1994-1997 coincides well with the autocorrelation. Furthermore, it is found that the function of blackout probability vs. blackout size exhibits power law distribution.
Universal power law for front propagation in all fiber resonators.
Coulibaly, S; Taki, M; Tlidi, M
2014-01-13
We consider a bistable system consisting of all fiber cavity driven by an external injected continuous wave. We report on front propagation in a high finesse cavity. We study the asymptotic behavior of the front velocity. We show that the front velocity is affected by the distance from the critical point associated with bistability. We provide a scaling low governing its evolution near the up-switching point of the bistable curve. We show also that the velocity of front propagation obeys a generic power law when the front velocity approaches asymptotically its linear growing value.
Shannon Information and Power Law Analysis of the Chromosome Code
Directory of Open Access Journals (Sweden)
J. A. Tenreiro Machado
2012-01-01
Full Text Available This paper studies the information content of the chromosomes of twenty-three species. Several statistics considering different number of bases for alphabet character encoding are derived. Based on the resulting histograms, word delimiters and character relative frequencies are identified. The knowledge of this data allows moving along each chromosome while evaluating the flow of characters and words. The resulting flux of information is captured by means of Shannon entropy. The results are explored in the perspective of power law relationships allowing a quantitative evaluation of the DNA of the species.
Thermal emission in fatigue described by power laws
Directory of Open Access Journals (Sweden)
Gallinatti A.E.
2010-06-01
Full Text Available In the present work, a theoretical model proposed by the literature and focused on the relationship between microplasticizations thermal behaviour and fatigue scatter is analysed and applied to fatigue test results of standard and notched steel specimens. The same experimental data are subjected to the TCM (Two Curves Method thermographic elaboration technique, in order to quickly evaluate fatigue limit values. TCM method has been modified, aiming at interpolating thermal data referred to the region of loads upper than fatigue limit with a non linear regression law having the same mathematical structure of the theoretical model equations (power laws.
Properties of hard alloys on the basis of WC-Co with the additives of nanodisperse TiN
International Nuclear Information System (INIS)
The addition of nanodisperse titanium nitride (specific surface area of 20 - 30 m2/g, medium diameter of grains of 50 - 100 nm) to the starting hard alloy WC-Co in the stage of wet grinding allows to get some advantages: the growth of WC grains is retarded by the nanoparticles of TiN, being as a barrier for the process of secondary crystallization, and the toughness of hard alloy is being increased due to the formation of finely dispersed structure; the exploitation characteristics of cutting instruments are increased due to the volume alloying by means of titanium nitride having a decreased adhesion to the treated metal and decreased coefficient of friction; the formation of diffusion porosity is being eliminated due to the small size of TiN during the unavoidable dissolution of WC in TiN. (author)
Effects of Sorghum Flour Addition on Chemical and Rheological Properties of Hard White Winter Wheat
Directory of Open Access Journals (Sweden)
Ranya F. Abdelghafor
2013-11-01
Full Text Available This study was carried out to investigate the chemical and rheological properties of different blends prepared using hard white winter wheat (HWWW; Triticum aestivum Desf. and whole or decorticated sorghum (Sorghum bicolor. Whole and decorticated sorghum were used to replace 5, 10, 15 and 20% of wheat flour. Wheat samples had higher protein, moisture and calcium values and lower fat, ash, carbohydrates, iron and phosphorous values compared to whole and decorticated sorghum flours. Decortication of sorghum grains decreased moisture, ash, fat, crude protein, iron and phosphorous content, but increased carbohydrate content. Farinogram properties such as dough water absorption, development time and stability and Farinograph quality number decreased as the amount of substituted sorghum increased; whereas mixing tolerance index increased. Moreover, at fixed gluten levels, as sorghum flour increased in the blend, wet gluten, dry gluten and gluten index decreased. Increasing sorghum in the blend also decreased energy, resistance to extension and extensibility of the dough, but contributed to an increase in the ratio of resistance to extensibility. Furthermore, as fermentation time increased, energy, resistance to extension and the ratio number of energy to extension increased, whereas extensibility decreased.
A graph-dynamic model of the power law of practice and the problem-solving fan-effect.
Shrager, J; Hogg, T; Huberman, B A
1988-10-21
Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically. PMID:3175664
Power law distributions of patents as indicators of innovation.
Directory of Open Access Journals (Sweden)
Dion R J O'Neale
Full Text Available 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. Here we present evidence that the distribution of patents amongst applicants within many countries is well-described by power laws 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 Distributions of Patents as Indicators of Innovation
O'Neale, D R J
2012-01-01
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. Here we present evidence that the distribution of patents amongst applicants within many OECD countries is well-described by power laws with exponents that vary between 1.66 (Japan) and 2.37 (Poland). 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 R&D 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...
An inverse method for rheometry of power-law fluids
International Nuclear Information System (INIS)
This paper is concerned with the determination of the constitutive viscous parameters of dilute solutions of xanthan gum by means of an inverse method used in conjunction with finite element modeling of the governing system of partial differential equations. At low concentrations xanthan gum behaves as a shear-thinning, power-law non-Newtonian fluid. Finite element modeling is used to simulate the pressure-driven flow of xanthan gum solutions in a microchannel T-junction. As the flow is forced to turn the corner of the T-junction a range of shear rates, and hence viscosities, is produced. It is shown that the statistical properties of the velocity field are sensitive to the constitutive parameters of the power-law model. The inverse method is shown to be stable and accurate, with measurement error in the velocity field translating to small errors in the rheological parameter estimation. Due to the particular structure of the inverse map, the error propagation is substantially less than the estimate from the Hadamard criterion
Air-chemistry "turbulence": power-law scaling and statistical regularity
Directory of Open Access Journals (Sweden)
H.-m. Hsu
2011-08-01
Full Text Available With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO_{2}, NO_{x}, CO, SO_{2}, and O_{3} and aerosol (PM_{10} measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, plain/hill, and industrial/agricultural locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, and intermediate (20 ~ 30 days peaks are also identified with the continuous wavelet transform (CWT. The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of −5/3 and −1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. These exponents are mostly independent of the averages and standard deviations of time series measured at various geographic settings, i.e., the spatial inhomogeneities. In other words, they possess dominant universal structures. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, −3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are important structural information, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.
Power-law Growth and Punctuated Equilibrium Dynamics in Water Resources Systems
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.
Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The shear-thinning influence on the core-annular flow stability of two immiscible power-law fluids is considered by making a linear stability analysis.The flow is driven by an axial pressure gradient in a straight pipe with the interface between the two fluids occupied by an insoluble surfactant.Given the basic flow for this core-annular arrangement,the analytical solution is obtained with respect to the power-law fluid model.The linearized equations for the evolution of infinitesimal disturbances are derived and the stability problem is formulated as a generalized matrix eigenvalue problem,which is solved by using the software package Matlab based on the QZ algorithm.The shear-thinning property is found to have marked influence on the power-law fluid core-annular flow stability,which is reflected in various aspects.First,the capillary instability is magnified by the shear-thinning property,which may lead to an essential difference between power-law and Newtonian fluid flows.Especially when the interface is close to the pipe wall,the power-law fluid flow may be unstable while the Newtonian fluid flow is stable.Second,under disturbances to the interface a velocity discontinuity at the interface appears which is destabilizing to the flow.The magnitude of this velocity discontinuity is affected by the power-law index and the flow stability is influenced correspondingly.Besides,the shear-thinning property may induce new stability modes which do not appear in the Newtonian fluid flow.The flow stability shows much dependence on the interface location,the role of which was neglected in most previous studies.The shear-thinning fluid flow is more unstable to long wave disturbances when the interface is close to the pipe wall,while the Newtonian fluid flow is more unstable when the interface is close to the pipe centerline.But this trend is changed by the addition of interfacial surfactant,for which the power-law fluid flow is more stable no matter where the interface is
Lifetimes of metastable ion clouds in a Paul trap: Power-law scaling
Weiss, D. K.; Nam, Y. S.; Blümel, R.
2016-04-01
It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime τ¯m of the metastable cloud follows a power law, τ¯m˜(γ-γc) -β , where γc is the value of the damping constant at which the transition occurs. The exponent β depends on the trap control parameter q , but is independent of both the number of particles N stored in the trap and the trap control parameter a , which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given a and q , γc scales approximately like γc=C ln[ln(N ) ] +D as a function of N , where C and D are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.
Resetting of fluctuating interfaces at power-law times
Gupta, Shamik; Nagar, Apoorva
2016-11-01
What happens when the time evolution of a fluctuating interface is interrupted by resetting to a given initial configuration after random time intervals τ distributed as a power-law ∼ {τ }-(1+α ); α \\gt 0? For an interface of length L in one dimension, and an initial flat configuration, we show that depending on α, the dynamics in the limit L\\to ∞ exhibit a spectrum of rich long-time behavior. It is known that without resetting, the interface width grows unbounded with time as {t}β in this limit, where β is the so-called growth exponent characteristic of the universality class for a given interface dynamics. We show that introducing resetting leads to fluctuations that are bounded at large times for α \\gt 1. Corresponding to such a reset-induced stationary state is a distribution of fluctuations that is strongly non-Gaussian, with tails decaying as a power-law. The distribution exhibits a distinctive cuspy behavior for a small argument, implying that the stationary state is out of equilibrium. For α \\lt 1, on the contrary, resetting to the flat configuration is unable to counter the otherwise unbounded growth of fluctuations in time, so that the distribution of fluctuations remains time dependent with an ever-increasing width, even at long times. Although stationary for α \\gt 1, the width of the interface grows forever with time as a power-law for 1\\lt α \\lt {α }({{w})}, and converges to a finite constant only for larger α, thereby exhibiting a crossover at {α }({{w})}=1 + 2β . The time-dependent distribution of fluctuations exhibits for α \\lt 1 and for small arguments further interesting crossover behavior from cusp to divergence across {α }({{d})}=1-β . We demonstrate these results by exact analytical results for the paradigmatic Edwards–Wilkinson (EW) dynamical evolution of the interface, and further corroborate our findings by extensive numerical simulations of interface models in the EW and Kardar–Parisi–Zhang universality
Reciprocity and the Emergence of Power Laws in Social Networks
Schnegg, M
2006-01-01
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 gamma ~ 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 distributio...
Deviations from uniform power law scaling in nonstationary time series
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.
Exponential and power laws in public procurement markets
Kristoufek, Ladislav; Skuhrovec, Jiri
2012-07-01
We analyze for the first time a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40000 public procurements in the Czech Republic between 2006 and 2011, focusing on the distributional properties of the variables of interest. We uncover several scaling laws —the exponential law for the number of bidders, and the power laws for the total revenues and total spendings of the participating companies, which even follows Zipf's law for the 100 most spending institutions. We propose an analogy between extensive and non-extensive systems in physics and the public procurement market situations. Through an entropy maximization, such analogy yields some interesting results and policy implications with respect to the Maxwell-Boltzmann and Pareto distributions in the analyzed quantities.
Keeping the edge: an accurate numerical method to solve the stream power law
Campforts, B.; Govers, G.
2015-12-01
Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.
Bose-Einstein condensation in dark power-law laser traps
International Nuclear Information System (INIS)
We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order l allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a 'finger' or of a 'hockey puck' in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.
Moduli of curve families and (quasi-)conformality of power-law entropies
Kalogeropoulos, Nikos
2016-03-01
We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the calculations of the moduli of curve families for a cylinder and for an annulus in ℝn. The underlying motivation for these studies is that the definitions and some properties of the modulus of a curve family resembles those of the Tsallis entropy, when the latter is seen from a micro-canonical viewpoint. We comment on the origin of the conjectured invariance of the Tsallis entropy under Möbius transformations of the non-extensive (entropic) parameter. Needing techniques applicable to both locally Euclidean and fractal classes of spaces, we examine the behavior of the Tsallis functional, via the modulus, under quasi-conformal maps. We comment on properties of such maps and their possible significance for the dynamical foundations of power-law entropies.
Degeneracies and scaling relations in general power-law models for gravitational lenses
Wucknitz, O
2002-01-01
The time delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. The most important uncertainty is related to the mass model used. We discuss a family of models with a separable radial power-law and an arbitrary angular dependence for the potential psi = r^beta * F(theta). Isothermal potentials are a special case of these models with beta=1. An additional external shear is used to take into account perturbations from other galaxies. Using a simple linear formalism for quadruple lenses, we can derive H0 as a function of the observables and the shear. If the latter is fixed, the result depends on the assumed power-law exponent according to H0 proportional to (2-beta)/beta. The effect of external shear is quantified by introducing a `critical shear' gamma_c as a measure for the amount of shear that changes the result significantly. The analysis shows, that in the gene...
Fractal Analysis of Power-Law Fluid in a Single Capillary
Institute of Scientific and Technical Information of China (English)
YUN Mei-Juan; YU Bo-Ming; Xu Peng; CAI Jian-Chao
2008-01-01
The fractal expressions for flow rate and hydraulic conductivity for power-law fluids in a single capillary are derived based on the fxactal nature of tortuous capillaries.Every parameter in the proposed expressions has clear physical meaning.The flow rate and hydraulic conductivity for power-law fluids are found to be related to the tortuosity fractal dimension and the power-law index.Tjle flow rate for power-law fluids increases with the increasing power-law index but decreases with the increasing tortuosity fractal dimension.Good agreement between the model predictions for flow in a fractal capillary and in a converging-diverging duct is obtained.The results suggest that the fractal capillary model can be used to model the power-law fluids with different rheological properties.
Power-law distribution functions derived from maximum entropy and a symmetry relationship
Peterson, G. J.; Dill, K. A.
2011-01-01
Power-law distributions are common, particularly in social physics. Here, we explore whether power-laws might arise as a consequence of a general variational principle for stochastic processes. We describe communities of 'social particles', where the cost of adding a particle to the community is shared equally between the particle joining the cluster and the particles that are already members of the cluster. Power-law probability distributions of community sizes arise as a natural consequence...
Numerical Study of Thermal Boundary Layer on a Continuous Moving Surface in Power Law Fluids
Institute of Scientific and Technical Information of China (English)
Hao ZHANG; Xinxin ZHANG; Liancun ZHENG
2007-01-01
This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.
Kramers escape rate in overdamped systems with the power-law distribution
Zhou, Yanjun; Du, Jiulin
2014-01-01
Kramers escape rate in the overdamped systems with the power-law distribution is studied. By using the mean first passage time, we derive the escape rate for the power-law distribution and obtain the Kramers' infinite barrier escape rate in this case. It is shown that the escape rate for the power-law distribution extends the Kramers' overdamped result to the relatively low barrier. Furthermore, we apply the escape rate for the power-law distribution to the unfolding of titin and show a bette...
Existence of Hierarchies and Human's Pursuit of Top Hierarchy Lead to Power Law
Yu, Shuiyuan; Liu, Haitao
2016-01-01
The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these seemingly unrelated systems share great similarity. Through a detailed analysis of natural language texts and simulation experiments based on the proposed 'Hierarchical Selection Model', we found that the existence of hierarchies and human's pursuit of top hierarchy lead to the power law. Further, the power law is a statistical and emergent performance of hierarchies, and it is the universality of hierarchies that contributes to the ubiquity of the power law.
Universal Power Law for Relationship between Rainfall Kinetic Energy and Rainfall Intensity
Directory of Open Access Journals (Sweden)
Seung Sook Shin
2016-01-01
Full Text Available Rainfall kinetic energy has been linked to linear, exponential, logarithmic, and power-law functions using rainfall intensity as an independent variable. The power law is the most suitable mathematical expression used to relate rainfall kinetic energy and rainfall intensity. In evaluating the rainfall kinetic energy, the empirical power laws have shown a larger deviation than other functions. In this study, universal power law between rainfall kinetic energy and rainfall intensity was proposed based on the rainfall power theory under an ideal assumption that drop-size is uniformly distributed in constant rainfall intensity. An exponent of the proposed power law was 11/9 and coefficient was estimated at 10.3 from the empirical equations of the existing power-law relation. The rainfall kinetic energy calculated by universal power law showed >95% concordance rate in comparison to the average values calculated from exponential and logarithmic functions used in soil erosion model such as USLE, RUSLE, EUROSEM, and SEMMA and <5% relative difference as compared to the average rainfall kinetic energies calculated by other empirical functions. Therefore, it is expected that power law of ideal assumption may be utilized as a universal power law in evaluating rainfall kinetic energy.
Effect of nanocrystalline TiC powder addition on the hardness and wear resistance of cast iron
Energy Technology Data Exchange (ETDEWEB)
Razavi, Mansour [Materials and Energy Research Center, P.O. Box 1455-4777, Tehran (Iran, Islamic Republic of)], E-mail: m-razavi@merc.ac.ir; Rahimipour, Mohammad Reza [Materials and Energy Research Center, P.O. Box 1455-4777, Tehran (Iran, Islamic Republic of); Rajabi-Zamani, Amir Hossein [Materials and Energy Research Center, P.O. Box 1455-4777, Tehran (Iran, Islamic Republic of)
2007-04-25
In this research, the feasibility of the addition of nanocrystalline TiC particles - synthesized via mechanical alloying - to iron matrix melt was investigated. For the preparation of TiC, impure titanium chips and carbon black were placed in a high-energy ball mill and sampled after different milling time. XRD studies showed that at milling times more than 15 h, TiC was synthesized. It was observed from the peak broadening of the diffraction patterns that the TiC crystallites were in the scale of nanometer. 0.96 wt.% TiC synthesized after 15 h was added to a 4 wt.% C cast iron melt. It was observed that this small amount of TiC was enough to improve the structure, hardness and wear resistance of the cast iron significantly.
Glitch observation and hard X-ray power law measurement in PSR J1119-6127
Archibald, R. F.; Tendulkar, S. P.; Scholz, P. A.; Kaspi, V. M.
2016-07-01
We report on Swift-XRT, NuSTAR and Fermi spectral and timing observations of PSR J1119-6127, a rotation-powered high magnetic field pulsar that showed a magnetar-like burst on 2016 July 28, 01:27:51 UT (ATel #9274, ATel #9282).
Indian Academy of Sciences (India)
Chaudry Masood Khalique
2013-03-01
In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.
Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source
Energy Technology Data Exchange (ETDEWEB)
Hayat, T. [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan); Department of Mathematics, College of Sciences, King Saud University P.O. Box 2455, Riyadh 11451 (Saudi Arabia); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan); Qasim, M. [Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); Obaidat, S. [Department of Mathematics, College of Sciences, King Saud University P.O. Box 2455, Riyadh 11451 (Saudi Arabia)
2012-02-15
Highlights: Black-Right-Pointing-Pointer Mathematical model for Jeffery fluid is designed. Black-Right-Pointing-Pointer Power law heat flux is taken. Black-Right-Pointing-Pointer Analysis with heat source is performed. Black-Right-Pointing-Pointer Solution to nonlinear problem is constructed. Black-Right-Pointing-Pointer Convergence of developed series solution is ensured. - Abstract: The aim of this paper is to examine the flow of an incompressible Jeffery fluid over a stretching surface. In addition the heat transfer process with power law heat flux and heat source in the presence of thermal radiation is considered. Homotopic solutions for velocity and temperature fields are developed. The related convergence analysis is carried out very carefully. The plotted results are discussed for flow and heat transfer characteristics.
Reciprocity and the Emergence of Power Laws in Social Networks
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.
Diffusion-limited aggregation with power-law pinning.
Hentschel, H G E; Popescu, M N; Family, F
2004-01-01
Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth R(-gamma)(N) (where R(N) is the radius of the N-particle cluster). For gamma>1 the growth pattern is in the same universality class as diffusion limited aggregation (DLA), while for gammaDLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at gamma=1/2, significantly smaller than might be expected from the lower bound alpha(min) approximately 0.67 of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for D(gamma) both close to the breakdown of DLA universality class, i.e., gamma less, similar 1, and close to the pinning transition, i.e., gamma greater, similar 1/2. PMID:14995617
Consistency relation in power law G-inflation
International Nuclear Information System (INIS)
In the standard inflationary scenario based on a minimally coupled scalar field, canonical or non-canonical, the subluminal propagation of speed of scalar perturbations ensures the following consistency relation: r ≤ −8nT, where r is the tensor-to-scalar-ratio and nT is the spectral index for tensor perturbations. However, recently, it has been demonstrated that this consistency relation could be violated in Galilean inflation models even in the absence of superluminal propagation of scalar perturbations. It is therefore interesting to investigate whether the subluminal propagation of scalar field perturbations impose any bound on the ratio r/|nT| in G-inflation models. In this paper, we derive the consistency relation for a class of G-inflation models that lead to power law inflation. Within these class of models, it turns out that one can have r > −8nT or r ≤ −8nT depending on the model parameters. However, the subluminal propagation of speed of scalar field perturbations, as required by causality, restricts r ≤ −(32/3) nT
Quantum healing of classical singularities in power-law spacetimes
Energy Technology Data Exchange (ETDEWEB)
Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)
2007-07-07
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.
Power law distribution of seismic rates: theory and data
Saichev, A
2004-01-01
We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 x 5 km^2 and time intervals dt =1, 10, 100 and 1000 days. We find a stable power law tail P(r) ~ 1/r^{1+mu} with exponent mu \\approx 1.6 for all time intervals. These observations are explained by a simple stochastic branching process previously studied by many authors, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. We develop the full theory in terms of generating functions for describing the space-time organization of earthquake sequences and develop several approximations to solve the equations. The calibration of the theory to the empirical observations shows that it is essential to augment the ETAS model by taking account of th...
Dexter, Jason
2013-01-01
We propose a new model of the steep power law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, the inner radii of radiation pressure dominated accretion discs are expected to i) become effectively optically thin and ii) produce significant luminosities. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energy. These spectra sum together to form a steep power law tail to the spectrum. A given photon energy on this tail corresponds to a narrow range in radius, so that local vertical oscillations of the disc naturally produce high quality high-frequency quasi-periodic oscillations (HFQPOs) in the hard X-ray band. The two lowest order modes have a robust frequency ratio of ~1.53. This model explains the appearance of steep power law spectra and HFQPOs at high luminosity, the 3:2 HFQPO frequency ratios, and their association with the power law spectral component. We predict an increase in QPO qu...
Directory of Open Access Journals (Sweden)
E. Dologlou
2009-01-01
Full Text Available The power law relation between the stress drop of "non thrust" earthquakes and the lead time of precursory Seismic Electric Signals (SES, obtained by Dologlou (2008a, has been tested by using additional data from the most recent earthquake that occurred on 8 June 2008, in Andravida, NW. Peloponnesus, Greece and from two other destructive earthquakes that occurred in the past in Ionian sea. A critical exponent α=0.33 is derived which is close to the one (e.g. 0.29 reported by Dologlou (2008a. The above preliminary result strengthens the hypothesis that probably signatures of criticality are present in the earthquake preparation and precursory SES processes and that both phenomena are governed by same physics.
Modified bosonic gas trapped in a generic 3-dim power law potential
Energy Technology Data Exchange (ETDEWEB)
Castellanos, E., E-mail: elias@zarm.uni-bremen.de; Laemmerzahl, C., E-mail: claus.laemmerzahl@zarm.uni-bremen.de
2014-04-04
We analyze the consequences caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose–Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the condensation temperature is shifted as a consequence of such deformation and show that this fact could be used to provide bounds on the deformation parameters. Additionally, we show that the shift in the condensation temperature, described as a non-trivial function of the number of particles and the trap parameters, could be used as a criterion to analyze the effects caused by a deformed dispersion relation in weakly interacting systems and also in finite size systems.
Mathematical modeling for laminar flow of power law fluid in porous media
Energy Technology Data Exchange (ETDEWEB)
Silva, Renato A.; Mesquita, Maximilian S. [Universidade Federal do Espirito Santo (UFES), Sao Mateus, ES (Brazil). Centro Universitario Norte do Espirito Santo. Dept. de Engenharias e Computacao
2010-07-01
In this paper, the macroscopic equations for laminar power-law fluid flow is obtained for a porous medium starting from traditional equations (Navier-Stokes). Then, the volume averaging is applied in traditional transport equations with the power-law fluid model. This procedure leads to macroscopic transport equations set for non-Newtonian fluid. (author)
Numerical tools for obtaining power-law representations of heavy-tailed datasets
Mansfield, Marc L.
2016-01-01
Many empirical datasets have highly skewed, non-Gaussian, heavy-tailed distributions, dominated by a relatively small number of data points at the high end of the distribution. Consistent with their role as stable distributions, power laws have frequently been proposed to model such datasets. However there are physical situations that require distributions with finite means. Such situations may call for power laws with high-end cutoffs. Here, I present a maximum-likelihood technique for determining an optimal cut-off power law to represent a given dataset. I also develop a new statistical test of the quality of fit. Results are demonstrated for a number of benchmark datasets. Non-power-law datasets can frequently be represented by power laws, but this is a trivial result unless the dataset spans a broad domain. Nevertheless, I demonstrate that there are non-power-law distributions, including broad log-normal distributions, whose tails can be fit to power laws over many orders of magnitude. Therefore, caution is called for whenever power laws are invoked to represent empirical data. Supplementary material in the form of one pdf file available from the Journal web page at: http://dx.doi.org/10.1140/epjb/e2015-60452-3
Numerical Modeling of the Flow of a Power Law Ceramic Slurry in the Tape Casting Process
DEFF Research Database (Denmark)
Jabbari, Masoud; Hattel, Jesper Henri
2012-01-01
interest to be able to control it. In the present work the flow of La0.85Sr0.15MnO3 (LSM) material in the doctor blade region is modelled numerically with ANSYS Fluent in combination with an Ostwald power law constitutive equation. Based on rheometer experiments the constants in the Ostwald power law...
A Possible Origin of Power-Law Distribution in Stock Markets
Institute of Scientific and Technical Information of China (English)
杨纯斌; 蔡勖
2002-01-01
The origin of the power-law distribution in stock markets is discussed from the point of view of self-organized criticality. An analytical expression for the distribution is given from a simple model consideration. We see that power-law increasing or decreasing distribution functions can have the same origin, depending on the values of the parameters.
On the structure and phase transitions of power-law Poissonian ensembles
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.
Chen, Yanguang
2013-01-01
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through averaging an exponential distribution. For the distributions defined in a 1-dimension space, the scaling exponent is 1; while for those defined in a 2-dimension space, the scaling exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distribution. Third, it is the real power-law distribution that can be related with fractal dimension. ...
Mobile user forecast and power-law acceleration invariance of scale-free networks
Institute of Scientific and Technical Information of China (English)
Guo Jin-Li; Guo Zhao-Hua; Liu Xue-Jiao
2011-01-01
This paper studies and predicts the number growth of China's mobile users by using the power-law regression.We find that the number growth of the mobile users follows a power law.Motivated by the data on the evolution of the mobile users,we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model,in which the nodes grow following a power-law acceleration.The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process.This result shows that the model generates appropriate power-law connectivity distributions.Therefore,we find a power-law acceleration invariance of the scale-free networks.The numerical simulations of the models agree with the analytical results well.
Echeverria, J. C.; Rodriguez, E.; Aguilar-Cornejo, M.; Alvarez-Ramirez, J.
2016-10-01
In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
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 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference. PMID:16090049
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 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.
AEGIS: A MULTIWAVELENGTH STUDY OF SPITZER POWER-LAW GALAXIES
International Nuclear Information System (INIS)
This paper analyzes a sample of 489 Spitzer/Infrared Array Camera (IRAC) sources in the Extended Groth Strip (EGS), whose spectral energy distributions fit a red power law (PL) from 3.6 to 8.0 μm. The median redshift for sources with known redshifts is (z) = 1.6. Though all or nearly all of the sample galaxies are likely to be active galactic nuclei (AGNs), only 33% were detected in the EGS X-ray survey (AEGIS-X) using 200 ks Chandra observations. The detected sources are X-ray luminous with L X>1043 erg s-1 and moderately to heavily obscured with N H>1022 cm-2. Stacking the X-ray-undetected sample members yields a statistically significant X-ray signal, suggesting that they are on average more distant or more obscured than sources with X-ray detections. The ratio of X-ray to mid-infrared fluxes suggests that a substantial fraction of the sources undetected in X-rays are obscured at the Compton-thick level, in contrast to the X-ray-detected sources, all of which appear to be Compton thin. For the X-ray-detected PL sources with redshifts, an X-ray luminosity L X ∼ 1044 erg s-1 marks a transition between low-luminosity, blue sources dominated by the host galaxy to high-luminosity, red PL sources dominated by nuclear activity. X-ray-to-optical ratios, infrared variability, and 24 μm properties of the sample are consistent with the identification of infrared PL sources as active nuclei, but a rough estimate is that only 22% of AGNs are selected by the PL criteria. Comparison of the PL selection technique and various IRAC color criteria for identifying AGNs confirms that high-redshift samples selected via simple IRAC colors may be heavily contaminated by starlight-dominated objects.
Major power law slip-weakening in laboratory gouge friction
Chambon, G.; Schmittbuhl, J.; Corfdir, A.
2003-04-01
We performed gouge-shearing experiments in a large-displacement ring-shear apparatus. The granular gouge (quartz sand) undergoes significant slip-weakening over seismic-like distances (0.5 m) and minor velocity-weakening over microscopic length scales (100 μm). The reproducible decrease of gouge effective friction μ with shear displacement δ follows a power law: μ = μ_0 + A δ-β, with β = 0.4. Such a slip-weakening process can be accounted for in an extended rate- and state-dependent friction law through a supplementary state variable. However, unlike classical state variables, the evolution law governing this new variable does not involve any characteristic length scale. Accordingly, slip-weakening is found independent of gouge grain size. Careful checks were performed to insure that observed weakening constitutes a real rheological property of the gouge. Moreover, microscopic origin of the slip-weakening has been investigated by means of a Correlation Image Velocimetry (CIV) technique applied to digital pictures of the sample. Most of the deformation appears localized in a 7 grain-wide, comminuted shear band. Nevertheless, CIV also reveals an intermittent, ongoing deformation outside this zone, whose magnitude slowly diminishes as shear displacement increases. This microscopic relaxation denotes a progressive decoupling between the shear zone and the bulk of the sample. Slow decrease of spatially-averaged shear strain <~ngleγrangle is well modeled by a hyperbolic law in displacement δ, without any characteristic length scale: <~ngleγrangle = γ_0 + a δ-1. We interpret the macroscopic slip-weakening as a consequence of the observed decoupling at micro-scale. When extrapolated to faults, this result shows that decimetric weakening distances, frequently reported during earthquakes, can be produced by complex structuring processes inside the gouge layer.
POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING
Energy Technology Data Exchange (ETDEWEB)
Addison, Graeme E.; Dunkley, Joanna [Sub-department of Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH (United Kingdom); Hajian, Amir; Das, Sudeep; Hincks, Adam D.; Page, Lyman A.; Staggs, Suzanne T. [Joseph Henry Laboratories of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544 (United States); Viero, Marco [Department of Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Bond, J. Richard [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada); Devlin, Mark J.; Reese, Erik D. [Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104 (United States); Halpern, Mark; Scott, Douglas [Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z4 (Canada); Hlozek, Renee; Marriage, Tobias A.; Spergel, David N. [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544 (United States); Moodley, Kavilan [Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041 (South Africa); Wollack, Edward [NASA/Goddard Space Flight Center, Code 665, Greenbelt, MD 20771 (United States)
2012-06-20
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 {mu}m; 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}{proportional_to}l{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{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.
Flow of power-law fluids in fixed beds of cylinders or spheres
Singh, John P.
2012-10-29
An ensemble average of the equations of motion for a Newtonian fluid over particle configurations in a dilute fixed bed of spheres or cylinders yields Brinkman\\'s equations of motion, where the disturbance velocity produced by a test particle is influenced by the Newtonian fluid stress and a body force representing the linear drag on the surrounding particles. We consider a similar analysis for a power-law fluid where the stress τ is related to the rate of strain e by τ = 2m en-1e, where m and n are constants. In this case, the ensemble-averaged momentum equation includes a body force resulting from the nonlinear drag exerted on the surrounding particles, a power-law stress associated with the disturbance velocity of the test particle, and a stress term that is linear with respect to the test particle\\'s disturbance velocity. The latter term results from the interaction of the test particle\\'s velocity disturbance with the random straining motions produced by the neighbouring particles and is important only in shear-thickening fluids where the velocity disturbances of the particles are long-ranged. The solutions to these equations using scaling analyses for dilute beds and numerical simulations using the finite element method are presented. We show that the drag force acting on a particle in a fixed bed can be written as a function of a particle-concentration-dependent length scale at which the fluid velocity disturbance produced by a particle is modified by hydrodynamic interactions with its neighbours. This is also true of the drag on a particle in a periodic array where the length scale is the lattice spacing. The effects of particle interactions on the drag in dilute arrays (periodic or random) of cylinders and spheres in shear-thickening fluids is dramatic, where it arrests the algebraic growth of the disturbance velocity with radial position when n≥ 1 for cylinders and n≥ 2 for spheres. For concentrated random arrays of particles, we adopt an
Perera-Burgos, Jorge Adrián; Méndez-Alcaraz, José Miguel; Pérez-Ángel, Gabriel; Castañeda-Priego, Ramón
2016-09-14
Depletion forces are a particular class of effective interactions that have been mainly investigated in binary mixtures of hard-spheres in bulk. Although there are a few contributions that point toward the effects of confinement on the depletion potential, little is known about such entropic potentials in two-dimensional colloidal systems. From theoretical point of view, the problem resides in the fact that there is no general formulation of depletion forces in arbitrary dimensions and, typically, any approach that works well in three dimensions has to be reformulated for lower dimensionality. However, we have proposed a theoretical framework, based on the formalism of contraction of the description within the integral equations theory of simple liquids, to account for effective interactions in colloidal liquids, whose main feature is that it does not need to be readapted to the problem under consideration. We have also shown that such an approach allows one to determine the depletion pair potential in three-dimensional colloidal mixtures even near to the demixing transition, provided the bridge functions are sufficiently accurate to correctly describe the spatial correlation between colloids [E. López-Sánchez et al., J. Chem. Phys. 139, 104908 (2013)]. We here report an extensive analysis of the structure and the entropic potentials in binary mixtures of additive hard-disks. In particular, we show that the same functional form of the modified-Verlet closure relation used in three dimensions can be straightforwardly employed to obtain an accurate solution for two-dimensional colloidal mixtures in a wide range of packing fractions, molar fractions, and size asymmetries. Our theoretical results are explicitly compared with the ones obtained by means of event-driven molecular dynamics simulations and recent experimental results. Furthermore, to assess the accuracy of our predictions, the depletion potentials are used in an effective one-component model to reproduce
A SECOND-ORDER MOMENT TURBULENCE MODEL FOR POWER LAW FLUID WITH PARTICLES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the model has better prediction result than the model. The model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.
Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid
Directory of Open Access Journals (Sweden)
Yazan Taamneh
2013-01-01
Full Text Available This study aims to numerically examine the fluid flow and heat transfer in a porous microchannel saturated with power-law fluid. The governing momentum and energy equations are solved by using the finite difference technique. The present study focuses on the slip flow regime, and the flow in porous media is modeled using the modified Darcy-Brinkman-Forchheimer model for power-law fluids. Parametric studies are conducted to examine the effects of Knudsen number, Darcy number, power law index, and inertia parameter. Results are given in terms of skin friction and Nusselt number. It is found that when the Knudsen number and the power law index decrease, the skin friction on the walls decreases. This effect is reduced slowly while the Darcy number decreases until it reaches the Darcy regime. Consequently, with a very low permeability the effect of power law index vanishes. The numerical results indicated also that when the power law index decreases the fully-developed Nusselt number increases considerably especially, in the limit of high permeability, that is, nonDarcy regime. As far as Darcy regime is concerned the effects of the Knudsen number and the power law index of the fully-developed Nusselt number is very little.
Can power-law scaling and neuronal avalanches arise from stochastic dynamics?
Directory of Open Access Journals (Sweden)
Jonathan Touboul
Full Text Available 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.
Energy consumption reduction in existing HVAC-R systems via a power law controlling kit
International Nuclear Information System (INIS)
This paper presents an alternative solution for reducing energy consumption in heating, ventilation, air conditioning and refrigeration (HVAC-R) systems. For that, an existing typical commercial refrigeration system was equipped with a novel control system based on a power law, using a frequency inverter and a programmable logic controller (PLC). Hence, it was possible to compare the operation and energy consumption of the system with the power law control and with the on-off system, quantifying the obtained gains. The experimental unit consisted of a cooling chamber, an enclosing chamber (antechamber), and a vapor compression refrigeration system, i.e., an example of a practical commercial cooling system. A set of graphs shows the experimental measurements performed with the two systems. In this way, the measured temperatures in some selected points of the two systems, as well as the consumption in kWh for a period of 6 h and 10 min were compared in the tests. The main conclusions of this work are: i) The system operating with the power law control with respect to the conventional on-off control, showed energy consumption savings of up to 31% in a test period of 6 h and 10 min, and ii) The system compressor cycling frequency in the system operating with the power law control is smaller than with the traditional on-off system. Therefore, the study shows that the developed power law control kit has potential to be installed in any existing system with immediate significant energy savings with no need for HVAC-R hardware changes. - Highlights: • An energy consumption reduction strategy for HVAC-R systems is presented. • Power law and on-off control actions are experimentally compared. • Energy savings of 31% were obtained with power law control. • Compressor cycling frequency is smaller with power law control. • Power law control kit has potential to be installed in any existing system
The double power law in human collaboration behavior: The case of Wikipedia
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.
Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media
Directory of Open Access Journals (Sweden)
Meijuan Yun
2014-01-01
Full Text Available We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State
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.
A SIMILARITY METHOD FOR LAMINAR WAKE OF POWER-LAW FLUID FLOW AROUND A FLAT PLATE
Institute of Scientific and Technical Information of China (English)
Liu Cun-fang; Wang Mei-xia
2003-01-01
Based on the characteristic equation for power-law fluid and the Prandtl boundary layer equation, using the similarity method similar to that of Newtonian fluids, two similarity variables were given and a normal differential equation was derived for the laminar wake of power-law fluid flow produced by a flat plate. And numerical results were obtained. The results show that the power-law index n has evident influence on the velocity distribution in the wake. In the wake, velocity gradient is larger, and the wake is narrower for larger n.
Energy Technology Data Exchange (ETDEWEB)
Song, M.H.
1981-10-01
The effect of the addition of yttrium on the elevated temperature tensile properties and hardness of an Fe-34% Ni-12% Cr candidate LMFBR cladding and duct alloy was investigated. Tensile tests were performed from room temperature to 800/sup 0/C in 100/sup 0/C steps at strain rates of 2.2 x 10/sup -3/ and 2.2 x 10/sup -4/ sec/sup -1/. Hardness tests were performed from room temperature to 850/sup 0/C in 50/sup 0/C steps. The addition of 0.1% yttrium decreased the yield stress and ultimate tensile stress in the test temperature range employed. Hardness also decreased over this test temperature range. In tensile tests, dynamic strain aging behavior occurred both for the undoped and doped alloy in the temperature range from 200 to 600/sup 0/C and 300 to 600/sup 0/C for the lower and higher strain rate, respectively.
Comment on 'Generalized Heisenberg algebra coherent states for power-law potentials'
Iqbal, Shahid
2011-01-01
We argue that the statistical features of generalized coherent states for power-law potentials based on Heisenberg algebra, presented in a recent paper by Berrada et al (Phys. Lett. A, 375, 298 (2011)) are incorrect.
Symmetries of boundary layer equations of power-law fluids of second grade
Institute of Scientific and Technical Information of China (English)
Mehmet Pakdemirli; Yi(g)it Aksoy; Muhammet Y(u)r(u)soy; Chaudry Masood Khalique
2008-01-01
A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incom-pressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classifica-tion with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
A penalty method for approximations of the stationary power-law Stokes problem
Directory of Open Access Journals (Sweden)
Lew Lefton
2001-01-01
Full Text Available We study approximations of the steady state Stokes problem governed by the power-law model for viscous incompressible non-Newtonian flow using the penalty formulation. We establish convergence and find error estimates.
Research on power-law acoustic transient signal detection based on wavelet transform
Han, Jian-hui; Yang, Ri-jie; Wang, Wei
2007-11-01
Aiming at the characteristics of acoustic transient signal emitted from antisubmarine weapon which is being dropped into water (torpedo, aerial sonobuoy and rocket assisted depth charge etc.), such as short duration, low SNR, abruptness and instability, based on traditional power-law detector, a new method to detect acoustic transient signal is proposed. Firstly wavelet transform is used to de-noise signal, removes random spectrum components and improves SNR. Then Power- Law detector is adopted to detect transient signal. The simulation results show the method can effectively extract envelop characteristic of transient signal on the condition of low SNR. The performance of WT-Power-Law markedly outgoes that of traditional Power-Law detection method.
Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems
Rodin, Aleksandr; Fogler, Michael
2011-03-01
Observation of power-law dependence of conductance on temperature and voltage has been reported for a wide variety of low-dimensional systems(nano-wires, nano-tubes, and conducting polymers). This behavior has been attributed to the Luttinger liquid effects expected in a pure one-dimensional wire. However, the systems studied were neither one-dimensional nor defect-free. Using numerical simulations we show that the power-law behavior can arise from variable-range hopping in an ensemble of non-interacting disordered wires connected in parallel. This power-law behavior holds in restricted ranges of voltage and temperature, typical of experimental situations. Physically, it comes from rare, but highly conducting hopping paths that appear by chance in some members of the ensemble. The power-law exponents and their dependence on system parameters are consistent with the great majority of available empirical data. Supported by Grant NSF DMR-0706654.
Holographic f(T)-gravity model with power-law entropy correction
Karami, K.; Asadzadeh, S.; Abdolmaleki, A.; Safari, Z.
2011-01-01
Using a correspondence between the f(T)-gravity with the power-law entropy corrected version of the holographic dark energy model, we reconstruct the holographic f(T)-gravity model with power-law entropy correction. We fit the model parameters by using the latest observational data including type Ia supernovea, baryon acoustic oscillation, cosmic microwave background, and Hubble parameter data. We also check the viability of our model using a cosmographic analysis approach. Using the best-fit...
Power-law entropy-corrected HDE and NADE in Brans-Dicke cosmology
Sheykhi, A.; Karami, K.; Jamil, Mubasher; Kazemi, E.; Haddad, M
2011-01-01
Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relev...
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model
Teka, Wondimu; Stockton, David; Santamaria, Fidel
2016-01-01
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. PMID:26937967
Chimera patterns induced by distance-dependent power-law coupling in ecological networks
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schoell, Eckehard
2016-01-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long range interaction the coupling topology can be varied from local via nonlocal to global coupling. To expl...
Directory of Open Access Journals (Sweden)
Yan Zhang
2011-01-01
Full Text Available The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.
Power law in the angular velocity distribution of a granular needle
Piasecki, J.; Viot, P.
2005-01-01
We show how inelastic collisions induce a power law with exponent -3 in the decay of the angular velocity distribution of anisotropic particles with sufficiently small moment of inertia. We investigate this question within the Boltzmann kinetic theory for an elongated granular particle immersed in a bath. The power law persists so long as the collisions are inelastic for a large range of angular velocities provided the mass ratio of the anisotropic particle and the bath particles remains smal...
Important Property of GRB Pulse: Power-Law Indices of Time Properties on Energy
Indian Academy of Sciences (India)
Zhao-Yang Peng
2014-09-01
The dependence of pulse temporal properties (pulse width, pulse rise width and pulse decay width) on energy is power-law function. Some correlated relationships between the power-law indices of the pulse time properties on energy and the spectral lags, relative spectral lags, spectral parameters of band function, and photon flux using a well-separated long-duration -ray burst (GRB) pulse sample is demonstrated here. We argue that the curvature effect can explain the correlated properties.
Power-law and intermediate inflationary models in f( T)-gravity
Rezazadeh, K.; Abdolmaleki, A.; Karami, K.
2016-01-01
We study inflation in the framework of f( T)-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in f( T)-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law f( T) function and investigate the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, the power-law and intermediate inflationary models in f( T)-gravity can be compatible with the observational results of Planck 2015 at 68% CL. We find that in our f( T) setting, the potentials responsible for the both power-law and intermediate inflationary models have the power-law form V( ϕ) ∝ ϕ m but the power m is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of f( T)-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, is that the self-interacting quartic potential V( ϕ) ∝ ϕ 4 which has special reheating properties, can be consistent with the Planck 2015 data in our f( T) scenario while it is ruled out in the standard inflationary scenario.
Why credit risk markets are predestined for exhibiting log-periodic power law structures
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.
Influence of aging treatments and alloying additives on the hardness of Al-11Si-2.5Cu-Mg alloys
International Nuclear Information System (INIS)
This study investigated the effects of cooling rate, heat treatment as well as additions of Mn and Sr on hardness and hardening characteristics in Al-11Si-2.5Cu-Mg alloys. The results of scanning electron microscopy reveal that the age-hardening behaviour is related to the precipitation sequence of alloy. An energy dispersive spectroscopy analysis was used to identify the precipitated phases. The results also show that the hardness of the solution heat-treated samples is higher in air-cooled alloys than in furnace-cooled ones. Furthermore, the hardness observed in solution heat-treated samples is higher than in as-cast samples for air-cooled alloys, with the highest hardness level in the non-modified alloys. The highest hardness levels among the artificially aged samples were observed in the non-modified, air-cooled alloys. These levels occur after aging for longer times at lower temperatures (e.g. 30 h at 155 oC). The alloys studied did not display any softening after 44 h at 155 oC, whereas at 180 oC, softening was noted to occur after 10-15 h. At short aging times of 5-10 h, high hardness values may be obtained by aging at 180 oC. At aging temperatures of 200 oC, 220 oC and 240 oC, softening began after 2 h had elapsed. The cooling rate during solidification does not appear to have any significant effect on the precipitation characteristics and hardness of the Sr-modified alloys at certain aging temperatures. On the other hand, the effects of cooling rate may be clearly observed in the non-modified alloys. Manganese has a minimal effect on the hardness of the aged samples as it diminishes the potential action of age-hardening, while strontium lessens the hardness of the artificially aged samples. The effect of strontium, however, is more pronounced in the air-cooled alloys than in the furnace-cooled alloys. Strontium also has a noticeable effect on the reduction of hardness in aged Mg-containing Al-Si-Cu alloys, in that it affects the precipitates containing Cu
International Nuclear Information System (INIS)
Highlights: ► The microstructure and hardness of deposited Ti-6Al-4V blocks are investigated. ► Hardness is influenced by post heat treatment rather than by process parameters. ► Microstructure within the prior β-grains varies to some extent from grain to grain. ► A 600 °C/4 h treatment significantly increased the average hardness. - Abstract: Additive layer manufacturing offers a potential for time and cost savings, especially for aerospace components made from costly titanium alloys. In this paper, the morphology, microstructure, chemical composition, and hardness of additive manufactured Ti-6Al-4V blocks are investigated and discussed. Blocks (7 beads wide, 7 layers high) were deposited using Ti-6Al-4V wire and a Nd:YAG laser. Two different sets of parameters are used and three different post heat treatment conditions (as-built, 600 °C/4 h, 1200 °C/2 h) are investigated. The experiments reveal elementary properties of additive manufactured Ti-6Al-4V material in correlation to process parameters and heat treatments, which are discussed comprehensively.
Energy Technology Data Exchange (ETDEWEB)
Brandl, Erhard, E-mail: erhard.brandl@eads.net [EADS Innovation Works, Metallic Technologies and Surface Engineering, D-81663 Munich (Germany); Schoberth, Achim, E-mail: achim.schoberth@eads.net [EADS Innovation Works, Metallic Technologies and Surface Engineering, D-81663 Munich (Germany); Leyens, Christoph, E-mail: christoph.leyens@tu-dresden.de [Technical University of Dresden, Institute of Materials Science, Chair of Materials Technology, Berndt-Bau, Helmholtzstr. 7, D-01062 Dresden (Germany)
2012-01-15
Highlights: Black-Right-Pointing-Pointer The microstructure and hardness of deposited Ti-6Al-4V blocks are investigated. Black-Right-Pointing-Pointer Hardness is influenced by post heat treatment rather than by process parameters. Black-Right-Pointing-Pointer Microstructure within the prior {beta}-grains varies to some extent from grain to grain. Black-Right-Pointing-Pointer A 600 Degree-Sign C/4 h treatment significantly increased the average hardness. - Abstract: Additive layer manufacturing offers a potential for time and cost savings, especially for aerospace components made from costly titanium alloys. In this paper, the morphology, microstructure, chemical composition, and hardness of additive manufactured Ti-6Al-4V blocks are investigated and discussed. Blocks (7 beads wide, 7 layers high) were deposited using Ti-6Al-4V wire and a Nd:YAG laser. Two different sets of parameters are used and three different post heat treatment conditions (as-built, 600 Degree-Sign C/4 h, 1200 Degree-Sign C/2 h) are investigated. The experiments reveal elementary properties of additive manufactured Ti-6Al-4V material in correlation to process parameters and heat treatments, which are discussed comprehensively.
M.E. Moussa; M.A. Waly; A.M. El-Sheikh
2014-01-01
The effect of Ca addition on modification of primary Mg2Si, hardness and wear behavior in Mg–5 wt.%Si hypereutectic alloy has been investigated. The results showed clearly that without Ca addition, most of primary Mg2Si appeared as coarse dendritic morphology with average size of about 215 μm. With the addition of 0.1 wt.%Ca, the average size of primary Mg2Si decreased to about 98 μm, but their morphologies did not significantly changed. As the addition level of Ca increased to 0.3 wt.%, the ...
Eadie, Chris; Favis-Mortlock, David
2010-05-01
distribution is fitted, but a much longer recurrence interval — on the order of 1000 years — using the USA's standard LP3 method. In addition Pandey et al. (1998) found that fitting a power-law distribution, compared with fitting a Generalized Extreme Value distribution, can lead to a large decrease in the predicted return period for a given flood event. Both these findings have obvious implications for river management design. Power-law distributions have been fitted to fluvial discharge data by many authors (most notably by Malamud et al., 1996 and Pandey et al., 1998), who then use these fitted distributions to estimate flow probabilities. These authors found that the power-law performed as well or better than many of the distributions currently used around the world, despite utilising fewer parameters. The power-law has not, however, been officially adopted by any country for fitting to fluvial discharge data. This paper demonstrates a statistically robust method, based on Maximum Likelihood Estimation, for fitting a power-law distribution to mean daily streamflows. The fitted distribution is then used to calculate return periods, which are compared to the return periods obtained by other, more commonly used, distributions. The implications for river management, extremes of flow in particular, are then explored.
Rovatti, L.; Lemke, J. N.; Emami, A.; Stejskal, O.; Vedani, M.
2015-12-01
Fe-based hardfacing alloys containing high volume fraction of hard phases are a suitable material to be deposited as wear resistant thick coatings. In the case of alloys containing high amount of interstitial alloying elements, a key factor affecting the performance is dilution with the substrate induced by the coating process. The present research was focused on the analysis of V-bearing Fe-based alloys after calibrated carbon and vanadium additions (in the range from 3 to 5 wt.%) to a commercial Fe-C-B-Ni hardfacing alloy. Vanadium carbides with a petal-like morphology were observed in the high-V hypereutectic alloys allowing to reach hardness values above 700 HV. The solidification range shifted to higher temperatures with increasing amount of vanadium addition and in the case of hypereutectic alloys, the gap remains close to that of the original alloy. In the last step of the research, the microstructural evolution after dilution was analyzed by casting the V-rich alloys on a steel substrate. The dilution, caused by the alloying element diffusion and the local melting of the substrate, modified the microstructure and the hardness for a relevant volume fraction of the hardfacing alloys. In particular, the drop of interstitial elements induced the transition from the hypereutectic to the hypoeutectic microstructure and the formation of near-spherical V-rich carbides. Even after dilution, the hardness of the new alloys remained higher than that measured in the original Fe-C-B-Ni alloy.
A stable and robust calibration scheme of the log-periodic power law model
Filimonov, V.; Sornette, D.
2013-09-01
We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time tc, defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.
Power-law tails in probability density functions of molecular cloud column density
Brunt, Chris
2015-01-01
Power-law tails are often seen in probability density functions (PDFs) of molecular cloud column densities, and have been attributed to the effect of gravity. We show that extinction PDFs of a sample of five molecular clouds obtained at a few tenths of a parsec resolution, probing extinctions up to A$_{{\\mathrm{V}}}$ $\\sim$ 10 magnitudes, are very well described by lognormal functions provided that the field selection is tightly constrained to the cold, molecular zone and that noise and foreground contamination are appropriately accounted for. In general, field selections that incorporate warm, diffuse material in addition to the cold, molecular material will display apparent core+tail PDFs. The apparent tail, however, is best understood as the high extinction part of a lognormal PDF arising from the cold, molecular part of the cloud. We also describe the effects of noise and foreground/background contamination on the PDF structure, and show that these can, if not appropriately accounted for, induce spurious ...
Energy Technology Data Exchange (ETDEWEB)
Inglis, A. R.; Ireland, J. [Solar Physics Laboratory, Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Dominique, M. [Solar-Terrestrial Center of Excellence, Royal Observatory of Belgium, Avenue Circulaire 3, B-1180, Brussels (Belgium)
2015-01-10
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 literature 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.
Power-law and intermediate inflationary models in $f(T)$-gravity
Rezazadeh, K; Karami, K
2015-01-01
We study inflation in the framework of $f(T)$-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in $f(T)$-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law form for the $f(T)$ function in the action and examine the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, in the considered $f(T)$-gravity scenario, the power-law and intermediate inflationary models can be compatible with the observational results of Planck 2015 at 68\\% CL. In our $f(T)$-gravity setting, the potentials responsible for both the power-law and intermediate inflationary models have the power-law form $V(\\phi ) \\propto {\\phi ^m}$ but the power $m$ is...
International Nuclear Information System (INIS)
The classical phase-shift theory of spectral line shapes is used to examine various aspects of the applicability of the power-law relations to the description of temperature variations of pressure broadening and shifting coefficients of the isolated atomic and rovibronic molecular lines in a wide temperature range. Model calculations performed for potentials of the Lennard-Jones type indicate that the temperature dependence exponents of the broadening and shifting can be related to the details of the intermolecular interactions. It is shown that they are sensitive to the range of temperatures assumed in the fit and therefore extreme care must be taken when the power-law temperature dependence is used as a scaling law. The problems of the failure of the power-law and of variations in the sign of pressure shift coefficients with increasing temperature are discussed. Very good fits of Frost's empirical formula for temperature dependence of pressure shift to the theoretical ones are obtained. -- Highlights: ► Classical theory of line shapes is used to examine the power-law relations. ► The broadening and shifting exponents depend on the range of temperatures in the fit. ► Extreme care must be taken when using the power-law dependence as a scaling law
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
Gutiérrez, Ricardo; Garrahan, Juan P; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity. PMID:26764669
Predicting the long tail of book sales: Unearthing the power-law exponent
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.
Park, Simsoo; Lee, Dong-Ryul
2003-09-01
Numerical solutions are presented for fully developed laminar flow for a modified power law fluid (MPL) in a rectangular duct. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian behavior at low shear rates, through a transition region, to power law behavior at higher shear rates. The analysis identified a dimensionless shear rate parameter which, for a given set of operating conditions, specifies where in the shear rate range a particular system is operating, i.e. in the Newtonian, transition, or power law regions. The numerical results of the friction factor times Reynolds number for the Newtonian and power law region are compared with previously published results showing agreement within 0.05% in the Newtonian region, and 0.9% and 5.1% in the power law region. Rheological flow curves were measured for three CMC-7H4 solutions and were found to be well represented by the MPL constitutive equation. The friction factor times Reynolds number values were measured in the transition region for which previous measurements were unavailable. Good agreement was found between experiment and calculation thus confirming the validity of the analysis.
International Nuclear Information System (INIS)
Research highlights: → The possibility of preparing high-hardness and flexural-fracture-strength WC-MgO composite with adding La2O3 using hot-pressing sintering method. → Adding trace La2O3 suppresses the decarburization during the hot-pressing sintering. → Adding trace La2O3 promotes the microstructural refinement. → Adding trace La2O3 enhances the particulate dispersion homogeneity and the particulate/matrix interfacial coherence. -- Abstract: A detailed investigation is carried out into the influences of the lanthanum oxide (La2O3) addition upon the microstructural characteristics and the mechanical properties of the WC-MgO composite bulk prepared by hot-pressing sintering. The results indicate that due to the unique properties of rare earth element such as high surface activity and large ionic radius, the addition of trace La2O3 can suppress the decarburization, promote the microstructural refinement and improve the particulate dispersion homogeneity and the particulate/matrix interfacial coherence. Consequently, the relative density of the sintered sample with 0.1 wt.% La2O3 addition can be increased by 4.2% as compared with the sample without La2O3 addition. Mechanical properties of bulks were determined by hardness test and flexural strength measurement. The results showed the possibility of preparing high hardness and fracture strength WC-MgO composite materials with the La2O3 added.
On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment
Institute of Scientific and Technical Information of China (English)
CHANG Zhe; CAO Xiao-Feng; GUAN Cheng-Bo; DENG Zong-Wei; HUANG Chao-Guang; YANG Chun-Bin; LI Xin
2008-01-01
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update: to increase by 1 with probability fl, to decrease by 1 with probability f2, or remain unchanged with probability 1-f1-f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.
Phase diagram of power law and Lennard-Jones systems: crystal phases.
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed. PMID:25362319
Predicted and verified evolution of power-law exponent in product market
Hisano, Ryohei; Mizuno, Takayuki
2011-01-01
Power-law distributions constitute a generic empirical statistical regularity found in many complex systems. A recently developed theory finds that the interplay between one of the most universal ingredient, i.e., stochastic proportional growth, and stochastic birth and death processes, leads to generic power law distributions together with a non-universal exponent which depends explicitly on the characteristics of growth, birth and death. In particular, the theory rationalizes Zipf's law and explains deviations from it, for instance for the distribution of firm and of city sizes. Here, we report the first complete test of the theory, based on the empirical analysis from a real world complex phenomenon, namely the dynamics of market shares in the consumer electronics market. We estimate directly from the data the average growth rate of market shares, their standard deviation, the birth rates as well as the "death" hazard rate of products. When plugged in the theory, this predicts the power law exponent of the...
Stability of a power law relation between characteristics of earthquakes and electric precursors
Directory of Open Access Journals (Sweden)
E. Dologlou
2012-05-01
Full Text Available New data were used to test the credibility of a previously reported power law relation between the stress drop of earthquakes and the lead time of precursory SES. Here, we found that the critical exponent of this power law is very sensitive and remains stable around 0.33 only for appropriate sets of data. This value is in full agreement with the reported one in literature for critical phenomena. That means this power law is not an artifact, but probably implies that real physical dynamic processes evolving to criticality are present in the pre-focal area when the SES is emitted. An attempt to advance the underlying physics of the interconnection of the stress drop and the lead time of the precursory SES is still in progress.
Similarity solutions for non-Newtonian power-law fluid flow
Institute of Scientific and Technical Information of China (English)
D.M.WEI; S.AL-ASHHAB
2014-01-01
The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindel¨of theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva-ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2015-04-15
Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
Energy Technology Data Exchange (ETDEWEB)
Travesset, Alex, E-mail: trvsst@ameslab.gov [Department of Physics and Astronomy and Ames Lab, Iowa State University Ames, Ames, Iowa 50011 (United States)
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Alves, Luiz G A; Lenzi, Ervin K; Mendes, Renio S
2014-01-01
We report on the existing connection between power-law distributions and allometries. As it was first reported in [PLoS ONE 7, e40393 (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 labour, illiteracy, income, sanitation and unemployment). Our analysis reveal 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 residua...
Zhao, Kai; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2014-01-01
Human mobility has been empirically observed to exhibit Levy 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 analyze urban human mobility and we propose to explain the Levy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bicycle, 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 e...
Modes of Collaboration in Modern Science - Beyond Power Laws and Preferential Attachment
Milojević, Staša
2010-01-01
The goal of the study is to determine the underlying processes leading to the observed collaborator distribution in modern scientific fields, with special attention to non-power law behavior. Nanoscience is used as a case study of a modern interdisciplinary field, and its coauthorship network for 2000-04 period is constructed from NanoBank database. We find three collaboration modes that correspond to three distinct ranges in the distribution of collaborators: (1) for authors with fewer than 20 collaborators (the majority) preferential attachment does not hold and they form a log-normal "hook" instead of a power law, (2) authors with more than 20 collaborators benefit from preferential attachment and form a power law tail, and (3) authors with between 250 and 800 collaborators are more frequent than expected because of the hyperauthorship practices in certain subfields.
A power-law distribution of phase-locking intervals does not imply critical interaction
Botcharova, Maria; Berthouze, Luc
2012-01-01
Neural synchronisation plays a critical role in information processing, storage and transmission. Characterising the pattern of synchronisation is therefore of great interest. It has recently been suggested that the brain displays broadband criticality based on two measures of synchronisation - phase locking intervals and global lability of synchronisation - showing power law statistics at the critical threshold in a classical model of synchronisation. In this paper, we provide evidence that, within the limits of the model selection approach used to ascertain the presence of power law statistics, the pooling of pairwise phase-locking intervals from a non-critically interacting system can produce a distribution that is similarly assessed as being power law. In contrast, the global lability of synchronisation measure is shown to better discriminate critical from non critical interaction.
On the scaling range of power-laws originated from fluctuation analysis
Dariusz, Grech
2012-01-01
We extend our previous study of scaling range properties done for detrended fluctuation analysis (DFA) \\cite{former_paper} 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 $R^2$ of the fit to the considered scaling law imposed by DMA or MDMA schemes. 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 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 ...
POWER LAW DISTRIBUTION AND SELF-ORGANIZED CRITICALITY OF DISPERSED PARTICLES
Institute of Scientific and Technical Information of China (English)
Degang Ma; Lihe Chai
2005-01-01
Research on particulate characteristics has been an important frontier in physics and chemistry during the past decades. It has however been mostly focused on granular materials with short-range interactions. In this work, it was found that the power law of particle size distribution applied to the long-range interacting system of floating dust in air,from which we deduced that self-organized criticality might hold for floating dust just as granular materials with short-range interactions. This feature may reveal underlying kinetic mechanisms, important in dispersed particle systems.In industry, power law of size distribution of dispersed particles can be used to investigate the change of dust size, and the power law parameter could be taken as an important index for dust separation.
Bose-Einstein condensation in dark power-law laser traps
Jaouadi, Amine; Telmini, Mourad; De Lesegno, Bruno Viaris; Pruvost, Laurence; Charron, Eric
2009-01-01
We investigate theoretically the phase transition of interacting Bose gases in shaped optical traps. One-, two- and three-dimensional power-law trapping potentials are created using two crossing blue-detuned Laguerre-Gaussian laser beams. Controlling their associated azimuthal order l allows for the exploration of a multitude of power-law trapping situations ranging from the harmonic trap to a quasi-homogeneous Bose gas. For an arbitrary condensate occupation number and when compared to a harmonic trap of the same size, higher transition temperatures can be obtained with larger values of l. This effect results in a substantial acceleration of the condensation dynamics.
Power-law entropy-corrected HDE and NADE in Brans-Dicke cosmology
Sheykhi, A; Jamil, M; Kazemi, E; Haddad, M
2011-01-01
Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields in and out the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution.
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
Ebrahimi, Esmaeil
2010-01-01
A so called "power-law entropy-corrected holographic dark energy" (PLECHDE) was recently proposed to explain the dark energy dominated universe. This model is based on the power-law corrections to black hole entropy which appear in dealing with the entanglement of quantum fields between inside and outside of the horizon. In this paper, we suggest a correspondence between interacting PLECHDE and tachyon, quintessence, K-essence and dilaton scalar field models of dark energy in a non-flat FRW universe. Then, we reconstruct the potential terms accordingly, and present the dynamical equations which describe the evolution of the scalar field dark energy models.
Scalar Field Reconstruction of Power-Law Entropy-Corrected HDE
Ebrahimi, Esmaeil; Sheykhi, Ahmad(Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz, 71454, Iran)
2010-01-01
A so called "power-law entropy-corrected holographic dark energy" (PLECHDE) was recently proposed to explain the dark energy dominated universe. This model is based on the power-law corrections to black hole entropy which appear in dealing with the entanglement of quantum fields between inside and outside of the horizon. In this paper, we suggest a correspondence between interacting PLECHDE and tachyon, quintessence, K-essence and dilaton scalar field models of dark energy in a non-flat FRW u...
Holographic and new agegraphic f(T)-gravity models with power-law entropy correction
Karami, K
2013-01-01
Using a correspondence between the f(T)-gravity with the power-law entropy corrected versions of the holographic and new agegraphic dark energy models, we reconstruct the holographic and new agegraphic f(T)-gravity models with power-law entropy correction. We also obtain the equation of state parameters of the selected models due to torsion contribution. Our results show that the equation of state parameters can accommodate the transition from the quintessence state to the phantom regime at recent stage.
Gelled propellant flow: Boundary layer theory for power-law fluids in a converging planar channel
Kraynik, Andrew M.; Geller, A. S.; Glick, J. H.
1989-10-01
A boundary layer theory for the flow of power-law fluids in a converging planar channel has been developed. This theory suggests a Reynolds number for such flows, and following numerical integration, a boundary layer thickness. This boundary layer thickness has been used in the generation of a finite element mesh for the finite element code FIDAP. FIDAP was then used to simulate the flow of power-law fluids through a converging channel. Comparison of the analytic and finite element results shows the two to be in very good agreement in regions where entrance and exit effects (not considered in the boundary layer theory) can be neglected.
Power-law clique-degree distributions in real-life networks
Xiao, W K; Jin, H Y; Ren, J; Song, Z W; Wang, B H; Yang, H F; Zhou, T; Zhu, M X; Feng, Qi; Jin, Hui-Yu; Ren, Jie; Song, Zhi-Wei; Wang, Bing-Hong; Xiao, Wei-Ke; Yang, Hong-Feng; Zhou, Tao; Zhu, Meng-Xiao
2006-01-01
The community structure and motif-modular-network hiberarchy are of great importance for understanding the relationship between structures and functions. In this letter, we propose a new measure, the clique-degree, which is an extension of degree and can be used to measure the density of cliques in networks. The empirical studies indicate the extensive existence of power-law clique-degree distributions in various real networks. By comparing with the randomized networks, we show that the power-law clique-degree distribution is independent to traditional scale-free property.
Estimation of Inflation parameters for Perturbed Power Law model using recent CMB measurements
Mukherjee, Suvodip; Joy, Minu; Souradeep, Tarun
2014-01-01
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 $m_{\\rm eff}$ 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 independent parameters, namely spectral index for tensor perturbation $\
Stability of Natural Convection of Power-law Fluid and non-Darcy Flow in Porous Media
Institute of Scientific and Technical Information of China (English)
Kong Xiangyan; Chen Guoquan; Wu Jianbing; Li Peichao; Lu Detang; Xu Xianzhi
2001-01-01
In the present work the effect of the power law exponent of power-law fluid and non-Darcy number of non-Darcy flow on stability of natural convection in porous media are studied. The computation analysis of effect of power law exponent of power-law fluid and non-Darcy number of non-Darcy flow in the rectangular duct on the transition Rayleigh number Ra*, which means the convective model transiting from stationary state to periodic solution. The duct has filled a porous medium saturated with the power-law non-Newtonian fluid or Newtonian fluid for non-Darcy flow, in which there is uniform internal heat generation per unit volume q. In this paper the relationship between the transition Rayleigh number Ra* and the power-law exponent n, Ra* and non-Darcy number Be, are shown .To these two aspects, the transition route from steady to chaotic convection is also obtained.
Directory of Open Access Journals (Sweden)
M.E. Moussa
2014-09-01
Full Text Available The effect of Ca addition on modification of primary Mg2Si, hardness and wear behavior in Mg–5 wt.%Si hypereutectic alloy has been investigated. The results showed clearly that without Ca addition, most of primary Mg2Si appeared as coarse dendritic morphology with average size of about 215 μm. With the addition of 0.1 wt.%Ca, the average size of primary Mg2Si decreased to about 98 μm, but their morphologies did not significantly changed. As the addition level of Ca increased to 0.3 wt.%, the average size of primary Mg2Si decreased significantly to about 50 μm and their morphologies changed to polyhedral shape. However, with further increasing Ca addition to 0.6 wt.% and 1 wt.%, some needle-like and blocky CaMgSi particles formed and the average size of primary Mg2Si increased slightly, which could described as over-modification. The present work showed that the optimal modification effect could be obtained when the Ca content in the investigated alloy reached 0.3 wt.%. The modification mechanism may be referred mainly due to poisoning effect resulting from the segregation of Ca atoms at the growth front of the Mg2Si and the adsorption effect of some Ca atoms in the Mg2Si crystal growth plane. The 0.3 wt.%Ca-added alloy has the highest hardness value and the best wear resistance among all other alloys. An excessive Ca addition resulted in the formation of some needle-like and blocky CaMgSi particles, which was detrimental to hardness and wear behavior of the 0.6 wt.% and 1 wt.%Ca-added alloys. The wear mechanism of investigated alloys is a mild abrasive oxidative wear with little adhesion.
Lillo, F
2006-01-01
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 .
Energy Technology Data Exchange (ETDEWEB)
Kotan, Hasan, E-mail: hkotan@konya.edu.tr [Department of Metallurgical Engineering and Materials Science, Necmettin Erbakan University, Dere Aşıklar Mah. Demet Sokak, Meram, Konya 42140 (Turkey); Darling, Kris A. [U.S. Army Research Laboratory, Weapons and Materials Research Directorate, RDRL-WMM-F, Aberdeen Proving Ground, MD 21005-5069 (United States); Scattergood, Ronald O.; Koch, Carl C. [Department of Materials Science and Engineering, NC State University, 911 Partners Way, Room 3078, Raleigh, NC 27695-7907 (United States)
2014-12-05
The motivation of this work was driven to improve the thermal stability in systems where polymorphic transformations can result in an additional driving force, upsetting the expected thermodynamic stability. In this study, Fe{sub 92}Ni{sub 8} alloys with Zr and nano-Y{sub 2}O{sub 3} additions were produced by ball milling and then annealed at high temperatures. Emphasis was placed on understanding the effects of dispersed nano-Y{sub 2}O{sub 3} particle additions and their effect on microstructural stability at and above the bcc-to-fcc transformation occurring at 700 °C in Fe–Ni systems. Results reveal that microstructural stability and hardness can be promoted by a combination of Zr and Y{sub 2}O{sub 3} additions, that being mostly effective for stability before and after phase transition, respectively. The mechanical strength of these alloys is achieved by a unique microstructure comprised a ultra-fine grain Fe base matrix, which contains dispersions of both nano-scale in-situ formed Zr base intermetallics and ex-situ added Y{sub 2}O{sub 3} secondary oxide phases. Both of these were found to be essential for a combination of high thermal stability and high mechanical strength properties. - Highlights: • Polymorphic transformations can limit the processing of nanostructured powders. • It causes a rapid grain growth and impairs the improved mechanical properties. • We aim to improve the hardness and thermal stability above the phase transformation. • Thermal stability is achieved by a combination of Zr and Y{sub 2}O{sub 3} additions. • Hardness is promoted by in-situ formed and ex-situ added secondary nano phases.
Holographic f(T)-gravity model with power-law entropy correction
Karami, K.; Asadzadeh, S.; Abdolmaleki, A.; Safari, Z.
2013-10-01
Using the correspondence between the f(T)-gravity model and the holographic dark energy model with the power-law entropy correction, we reconstruct the holographic f(T)-gravity model with the power-law entropy correction. We fit the model parameters by using the latest observational data including type Ia supernovae, baryon acoustic oscillations, cosmic microwave background, and Hubble parameter data. We also check the viability of our model using a cosmographic analysis approach. Using the best-fit values of the model, we obtain the evolutionary behavior of the effective torsion equation-of-state parameter of the power-law entropy-corrected holographic f(T)-gravity model, as well as the deceleration parameter of the Universe. We also investigate different energy conditions in our model. Furthermore, we examine the validity of the generalized second law of gravitational thermodynamics. Finally, we point out the growth rate of the matter density perturbation in our model. We conclude that in the power-law entropy-corrected holographic f(T)-gravity model, the Universe begins a matter-dominated phase and approaches a de Sitter regime at late times, as expected. It also can justify the transition from the quintessence state to the phantom regime in the near past, as indicated by recent observations. Moreover, this model is consistent with current data, it passes the cosmographic test, and it fits the data of the growth factor as well as the ΛCDM model.
Extended Power Law and Hall Anomaly of High-Temperature Superconductors
Institute of Scientific and Technical Information of China (English)
HE Li; HU Xiang; YIN Lan; XU Xiao-Lin; GUO Jian-Dong; LI Chuan-Yi; YIN Dao-Le
2009-01-01
Starting from the free energy of a moving vortex,we obtain the extended power law form of longitudinal resistivity pxx and the analytical form of Hall resistivity pxy.Based on them,we obtain a scaling relation which agrees well with the experimental data of different kinds of high-temperature superconductors.Fhrthermore,the theoretical results well fit the scaling results.
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
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)
Spatial and Temporal Stability of the Estimated Parameters of the Binary Power Law
The binary power law has become a standard approach for describing and quantifying spatial patterns of disease incidence and summarizing the spatial dynamics of disease over the course of an epidemic. However, the portability and temporal stability of parameter estimates of the binary form of the p...
Fingering instability in the flow of a power-law fluid on a rotating disc
Arora, Akash; Doshi, Pankaj
2016-01-01
A computational study of the flow of a non-Newtonian power law fluid on a spinning disc is considered here. The main goal of this work is to examine the effect of non-Newtonian nature of the fluid on the flow development and associated contact line instability. The governing mass and momentum balance equations are simplified using the lubrication theory. The resulting model equation is a fourth order non-linear PDE which describes the spatial and temporal evolutions of film thickness. The movement of the contact line is modeled using a constant angle slip model. To solve this moving boundary problem, a numerical method is developed using a Galerkin/finite element method based approach. The numerical results show that the spreading rate of the fluid strongly depends on power law exponent n. It increases with the increase in the shear thinning character of the fluid (n 1). It is also observed that the capillary ridge becomes sharper with the value of n. In order to examine the stability of these ridges, a linear stability theory is also developed for these power law fluids. The dispersion relationship depicting the growth rate for a given wave number has been reported and compared for different power-law fluids. It is found that the growth rate of the instability decreases as the fluid becomes more shear thinning in nature, whereas it increases for more shear thickening fluids.
Peristaltic Motion of Power-Law Fluid with Heat and Mass Transfer
Institute of Scientific and Technical Information of China (English)
T.Hayat; S.Hina; Awatif A.Hendi
2011-01-01
@@ The effects of wall properties and heat and mass transfer on the peristalsis in a power-law fluid are investigated.The solutions for the stream function, temperature, concentration and heat transfer coefficient are obtained.The axial velocity, temperature and mass concentration are studied for different emerging parameters.
New statistic for financial return distributions: power-law or exponential?
Pisarenko, V F
2004-01-01
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws or for exponentials correspondingly, regardless of the value of the exponent or of the form parameter. This is particularly useful for testing the structure of a distribution (power law or not, exponential or not) independently of the possibility of quantifying the values of the parameters. We apply these statistics to the distribution of returns of one century of daily data for the Dow Jones Industrial Average and over one year of 5-minutes data of the Nasdaq Composite index. Our analysis confirms previous works showing the tendency for the tails to resemble more and more a power law for the highest quantiles but we can detect clear deviations that suggest that the structure of the tails of the ...
Realization of power law inflation & variants via variation of the strong coupling constant
AlHallak, M.; Chamoun, N.
2016-09-01
We present a model of power law inflation generated by variation of the strong coupling constant. We then extend the model to two varying coupling constants which leads to a potential consisting of a linear combination of exponential terms. Some variants of the latter may be self-consistent and can accommodate the experimental data of the Planck 2015 and other recent experiments.
Directory of Open Access Journals (Sweden)
Pablo D. Mininni
2012-01-01
Full Text Available In the context of tackling the ill-posed inverse problem of motion estimation from image sequences, we propose to introduce prior knowledge on flow regularity given by turbulence statistical models. Prior regularity is formalised using turbulence power laws describing statistically self-similar structure of motion increments across scales. The motion estimation method minimises the error of an image observation model while constraining second-order structure function to behave as a power law within a prescribed range. Thanks to a Bayesian modelling framework, the motion estimation method is able to jointly infer the most likely power law directly from image data. The method is assessed on velocity fields of 2-D or quasi-2-D flows. Estimation accuracy is first evaluated on a synthetic image sequence of homogeneous and isotropic 2-D turbulence. Results obtained with the approach based on physics of fluids outperform state-of-the-art. Then, the method analyses atmospheric turbulence using a real meteorological image sequence. Selecting the most likely power law model enables the recovery of physical quantities, which are of major interest for turbulence atmospheric characterisation. In particular, from meteorological images we are able to estimate energy and enstrophy fluxes of turbulent cascades, which are in agreement with previous in situ measurements.
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.
Fitting Power-laws in empirical data with estimators that work for all exponents
Hanel, Rudolf; Liu, Bo; Thurner, Stefan
2016-01-01
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main 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. Here we show that 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 com...
Is it a power law distribution? The case of economic contractions
Pueyo, Salvador
2013-01-01
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a central role in complex systems theory; therefore, the current limitations in the identification of this distribution in empirical data are a major obstacle to pursue the insights that the complexity approach offers in many fields. This paper addresses this issue by introducing a reliable methodology with a solid theoretical foundation, the Taylor Series-Based Power Law Range Identification Method. When applied to time series from 39 countries, this method reveals a well-defined power law in the relative per capita GDP contractions that span from 5.53% to 50%, comprising 263 events. However, this observation does not suffice to attribute recessions to some specific mechanism, such as self-organized criticality. The paper highlights a set of points requiring more study so as to d...
Carrano, Charles S.; Rino, Charles L.
2016-06-01
We extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two-component inverse power law spectrum. The two-component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two-dimensional field-aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self-similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large- and small-scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.
Shrivastava, Rajan; Malik, Chetan; Ghosh, Subhendu
2016-06-01
Open channel current noise in synthetic peptide S6 of KvAP channel was investigated in a voltage clamp experiment on bilayer lipid membrane (BLM). It was observed that the power spectral density (PSD) of the component frequencies follows power law with different slopes in different frequency ranges. In order to know the origin of the slopes PSD analysis was done with signal filtering. It was found that the first slope in the noise profile follows 1 / f pattern which exists at lower frequencies and has high amplitude current noise, while the second slope corresponds to 1 /f 2 - 3 pattern which exists at higher frequencies with low amplitude current noise. In addition, white noise was observed at very large frequencies. It was concluded that the plausible reason for the multiple power-law scaling is the existence of different modes of non-equilibrium ion transport through the S6 channel.
PLNoise: a package for exact numerical simulation of power-law noises
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 -1algorithm 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.W. Brown, J
Naeem, Haider T.; Mohammed, Kahtan S.; Ahmad, Khairel R.
2015-10-01
The main object of this study is to investigate the effect of friction stir processing (FSP) on the microstructure and hardness of Al-Zn-Mg-Cu alloys that were produced via casting with the addition of 5 wt % nickel. Furthermore, a single-pass FSP with a rotational speed of 1500 rpm and a traveling speed of 40 mm/min was performed on the alloys. The FSP-treated cast alloys were homogenized, aged at 120°C for 24 h, retrogressed at 180°C for 30 min, and then re-aged at 120°C for 24 h. Microstructural evaluations via optical microscopy and scanning electron microscopy, as well as with energy dispersive X-ray spectroscopy were conducted. In addition, X-ray diffraction analysis was performed to detect the intermetallics and phases of the Al-Zn-Mg-Cu-Ni alloys. Before FSP, the microstructural observations indicated the presence of coarse Ni dispersed particles with a precipitate phase within the matrix. After FSP treatment, the grain refinement led to the uniform space distribution of Ni dispersed particles in the stir zone. The Vickers hardness values for the Al-Zn-Mg-Cu-Ni alloy increased after age tempering at T6 and retrogression and re-aging (RRA) treatment because of the increased precipitation and particles dispersity. The hardness of the Al-Zn-Mg-Cu-Ni alloy was enhanced after FSP and a series of heat treatments, especially the RRA process, because of the stirring action of the FSP tool, the grain refinement, the appearance of additional precipitates, and the refinement of dispersed Ni particles.
Petersen, Alexander; Yang, Jae-Suk; Stanley, H Eugene
2008-01-01
We provide a simple and intuitive stochastic process that accounts for the observed probability density functions governing career longevity in several professional sports leagues in various countries. Our mechanism characterizes the probability density functions governing career longevity with two parameters, \\alpha and \\tau . The exponent \\alpha < 1 characterizes the scaling in the power-law regime, which is followed by an exponential cutoff after a critical value \\tau, representing the mean lifetime in each sport. In addition, we also show that the probability density functions of career statistical metrics within each sport follow directly from the density functions of career longevity. Thus, our process is a universal mechanism describing longevity in a competitive environment, with the exponent \\alpha representing the role of experience and reputation in career development. Because net career tallies of in-game success ultimately serve as a metric for classifying careers, our findings provide a robus...
The hidden flat like universe II. Quasi inverse power law inflation by f ( T ) f(T) gravity
El Hanafy, W.; Nashed, G. G. L.
2016-08-01
In a recent work, a particular class of f(T) gravity, where T is the teleparallel torsion scalar, has been derived. This class has been identified by flat-like universe (FLU) assumptions (El Hanafy and Nashed 2015). The model is consistent with the early cosmic inflation epoch. A quintessence potential has been constructed from the FLU f(T)-gravity. We show that the first order potential of the induced quintessence is a quasi inverse power law inflation with an additional constant providing an end of the inflation with no need to an extra mechanism. At e-folds N_{*}= 55 before the end of the inflation, this type of potential can perform both E and B modes of the cosmic microwave background (CMB) polarization pattern.
Power laws and self-organized criticality in theory and nature
Marković, Dimitrije; Gros, Claudius
2014-03-01
Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real
Wang, Yongyong; Dong, Xiao; Song, Xiaohui; Wang, Jinfeng; Li, Gong; Liu, Riping
2016-05-01
The thermal and mechanical properties of Zr57Al15Co28- X Ag X ( X = 0 and 8) amorphous alloys were investigated using differential scanning calorimetry, in situ high-pressure angle dispersive X-ray diffraction measurements with synchrotron radiation, and nanoindentation. Results show that Ag doping improves effective activation energy, nanohardness, elastic modulus, and bulk modulus. Ag addition enhances topological and chemical short-range orderings, which can improve local packing efficiency and restrain long-range atom diffusion. This approach has implications for the design of the microstructure- and property-controllable functional materials for various applications.
Sato, Haruo
2016-01-01
Peak delay and envelope broadening of an S-wavelet with travel distance increasing are seen in short-period seismograms of small earthquakes. Those phenomena are results of scattering by random velocity inhomogeneities in the earth medium. As shown in sonic well-log data we may suppose that random velocity fluctuation has power-law spectra even in the seismic spectral range. As a simple mathematical model, we study how the envelope of a scalar wavelet varies in von Kármán-type random media, which have power-law spectra at large wavenumbers. Since the centre wavenumber of a wavelet is a unique scale in the power-law spectral range, using it as a reference, we divide the random media into the low-wavenumber spectral (long-scale) component and the high-wavenumber spectral (short-scale) component. For the wave propagation through the long-scale component of random media, we may apply the parabolic approximation to the wave equation. Using the Markov approximation, which is a stochastic extension of the phase screen method, we directly synthesize the energy density, which is the mean-square (MS) envelope of a wavelet in a given frequency band. The envelope duration increases according to the second power of travel distance. There is an additional factor, the wandering effect which increases the envelope duration according to the traveltime fluctuation. Wide angle scattering caused by the short-scale component of random media attenuates wave amplitude with travel distance increasing. We use the total scattering coefficient of the short-scale component as a measure of scattering attenuation per distance, which is well described by the Born approximation. Multiplying the exponential scattering attenuation factor by the MS envelope derived by the Markov approximation, we can synthesize the MS envelope reflecting all the spectral components of random media. When the random medium power spectra have a steep role-off at large wavenumbers, the envelope broadening is small and
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.
Some power law and scaling behaviors of forest and urban fire disasters
Song, Weiguo; Zheng, Hongyang
2010-05-01
Power-law distribution have been found in many actual systems, such as the earthquake, rainfall and forest fires etc, and considered as one of the characteristics of SOC(Self-Organized Critical) systems (introduced by P. Bak in 1987). It is found that there are three types of power-law relations in forest fire system, i.e. frequency-size distribution, frequency-interval distribution, and the relation between population density and fire probability. Some of these characteristics are attributed to the SOC. The frequency-interval distribution of forest fires showes periodic change, different to that of frequency-size distribution. On the base of the traditional forest fire model proposed by Drossel and Schwabl in 1992 (DS model), the effects of influencing factors to the forest fire are studied. A Weather-Driven forest fire model (WD model) was built, in which the igniting probability is calculated with the weather parameter, i.e. relative humility, instead of a constant. The results demonstrate that the temporal distribution agrees well with that of actual forest fire data. Furthermore, it is found that the change of weather data also exhibits a power-law relation with periodic fluctuations, implying that the external driving from weather parameters is the essential reason for the power-law behavior of fire intervals. In order to explore the temporal scaling behavior of forest and urban fires, Allan factor (AF), Fano factor (FF) and Detrended Fluctuation Analysis (DFA) are used to investigate the fire data in different countries or regions. It is found that both the forest and urban fires exhibit time-scaling behavior, and the scaling exponents of urban fires are larger than forest fires, signifying a more intense clustering. Similar power-law characterizes the relative humidity, and its AF and FF plot validate the existence of a strong link between weather and fires. By studying the forest fire area series, it is found that both the forest fire and the weather
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
Spectral properties of transitions between soft and hard state in GX 339-4
Stiele, H; Muñoz-Darias, T; Belloni, T M
2011-01-01
We present a study of the spectral properties during state transition of GX 339-4. Data are taken from the 2010 outburst of GX 339-4, which is densely covered by Rossi X-ray Timing Explorer, providing an excellent coverage of the state transitions between the low/hard state and the high/soft state. We select all observations within a certain hardness ratio range during the soft intermediate state (SIMS). This sample was chosen in such a way to comprise all observations that show a type-B quasi-periodic oscillation (QPO). In addition, we also investigate the spectra of hard intermediate state observations. The spectra, obtained from Proportional Counter Array data in the 10 to 40 keV range, are fitted with a power law and an additional high energy cut-off if needed. We find that the spectra are significantly harder during the SIMS of the soft-to-hard transition than they are during the hard-to-soft transition. This demonstrates that during the SIMS of the soft-to-hard transition not only the luminosity and pea...
Power law persistence in the atmosphere An ideal test bed for climate models
Bunde, A; Govindan, R B; Havlin, S; Koscielny-Bunde, E; Rybski, D; Vjushin, D; Bunde, Armin; Eichner, Jan; Govindan, Rathinaswamy; Havlin, Shlomo; Koscielny-Bunde, Eva; Rybski, Diego; Vjushin, Dmitry
2002-01-01
We review recent results on the appearance of long-term persistence in climatic records and how they can be used to evaluate climate models. The persistence can be characterized, for example, by the correlation C(s) of temperature variations separated by s days. We show that, contrary to previous expectations, C(s) decays for large s as a power law, C(s) ~ s^(-gamma). For continental stations, the exponent gamma is always close to 0.7, while for stations on islands gamma ~ 0.4. In contrast to the temperature fluctuations, the fluctuations of the rainfall usually cannot be characterized by long term power law correlations but rather by pronounced short term correlations. The universal persistence law for the temperature fluctuations on continental stations represents an ideal (and uncomfortable) test bed for the state of the art global climate models and allows to evaluate their performance.
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
International Nuclear Information System (INIS)
A so-called 'power-law entropy-corrected holographic dark energy' (PLECHDE) was recently proposed to explain the dark energy (DE)-dominated universe. This model is based on the power-law corrections to black hole entropy that appear when dealing with the entanglement of quantum fields between the inside and the outside of the horizon. In this paper, we suggest a correspondence between the interacting PLECHDE and the tachyon, quintessence, K-essence and dilaton scalar field models of DE in a non-flat Friedmann-Robertson-Walker universe. Then, we reconstruct the potential terms accordingly, and present the dynamical equations that describe the evolution of the scalar field DE models.
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi, Esmaeil [Department of Physics, Shahid Bahonar University, PO Box 76175, Kerman (Iran, Islamic Republic of); Sheykhi, Ahmad, E-mail: eebrahimi@uk.ac.ir, E-mail: sheykhi@uk.ac.ir [Department of Physics, Kerman Branch, Islamic Azad University, Kerman (Iran, Islamic Republic of)
2011-10-15
A so-called 'power-law entropy-corrected holographic dark energy' (PLECHDE) was recently proposed to explain the dark energy (DE)-dominated universe. This model is based on the power-law corrections to black hole entropy that appear when dealing with the entanglement of quantum fields between the inside and the outside of the horizon. In this paper, we suggest a correspondence between the interacting PLECHDE and the tachyon, quintessence, K-essence and dilaton scalar field models of DE in a non-flat Friedmann-Robertson-Walker universe. Then, we reconstruct the potential terms accordingly, and present the dynamical equations that describe the evolution of the scalar field DE models.
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
Ebrahimi, Esmaeil; Sheykhi, Ahmad
2011-10-01
A so-called 'power-law entropy-corrected holographic dark energy' (PLECHDE) was recently proposed to explain the dark energy (DE)-dominated universe. This model is based on the power-law corrections to black hole entropy that appear when dealing with the entanglement of quantum fields between the inside and the outside of the horizon. In this paper, we suggest a correspondence between the interacting PLECHDE and the tachyon, quintessence, K-essence and dilaton scalar field models of DE in a non-flat Friedmann-Robertson-Walker universe. Then, we reconstruct the potential terms accordingly, and present the dynamical equations that describe the evolution of the scalar field DE models.
Power-Law Entropy-Corrected HDE and NADE in Brans-Dicke Cosmology
Sheykhi, A.; Karami, K.; Jamil, M.; Kazemi, E.; Haddad, M.
2012-06-01
Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution. As a result we find that this model can provide the present cosmic acceleration and even the equation of state parameter of this model can cross the phantom line w D =-1 provided the model parameters are chosen suitably.
Statefinder Parameters for Coupled Quintessence Scenario in a Power Law Case
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We investigate a coupled quintessence scenario, which can provide a natural solution to the cosmic coincidence problem. We assume that the mass of dark matter particles depends on a power law function of the scalar field associated to dark energy and meanwhile the scalar field evolves in a power law potential. Since the dynamics of this system is dominated by an attractor solution, the mass of dark matter particles is forced to change with time as to ensure that the ratio between the energy densities of dark matter and dark energy becomes a constant at late times,and one thus solves the cosmic coincidence problem naturally. We then apply a statefinder diagnostic to this coupled quintessence scenario. It is shown that the evolving trajectory of this scenario in the s-r diagram is quite different from those of other dark energy models.
Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow
Matsubara, Yoshitsugu; Tadaki, Shin-ichi
2013-01-01
Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.
Deviations from uniform power-law scaling due to exposure to high altitude
Posiewnik, A.
2002-12-01
A major challenge in biological physics is the analysis of time series that are typically highly nonstationary. Viswanathan et al. (Phys. Rev. E 55 (1) (1997) 845-899) using techniques based on the Fano factor and the Allan factor functions, as well as on detrended fluctuation analysis showed that the scaling properties of the dynamics of healthy physiological systems in normal conditions are more stable than those of pathological systems-there is underlying loss of uniform power-law scaling in disease. Here we test, using the same techniques as Viswanathan et al. (1997), the hypothesis that deviations from uniform power-law scaling, similar to those seen in heart failure and deep apnea syndrome occur also for healthy subjects under pathological conditions (hypoxaemic stress during exposure to high altitude, over 6000 m).
Nonlinear Acoustics FDTD method including Frequency Power Law Attenuation for Soft Tissue Modeling
Jiménez, Noé; Sánchez-Morcillo, Víctor; Camarena, Francisco; Hou, Yi; Konofagou, Elisa E
2014-01-01
This paper describes a model for nonlinear acoustic wave propagation through absorbing and weakly dispersive media, and its numerical solution by means of finite differences in time domain method (FDTD). The attenuation is based on multiple relaxation processes, and provides frequency dependent absorption and dispersion without using computational expensive convolutional operators. In this way, by using an optimization algorithm the coefficients for the relaxation processes can be obtained in order to fit a frequency power law that agrees the experimentally measured attenuation data for heterogeneous media over the typical frequency range for ultrasound medical applications. Our results show that two relaxation processes are enough to fit attenuation data for most soft tissues in this frequency range including the fundamental and the first ten harmonics. Furthermore, this model can fit experimental attenuation data that do not follow exactly a frequency power law over the frequency range of interest. The main...
Zhu, Chen-Ping; Yang, Hui-Jie; Xiong, Shi-Jie; Gu, Zhi-Ming; Shi, Da-Ning; He, Da-Ren; Wang, Bing-Hong
2007-01-01
Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the updating of their states. We show with numerical simulation that these aptitudes can contribute to group formation or speciation in social fields. Moreover, they can lead to power-law topological correlations of complex networks. By coupling updating states of nodes with variation of connections in a network, structural properties with power-laws and functions like multifractality, spontaneous ranking and evolutionary branching of node states can emerge out simultaneously from the present self-organized model of coevolutionary process.
Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow
Matsubara, Yoshitsugu; Hieida, Yasuhiro; Tadaki, Shin-ichi
2013-09-01
Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.
Shear Force Distribution and Heat Transfer in Laminar Boundary Layer Flows for Power Law Fluid
Institute of Scientific and Technical Information of China (English)
郑连存; 张欣欣
2002-01-01
Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indicated that for power law exponents 0＜n≤1, the skin friction σ decreases with increasing n, and the dimensionless shear force decreases with increasing dimensionless velocity t. When Pr=1, the velocity distribution in the viscous boundary layer is the same as the temperature distribution in the thermal boundary layer and δ＝δT. For Pr＞1, the increase of the viscous diffusion exceeds that of thermal diffusion with increasing Pr, i.e., δT(t)＜δ(t). The thermal diffusion ratio increases with increasing n(0＜n≤1).
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.
The Distance-Decay Function of Geographical Gravity Model: Power Law or Exponential Law?
Chen, Yanguang
2015-01-01
The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be explained with the ideas from Euclidean geometry. This results in what is called dimension dilemma. In particular, the gravity model based on power law could not be derived from general principles by traditional ways. Consequently, a negative exponential function substituted for the inverse power function to serve for a distance-decay function for the gravity model. However, the exponential-based gravity model goes against the first law of geography. This paper is devoted to solve these kinds of problems by mathematical reasoning and empirical analysis. First, it can be proved that the distance exponent of the gravity model is essentially a fractal dimension. Thus the dimensional dilemma of the power-based gravity model can be resolved using the concepts from fractal geometry. Second, the exponential fun...
Pandya, Alex; Chandra, Mani; Gammie, Charles F
2016-01-01
Synchrotron emission and absorption determine the observational appearance of many astronomical systems. In this paper, we describe a numerical scheme for calculating synchrotron emissivities and absorptivities in all four Stokes parameters for arbitrary gyrotropic electron distribution functions, building on earlier work by Leung, Gammie, and Noble. We use this technique to evaluate the emissivities and the absorptivities for a thermal (Maxwell-J\\"uttner), isotropic power-law, and isotropic kappa distribution function. The latter contains a power-law tail at high particle energies that smoothly merges with a thermal core at low energies, as is characteristic of observed particle spectra in collisionless plasmas. We provide fitting formulae and error bounds on the fitting formulae for use in codes that solve the radiative transfer equation. The numerical method and the fitting formulae are implemented in a compact C library called ${\\tt symphony}$. We find that: the kappa distribution has a source function th...
Injection to the pick-up ion regime from high energies and induced ion power laws
Fahr, H -J; Verscharen, D
2008-01-01
Though pick-up ions (PUIs) are a well known phenomenon in the inner heliosphere, their phase-space distribution nevertheless is a theoretically unsettled problem. Especially the question of how pick-up ions form their suprathermal tails, extending to far above their injection energies, still now is unsatistactorily answered. Though Fermi-2 velocity diffusion theories have revealed that such tails are populated, they nevertheless show that resulting population densities are much less than seen in observations showing power-laws with a velocity index of ``-5''. We first investigate here, whether or not observationally suggested power-laws can be the result of a quasi-equilibrium state between suprathermal ions and magnetohydrodynamic turbulences in energy exchange with eachother. We demonstrate that such an equilibrium cannot be established. We furthermore show that Fermi-2 type energy diffusion in the outer heliosphere is too inefficient to determine the shape of the distribution function there. As we can show...
The Forbes 400, the Pareto power-law and efficient markets
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.
Maximum entropy power laws: An application to the tail of wealth distribution
Milaković, Mishael
2002-01-01
Statistical equilibrium denotes the distribution of wealth that can be achieved in the largest number of ways while satisfying a first moment constraint on the rate of growth in wealth portfolios. Maximizing entropy subject to a logarithmic constraint yields a power law distribution whose characteristic exponent depends positively on the minimum wealth level, and inversely on the rate of growth and the average number of changes in the composition of wealth portfolios. Put differently, the dis...
Pierpaolo Andriani; Bill McKelvey
2007-01-01
Practicing managers live in a world of ‘extremes’, but international business and management research is based on Gaussian statistics that rule out such extremes. On occasion, positive feedback processes among interactive data points cause extreme events characterized by power laws. They seem ubiquitous; we list 80 kinds of them – half each among natural and social phenomena. We use imposed tension and Per Bak's ‘self-organized criticality’ to argue that Pareto-based science and statistics (b...
A short account of a connection of Power Laws to the Information Entropy
Dover, Yaniv
2003-01-01
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order" (Boltzmann Entropy) of a complex, self interacting, self organized system. Since the Shannon entropy is equivalent to the Boltzmann's entropy under equilibrium, non interacting conditions, we interpret this result as the complex system making use of its intra-inter...
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
Sami El Boustani; Olivier Marre; Sébastien Béhuret; Pierre Baudot; Pierre Yger; Thierry Bal; Alain Destexhe (eds); Yves Frégnac
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...
Power-law entropy corrected holographic and new agegraphic f(R)-gravity models
Karami, K.; Khaledian, M. S.
2011-01-01
Motivated by the recent works of us [1], we establish a correspondence between f(R)-gravity with the power-law entropy corrected holographic dark energy (PLECHDE) and new agegraphic dark energy (PLECNADE) models. We reconstruct corresponding f(R)-gravities and obtain the equation of state parameters. We show that the selected f(R)-gravity models can accommodate the transition from the quintessence state to the phantom regime as indicated by the recent observations.
Digital Repository Service at National Institute of Oceanography (India)
Chakraborty, B.; Kodagali, V.N.
is that, it provides accurate results, when uses them within a well-defined parameter regime. The estimated root mean square (rms) relief roughness, conelation length, and exponent values for the top-and sub surface layer of the biogenous sediments from... Southern Oceans are computed (data obtained from authors on personal ground). These values are applied to determine power law parameters and presented in this paper. Fox and Hayes ([8] and references therein) had demonstrated the statistical and spectral...
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows.
Anbarlooei, H R; Cruz, D O A; Ramos, F; Silva Freire, A P
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
A Zonal Similarity Analysis Of Friction Factors: Case Study 1: Pipe Flow Of Power Law Fluids
Trinh, Khanh Tuoc
2010-01-01
A zonal similarity analysis of friction factors in pipe flow of power law fluids is presented. It uses the critical Reynolds number and friction factor at transition as estimates of the normalised velocity and distance between the wall and log-law layers and successfully collapses both Newtonian and non-Newtonian data for laminar, transition and turbulent flows. Key words: zonal similarity analysis, friction factor, Reynolds number, transition
Multistage Random Growing Small-World Networks with Power-Law Degree Distribution
Institute of Scientific and Technical Information of China (English)
LIU Jian-Guo; DANG Yan-Zhong; WANG Zhong-Tuo
2006-01-01
@@ We present a simple rule which could generate scale-free networks with very large clustering coefficient and very small average distance. These networks, called the multistage random growing networks (MRGNs), are constructed by a two-stage adding process for each new node. The analytic results of the power-law exponentγ = 3 and the clustering coefficient C = 0.81 are obtained, which agree with the simulation results approximately.
An Analysis of the Characteristics of the Thermal Boundary Layer in Power Law Fluid
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.
A power-law distribution for tenure lengths of sports managers
Aidt, Toke S.; Leong, Bernard; Saslaw, William C.; Sgroi, Daniel
2006-10-01
We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.
Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons
Sami El Boustani; Olivier Marre; Sébastien Béhuret; Pierre Baudot; Pierre Yger; Thierry Bal; Alain Destexhe; Yves Frégnac
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...
Ross, Nathan
2013-01-01
For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to infinity. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.
M. K. Chaube; Tripathi, D.; O. Anwar Bég; Shashi Sharma; PANDEY, V.S.
2015-01-01
A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profi...
Deviation from power law of the global earthquake seismic moment distribution
Serra, Isabel
2015-01-01
The distribution of earthquake seismic moment is of capital importance to evaluate seismic hazard, in particular regarding the most extreme events. Likelihood-ratio tests let to compare the performance of the most suitable probabilistic models when ?tted to the global CMT catalog. The conclusion is that the truncated gamma model outperforms the power law and the tapered Gutenberg-Richter models, being able to explain the empirical data both before and after the great Sumatra-Andaman earthquake of 2004.
Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow
Matsubara, Yoshitsugu; Hieida, Yasuhiro; Tadaki, Shin-ichi
2013-01-01
Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of flu...
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.
The Fractional Power Law of Wind Wave Growth in Deep Water for Short Fetch
Institute of Scientific and Technical Information of China (English)
GUAN Changlong; SUN Qun; Philippe Fraunie
2002-01-01
Combining the 3/2 power law proposed by Toba with the significant wave energy balance equation for windwaves, wave growth in deep water for short fetch is investigated. It is found that the variations of wave height and periodwith fetch have the form of power function with fractional exponents 3/8 and 1/4 respectively. Using these exponents in thepower functions and through data fitting, the concise wind wave growth relations for short fetch are obtained.
DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM
Energy Technology Data Exchange (ETDEWEB)
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K., E-mail: lzhao@fit.edu [Physics and Space Sciences Department, Florida Institute of Technology, Melbourne, FL 32901 (United States)
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 stochastic 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.
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. PMID:25121598
Logarithmic and power law input-output relations in sensory systems with fold-change detection.
Directory of Open Access Journals (Sweden)
Miri Adler
2014-08-01
Full Text Available 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.
NEW METHOD TO ESTIMATE SCALING OF POWER-LAW DEGREE DISTRIBUTION AND HIERARCHICAL NETWORKS
Institute of Scientific and Technical Information of China (English)
YANG Bo; DUAN Wen-qi; CHEN Zhong
2006-01-01
A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering func tion for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS (Kolmogorov-Smirnov) test statistics for 10 CNN (Connecting Nearest-Neighbor)networks.
Arita, Ken-ichiro
2014-01-01
Shell structures in single-particle energy spectra are investigated against regular tetrahedral type deformation using radial power-law potential model. Employing a natural way of shape parametrization which interpolate sphere and regular tetrahedron, we find prominent shell effects at rather large tetrahedral deformations, which bring about shell energies much larger than the cases of spherical and quadrupole type shapes. We discuss the semiclassical origin of these anomalous shell structures using periodic orbit theory.
Ormerod, P.; Mounfield, C
2001-01-01
Power law distributions of macroscopic observables are ubiquitous in both the natural and social sciences. They are indicative of correlated, cooperative phenomena between groups of interacting agents at the microscopic level. In this paper we argue that when one is considering aggregate macroeconomic data (annual growth rates in real per capita GDP in the seventeen leading capitalist economies from 1870 through to 1994) the magnitude and duration of recessions over the business cycle do inde...
Kiflawi, Moshe; Mann, Ofri; Meekan, Mark G
2016-10-21
Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes. PMID:27449788
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.
A two-exponent Mass-Size Power Law for Celestial Objects
Pérez-Mercader, J
1996-01-01
The Universe that we know is populated by structures made up of aggregated matter that organizes into a variety of objects; these range from stars to larger objects, such as galaxies or star clusters, composed by stars, gas and dust in gravitational interaction. We show that observations support the existence of a composite (two--exponent) power law relating mass and size for these objects. We briefly discuss these power laws and, in view of the similarity in the values of the exponents, ponder the analogy with power laws in other fields of science such as the Gutenberg--Richter law for earthquakes and the Hutchinson--MacArthu r or Damuth laws of ecology. We argue for a potential connection with avalanches, complex systems and punctuated equilibrium, and show that this interpretation of large scale--structure as a self--organized critical system leads to two $predictions$: (a) the large scale structures are fractally distributed and, (b), the fractal dimension is $1.65
Flow of power-law fluids in self-affine fracture channels.
Yan, Yiguang; Koplik, Joel
2008-03-01
The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values zeta=0.5 and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a different technique to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian, and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, are studied, and the non-Newtonian fluids are compared to the (previously studied) Newtonian case. We find a scaling relation between permeability and mean aperture in the low Reynolds number regime, generalizing an earlier result for Newtonian fluids. As the Reynolds number increases, we observe the same sequence of transitions to nonlinearity found in intergranular porous media. Furthermore, the permeability results may be collapsed into a master curve of friction factor vs Reynolds number, using a scaling similar to that employed for power-law fluids in porous media.
Power-law behavior in complex organizational communication networks during crisis
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.
AC losses in superconductors with a power-law constitutive relation
Energy Technology Data Exchange (ETDEWEB)
Agassi, Y.D., E-mail: yehoshua.agassi@navy.mil
2015-10-15
Highlights: • Derivation of power-law constitutive-relation from distributed Anderson–Kim theory. • The electric-field for HTS constitutive-relation satisfies nonlinear heat-equation. • For slab, AC losses scale as B{sub 0}{sup m}, m = 3–4 and I{sup 3} with field-amplitude and current, respectively. • Calculated pinning potential, AC-losses scaling is consistent with BSCCO data. - Abstract: The observed constitutive relation between the electrical field and current density in cuprates high temperature superconductors is a power-law of the current. This functional dependence is presumably related to the giant flux-creep domain. It is shown that this constitutive relation reflects the statistical spread of the pinning potential associated with creep motion of vortex bundles. The AC losses emanating from a power-law constitutive relation are calculated in an approach focused on the superconductor’s electric field. For a slab geometry in the presence of a parallel AC magnetic field or transport current, the calculated AC-loss scaling laws are consistent with BSCCO data and the critical state model. Extensions of the approach are briefly discussed.
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
Power-law scaling in daily rainfall patterns and consequences in urban stream discharges
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.
Experimental research on breakup of 2D power law liquid film☆
Institute of Scientific and Technical Information of China (English)
Lixing Xu; Zhenyan Xia; Mengzheng Zhang; Qing Du; Fuqiang Bai
2015-01-01
On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination, different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters (injection pressure, ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.
Excessive loss of information by the power-law ansatz for complex systems
Tsai, Sun-Ting; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming
2015-01-01
Physicists love simple laws and uncovering common causes among seemingly unrelated phenomena. An example is the connection between earthquakes and crumpling of a paper, built through the simple power law (SPL) believed to exist between the occurrence rate of their crackling noise and the pulse intensity. We provide, however, evidence to weaken such a link by showing that both systems in fact obey different and more complex laws. Our analyses are based on the Akaike information criterion (AIC) that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. AIC found that a shifted power law retains more information than SPL in the cases of crumpling sound, duration-time frequency of solar flare, web link, protein-domain frequency, and stock-market fluctuations. In the mean time, double power laws (DPL) should replace the Gutenberg-Richter law for earthquake, and the scale-free model for brain functional network, two-dimensional sandpile...
Distributed power-law seismicity changes and crustal deformation in the SW Hellenic ARC
Directory of Open Access Journals (Sweden)
A. Tzanis
2003-01-01
Full Text Available A region of definite accelerating seismic release rates has been identified at the SW Hellenic Arc and Trench system, of Peloponnesus, and to the south-west of the island of Kythera (Greece. The identification was made after detailed, parametric time-to-failure modelling on a 0.1° square grid over the area 20° E – 27° E and 34° N–38° N. The observations are strongly suggestive of terminal-stage critical point behaviour (critical exponent of the order of 0.25, leading to a large earthquake with magnitude 7.1 ± 0.4, to occur at time 2003.6 ± 0.6. In addition to the region of accelerating seismic release rates, an adjacent region of decelerating seismicity was also observed. The acceleration/deceleration pattern appears in such a well structured and organised manner, which is strongly suggestive of a causal relationship. An explanation may be that the observed characteristics of distributed power-law seismicity changes may be produced by stress transfer from a fault, to a region already subjected to stress inhomogeneities, i.e. a region defined by the stress field required to rupture a fault with a specified size, orientation and rake. Around a fault that is going to rupture, there are bright spots (regions of increasing stress and stress shadows (regions relaxing stress; whereas acceleration may be observed in bright spots, deceleration may be expected in the shadows. We concluded that the observed seismic release patterns can possibly be explained with a family of NE-SW oriented, left-lateral, strike-slip to oblique-slip faults, located to the SW of Kythera and Antikythera and capable of producing earthquakes with magnitudes MS ~ 7. Time-to-failure modelling and empirical analysis of earthquakes in the stress bright spots yield a critical exponent of the order 0.25 as expected from theory, and a predicted magnitude and critical time perfectly consistent with the figures given above. Although we have determined an approximate location
Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions
Corral, Alvaro
2012-01-01
Power-law distributions contain precious information about a large variety of processes in geoscience and elsewhere. Although there are sound theoretical grounds for these distributions, the empirical evidence in favor of power laws has been traditionally weak. Recently, Clauset et al. have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implem...
Hard electronics; Hard electronics
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-03-01
Hard material technologies were surveyed to establish the hard electronic technology which offers superior characteristics under hard operational or environmental conditions as compared with conventional Si devices. The following technologies were separately surveyed: (1) The device and integration technologies of wide gap hard semiconductors such as SiC, diamond and nitride, (2) The technology of hard semiconductor devices for vacuum micro- electronics technology, and (3) The technology of hard new material devices for oxides. The formation technology of oxide thin films made remarkable progress after discovery of oxide superconductor materials, resulting in development of an atomic layer growth method and mist deposition method. This leading research is expected to solve such issues difficult to be easily realized by current Si technology as high-power, high-frequency and low-loss devices in power electronics, high temperature-proof and radiation-proof devices in ultimate electronics, and high-speed and dense- integrated devices in information electronics. 432 refs., 136 figs., 15 tabs.
HEXTE Detections of Hard X-Ray Tails in Sco X-1
D'Amico, F; Rothschild, R E; Gruber, D
2000-01-01
We report the detection of a non-thermal hard X-ray component from Sco X-1 based upon the analysis of 20-220 keV spectra obtained with the HEXTE experiment onboard the RXTE satellite. We find that the addition of a power-law component to a thermal bremsstrahlung model is required to achieve a good fit in 5 of 16 observations analyzed. Using PCA data we were able to track the movement of the source along the Z diagram, and we found that the presence of the hard X-ray tail is not confined to a specific Z position. However, we do observe an indication that the power law index hardens with increasing mass accretion rate, as indicated from the position on the Z diagram. We find that the derived non-thermal luminosities are about 10% of that derived for the brightest of the atoll sources. These observations provide firm evidence for non-thermal X-ray activity in a Z source.
On the interplay between short and long term memory in the power-law cross-correlations setting
Kristoufek, Ladislav
2015-03-01
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equal to an average of separate Hurst exponents of the analyzed processes. Strength of short term memory has no effect on these asymptotic properties. Implications of these findings for the power-law cross-correlations concept are further discussed.
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. PMID:27505155
Institute of Scientific and Technical Information of China (English)
邓永菊; 郑华; 杨纯斌
2012-01-01
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random- walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.
On the interplay between short and long term memory in the power-law cross-correlations setting
Kristoufek, Ladislav
2014-01-01
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of the separate processes. The bivariate Hurst exponent is then equal to an average of the separate Hurst exponents of the analysed processes. Strength of the short term memory has no effect on these asymptotic properties.
Thelwall, Mike
2016-01-01
Identifying the statistical distribution that best fits citation data is important to allow robust and powerful quantitative analyses. Whilst previous studies have suggested that both the hooked power law and discretised lognormal distributions fit better than the power law and negative binomial distributions, no comparisons so far have covered all articles within a discipline, including those that are uncited. Based on an analysis of 26 different Scopus subject areas in seven different years...
International Nuclear Information System (INIS)
This paper presents the theoretical analysis of a flow driven by surface tension and gravity in an inclined circular tube. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Power-law model) that continuously flows into a circular tube owing to surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that quantitatively, the theoretical predictions of the governing equation were in excellent agreement with the solutions of the equation for horizontal tubes and the past experimental data. In addition, the predictions compared very well with the results of the force balance equation for steady
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
Keil, Petr; Herben, Tomás; Rosindell, James; Storch, David
2010-07-01
There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed 'pink noise': a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.
Wang, Q.; Yang, M.; Song, X. L.; Jia, J.; Xiang, Z. D.
2016-07-01
The conventional power law creep equation (Norton equation) relating the minimum creep rate to creep stress and temperature cannot be used to predict the long-term creep strengths of creep-resistant steels if its parameters are determined only from short-term measurements. This is because the stress exponent and activation energy of creep determined on the basis of this equation depend on creep temperature and stress and these dependences cannot be predicted using this equation. In this work, it is shown that these problems associated with the conventional power law creep equation can be resolved if the new power law equation is used to rationalize the creep data. The new power law creep equation takes a form similar to the conventional power law creep equation but has a radically different capability not only in rationalizing creep data but also in predicting the long-term creep strengths from short-term test data. These capabilities of the new power law creep equation are demonstrated using the tensile strength and creep test data measured for both pipe and tube grades of the creep-resistant steel 9Cr-1.8W-0.5Mo-V-Nb-B (P92 and T92).
On the power-law distributions of X-ray fluxes from solar flares observed with GOES
Li, You-Ping; Feng, Li; Zhang, Ping; Liu, Si-Ming; Gan, Wei-Qun
2016-10-01
The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality (SOC). In this paper, we first show that, so long as the shape of the normalized light curve is not correlated with the peak flux, the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the power-law frequency distribution of the peak flux, which may partially explain why power-law distributions are ubiquitous in the Universe. We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different: the higher energy channel has a harder distribution than the lower energy channel, which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites. The temperature (T) distribution, on the other hand, approaches a power-law distribution with an index of 2 for high values of T. Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.
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.
Hard electronics; Hard electronics
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-03-01
In the fields of power conversion devices and broadcasting/communication amplifiers, high power, high frequency and low losses are desirable. Further, for electronic elements in aerospace/aeronautical/geothermal surveys, etc., heat resistance to 500degC is required. Devices which respond to such hard specifications are called hard electronic devices. However, with Si which is at the core of the present electronics, the specifications cannot fully be fulfilled because of the restrictions arising from physical values. Accordingly, taking up new device materials/structures necessary to construct hard electronics, technologies to develop these to a level of IC were examined and studied. They are a technology to make devices/IC of new semiconductors such as SiC, diamond, etc. which can handle higher temperature, higher power and higher frequency than Si and also is possible of reducing losses, a technology to make devices of hard semiconducter materials such as a vacuum microelectronics technology using ultra-micro/high-luminance electronic emitter using negative electron affinity which diamond, etc. have, a technology to make devices of oxides which have various electric properties, etc. 321 refs., 194 figs., 8 tabs.
Evidence for Power-law tail of the Wealth Distribution in India
Sitabhra Sinha
2005-01-01
The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-4. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year under analysis). This provides a comparison with previous studies of wealth distribution, which have all been confined to Western advanced capitalist economies. We conclude with a...
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
Energy Technology Data Exchange (ETDEWEB)
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 [Dipartimento di Chimica “G. Ciamician”, Universita’ di Bologna, Via F. Selmi 2, 40126 Bologna (Italy); Venturini, Alessandro [Institute for the Organic Synthesis and Photoreactivity, National Research Council of Italy, Via Gobetti 101, 40129 Bologna (Italy)
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.
Power-Law Entropy Corrected Ricci Dark Energy and Dynamics of Scalar Fields
Pasqua, Antonio(Department of Physics, University of Trieste, Via Valerio, No. 2, 34127 Trieste, Italy); Jamil, Mubasher; Myrzakulov, Ratbay; Majeed, Bushra
2012-01-01
Motivated by the holographic principle, it has been suggested that the Dark Energy (DE) density can be inversely proportional to the area $A$ of the event horizon of the universe. However, this kind of model would have a casuality problem. In this work, we study the power-law entropy corrected holographic DE (PLECHDE) model in the non-flat Friedmann-Robertson-Walker universe, with the future event horizon replaced by the average radius of the Ricci scalar curvature. We derive the equation of ...
The Transient Elliptic Flow of Power-Law Fluid in Fractal Porous Media
Institute of Scientific and Technical Information of China (English)
宋付权; 刘慈群
2002-01-01
The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.
Robust Statistical Tests of Dragon-Kings beyond Power Law Distributions
Pisarenko, V. F.; Sornette, D.
2011-01-01
We ask the question whether it is possible to diagnose the existence of "Dragon-Kings" (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent c...
Void growth in copper during high-temperature power-law creep
Energy Technology Data Exchange (ETDEWEB)
Dzieciol, K. [Centre SMS, Ecole Nationale Superieure des Mines de Saint-Etienne, 158, cours Fauriel, F-42023 Saint-Etienne cedex 2 (France); Max-Planck Institut fuer Eisenforschung GmbH, Max-Planck Strasse 1, 40237, Duesseldorf (Germany); Borbely, A., E-mail: borbely@emse.fr [Centre SMS, Ecole Nationale Superieure des Mines de Saint-Etienne, 158, cours Fauriel, F-42023 Saint-Etienne cedex 2 (France); Max-Planck Institut fuer Eisenforschung GmbH, Max-Planck Strasse 1, 40237, Duesseldorf (Germany); Sket, F. [Helmholtz Zentrum fuer Materialien und Energie GmbH, Glienicker Strasse 100, 14109 Berlin (Germany); IMDEA Materials Institute, Calle Profesor Aranguren s/n, 28040 Madrid (Spain); Isaac, A. [Helmholtz Zentrum fuer Materialien und Energie GmbH, Glienicker Strasse 100, 14109 Berlin (Germany); Brazilian Synchrotron Light Laboratory, Caixa Postal 6192, Campinas SP 13083-970 (Brazil); Di Michiel, M.; Cloetens, P.; Buslaps, Th. [European Synchrotron Radiation Facility, 6 rue Jules Horowitz, BP 220, 38043 Grenoble cedex 9 (France); Pyzalla, A.R. [Helmholtz Zentrum fuer Materialien und Energie GmbH, Glienicker Strasse 100, 14109 Berlin (Germany)
2011-01-15
Growth of grain boundary voids during high-temperature power-law creep of metals is usually approximated as the growth of a hole in a nonlinearly viscous solid. Using synchrotron tomography, we show that the functional form of the continuum law is valid but that the real growth rates in copper are higher than the prediction of the viscous model by a factor of about 40. Submicrometer resolution tomography showing faceted void shapes as well as the large scatter of individual growth rates suggest that local dislocation glide has significative contribution to void growth.
The Anderson-Darling test of fit for the power law distribution from left censored samples
Coronel-Brizio, H F
2010-01-01
Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum likelihood estimators and tables of asymptotic percentage points for the A^2 statistic are given. The technique is illustrated for data from the Dow Jones Industrial Average index, an example of high theoretical and practical importance in Econophysics, Finance, Physics, Biology and, in general, in other related Sciences such as Complexity Sciences.
Power-law and intermediate inflationary models in f ( T )-gravity
Rezazadeh, K.; Abdolmaleki, A.; Karami, K.
2016-01-01
We study inflation in the framework of $f(T)$-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in $f(T)$-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law form for the $f(T)$ function in the action and examine the ...
Effects of diversity and procrastination in priority queuing theory: The different power law regimes
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 0procrastination,” 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.
Underdamped strain dynamics of a martensitic model with power-law interactions
Shankaraiah, N.; Puri, Sanjay; Shenoy, S. R.
2014-04-01
Focusing on conversion-time delays in athermal martensites, we present our results on underdamped strain dynamics of triple-well Landau free-energies with power-law anisotropic interactions for square-rectangle ferroelastic transition. After a temperature quench of 2% initial martensite seeds, the deterministic underdamped strain dynamics shows, interestingly, both fast conversions below a temperature and incubation delays above it, as in experiment and Monte Carlo simulations. On increasing damping constant, the fast conversions transform to incubation delays. Surprisingly, conversion-time delays have Vogel-Fulcher divergences as in Monte Carlo simulations. Microstructural evolutions are in good agreement with earlier studies.
A Closed-Form Method for LRU Replacement under Generalized Power-Law Demand
Laoutaris, Nikolaos
2007-01-01
We consider the well known \\emph{Least Recently Used} (LRU) replacement algorithm and analyze it under the independent reference model and generalized power-law demand. For this extensive family of demand distributions we derive a closed-form expression for the per object steady-state hit ratio. To the best of our knowledge, this is the first analytic derivation of the per object hit ratio of LRU that can be obtained in constant time without requiring laborious numeric computations or simulat...
Waters; Hughes; Mobley; Brandenburger; Miller
2000-08-01
In the recent literature concern has been raised regarding the validity of Kramers-Kronig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers-Kronig dispersion relations for application to these types of media are available. The developed dispersion relations are compared with measurements on several liquids, and agreement is found to better than 1 m/s over the experimentally available bandwidth. A discussion regarding the validity of these dispersion relations, in particular how the dispersion relations relate to the so-called Paley-Wiener conditions, forms the conclusion.
Light Fragment Production and Power Law Behavior in Au + Au Collisions
International Nuclear Information System (INIS)
Using charged-particle-exclusive measurements of Au+Au collisions in the LBL Bevalac's EOS time projection chamber, we investigate momentum-space densities of fragments up to 4He as a function of fragment transverse momentum, azimuth relative to the reaction plane, rapidity, multiplicity, and beam energy. Most features of these densities above a transverse momentum threshold are consistent with momentum-space coalescence, and, in particular, the increase in sideward flow with fragment mass is generally well described by a momentum-space power law
Mercan, Kadir; Demir, Çiğdem; 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.
Directory of Open Access Journals (Sweden)
Mercan Kadir
2016-01-01
Full Text Available 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.
Transport diffusion in one dimensional molecular systems: Power law and validity of Fick's law
Xu, Zhi-cheng; Zheng, Dong-qin; Ai, Bao-quan; Hu, Bambi; Zhong, Wei-rong
2015-10-01
The transport diffusion in one-dimensional molecular systems is investigated through non-equilibrium molecular dynamics and Monte Carlo methods. We have proposed the power law relationship of the transport diffusion coefficient with the temperature, the mass and the transport length, D* ∝ T*m*-1L*β, where β equals to 0.8 for small systems and zero for large systems. It is found that Fick's law is valid in long transport length but invalid in short transport length. Our results can provide a new perspective for understanding the microscopic mechanism of the molecular transport phenomena in low-dimensional systems.
Transport diffusion in one dimensional molecular systems: Power law and validity of Fick’s law
Zhi-cheng Xu; Dong-qin Zheng; Bao-quan Ai; Bambi Hu; Wei-rong Zhong
2015-01-01
The transport diffusion in one-dimensional molecular systems is investigated through non-equilibrium molecular dynamics and Monte Carlo methods. We have proposed the power law relationship of the transport diffusion coefficient with the temperature, the mass and the transport length, D* ∝ T*m*−1L*β, where β equals to 0.8 for small systems and zero for large systems. It is found that Fick’s law is valid in long transport length but invalid in short transport length. Our results can provide a n...
Extended power-law scaling of air permeabilities measured on a block of tuff
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M. Siena
2012-01-01
Full Text Available We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M, Extended Self-Similarity (ESS and a generalized version thereof (G-ESS. All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q, of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q with q, are consistent with a view of these data as a sample from a truncated version (tfBm of self-affine fractional Brownian motion (fBm. Since in theory the scaling exponents, ξ(q, of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well
An explanation for the universal 3.5 power-law observed in currency markets
Johnson, Nicholas A.; Johnson, Neil F.
We present a mathematical theory to explain a recent empirical finding in the Physics literature (Zhao et al., 2013) in which the distributions of waiting-times between discrete events were found to exhibit power-law tails with an apparent universal exponent: α ∼ 3.5 . This new theory provides the first ever qualitative and quantitative explanation of Zhao et al.'s surprising finding. It also provides a mechanistic description of the origin of the observed universality, assigning its cause to the emergence of dynamical feedback processes between evolving clusters of like-minded agents.
Power Law of Shear Viscosity in Einstein-Maxwell-Dilaton-Axion model
Ling, Yi; Zhou, Zhenhua
2016-01-01
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 testified numerically at low temperature $T$, namely, $\\eta/s\\sim T^\\kappa$, where the values of exponent $\\kappa$ coincide with the analytical results. We also find that the exponent $\\kappa$ is not affected by irrelevant current, but is reduced by the relevant current.
A generalized power-law scaling law for a two-phase imbibition in a porous medium
El-Amin, Mohamed
2013-11-01
Dimensionless time is a universal parameter that may be used to predict real field behavior from scaled laboratory experiments in relation to imbibition processes in porous media. Researchers work to nondimensionalize the time has been through the use of parameters that are inherited to the properties of the moving fluids and the porous matrix, which may be applicable to spontaneous imbibition. However, in forced imbibition, the dynamics of the process depends, in addition, on injection velocity. Therefore, we propose the use of scaling velocity in the form of a combination of two velocities, the first of which (the characteristic velocity) is defined by the fluid and the porous medium parameters and the second is the injection velocity, which is a characteristic of the process. A power-law formula is suggested for the scaling velocity such that it may be used as a parameter to nondimensionalize time. This may reduce the complexities in characterizing two-phase imbibition through porous media and works well in both the cases of spontaneous and forced imbibition. The proposed scaling-law is tested against some oil recovery experimental data from the literature. In addition, the governing partial differential equations are nondimensionalized so that the governing dimensionless groups are manifested. An example of a one-dimensional countercurrent imbibition is considered numerically. The calculations are carried out for a wide range of Ca and Da to illustrate their influences on water saturation as well as relative water/oil permeabilities. © 2013 Elsevier B.V.
The power-law spectra of energetic particles during multi-island magnetic reconnection
Drake, J F; Fermo, R L
2012-01-01
Power-law distributions are a near universal feature of energetic particle spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfv\\'enic ions in the solar wind and the hardest energetic electron spectra in flares all have energy fluxes with power-laws that depend on energy $E$ approximately as $E^{-1.5}$. We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omni-directional particle distribution $f(v,t)$ that is solved in closed form to reveal $v^{-5}$ (corresponding to an energy flux varying as $E^{-1.5}$) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state the total energy ...
Garanina, O S
2016-01-01
A multi-parametric family of stretch exponential distributions with various power law tails is introduced and is shown to describe adequately the empirical distributions of scientific citation of individual authors. The four-parametric families are characterized by a normalization coefficient in the exponential part, the power exponent in the power-law asymptotic part, and the coefficient for the transition between the above two parts. The distribution of papers of individual scientist over citations of these papers is studied. Scientists are selected via total number of citations in three ranges: 102-103, 103-104, and 104-105 of total citations. We study these intervals for physicists in ISI Web of Knowledge. The scientists who started their scientific publications after 1980 were taken into consideration only. It is detected that the power coefficient in the stretch exponent starts from one for low-cited authors and has to trend to smaller values for scientists with large number of citation. At the same tim...
Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales
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.
Analysis of Grassland Vegetation of the Southwest Heilongjiang Steppe (China) Using the Power Law
Institute of Scientific and Technical Information of China (English)
Mikinori TSUIKI; Yu-Sheng WANG; Yiruhan; Michio TSUTSUMI; Masae SHIYOMI
2005-01-01
In 1997, we conducted a vegetation survey in three semi-arid natural grasslands (steppes) withdifferent livestock grazing intensities in Southwest Heilongjiang Province, China. The dominant grasslandspecies was the grass Stipa baicalensis Roshev. Grasslands with light, intermediate, and heavy grazingintensities were located 10, 5, and 2 km from a village, respectively. Villagers use the steppe to raise cattle,horses, sheep, and goats. Each of the three grasslands was surveyed by placing 100 quadrats (50 cm×50 cm)along a 50 m line transect. Each quadrat was divided into four equal areas (25 cm×25 cm; S-quadrats) and allplant species occurring in each of these smaller areas were identified and recorded. These data were summa-rized into frequency distributions and the percentage of S-quadrats containing a given species and thevariance of each species were estimated. The power law was applied to these estimates. The power law wasused to evaluate the spatial heterogeneity and frequency of occurrence for each species in the grasslandcommunity. The lightly grazed grassland exhibited high spatial heterogeneity (caused by large plant size),the highest species diversity, and a high occurrence of S. baicalensis. In contrast, the heavily grazedgrassland exhibited high spatial heterogeneity (caused by patchy populations of small plant size), lowspecies diversity, and a low occurrence of S. baicalensis. We judged that the heavily grazed grassland wasovergrazed and exclusion of livestock from the degraded areas is necessary for recovery.
So You Think the Crab is Described by a Power-Law Spectrum
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.
Cyclotron maser emission from power-law electrons with strong pitch-angle anisotropy
Zhao, G Q; Wu, D J; Chen, L; Tang, J F; Liu, Q
2016-01-01
Energetic electrons with power-law spectrum are most commonly observed in astrophysics. This paper investigates electron cyclotron maser emission (ECME) from the power-law electrons, in which strong pitch-angle anisotropy is emphasized. The electron distribution function proposed in this paper can describe various types of pitch-angle anisotropy. Results show that the emission properties of ECME, including radiation growth, propagation, and frequency properties, depend considerably on the types of electron pitch-angle anisotropy, and different wave modes show different dependences on the pitch angle of electrons. In particular, the maximum growth rate of X2 mode rapidly decreases with respect to the electron pitch-angle cosine $\\mu_0$ at which the electron distribution peaks, while the growth rates for other modes (X1, O1, O2) initially increase before decreasing as $\\mu_0$ increases. Moreover, the O mode as well as the X mode can be the fastest growth mode, in terms of not only the plasma parameter but also ...
Power law scaling and ``Dragon-Kings'' in distributions of intraday financial drawdowns
Filimonov, Vladimir; Sornette, Didier
2015-05-01
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of epsilon-drawdowns and epsilon-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (dragon-kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.
Power laws in microrheology experiments on living cells: comparative analysis and modelling
Balland, M; Icard, D; Fereol, S; Asnacios, A; Browaeys, J; Henon, S; Gallet, F; Balland, Martial; Desprat, Nicolas; Icard, Delphine; Fereol, Sophie; Asnacios, Atef; Browaeys, Julien; Henon, Sylvie; Gallet, Francois
2006-01-01
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 micrometric bead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient $G_e(\\omega)$ is retrieved. Both $J(t)$ and $G_e(\\omega)$ exhibit power law behavior: $J(t)= A(t/t_0)^\\alpha$ and $\\bar G_e(\\omega)\\bar = G_0 (\\omega/\\omega_0)^\\alpha$, with the same exponent $\\alpha\\approx 0.2$. This power law behavior is very robust ; $\\alpha$ is distributed over a narrow range, and shows almost no dependance 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 $A_0$ and $G_0$appear very sensitive to these parameters. Whereas the exponents $\\alpha$ are normally distribu...
Universal inverse power-law distribution for temperature and rainfall in the UK region
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.
Effective power-law dependence of Lyapunov exponents on the central mass in galaxies
Delis, N; Kalapotharakos, C
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation $L\\propto m^p$ between the mean Lyapunov exponent $L$ of stellar orbits chaotically scattered by a supermassive black hole in the center of a galaxy and the mass parameter $m$, i.e. ratio of the mass of the black hole over the mass of the galaxy. The exponent $p$ is found numerically to obtain values in the range $p \\approx 0.3$--$0.5$. 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 black hole's sphere of influence. We thus predict $p=2/3-q$ with $q\\approx 0.1$--$0.2$. 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...
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Ma'zoozeh E. Abu-Amra
2008-04-01
Full Text Available In this paper we derive close form for the matrix elements for $hat H=-Delta +V$, where $V$ is a pure power-law potential. We use trial functions of the form $$ psi _n(r= sqrt{{frac{2eta ^{gamma/2}(gamma _n} {n!Gamma(gamma }}} r^{gamma - 1/2} e^{-frac{sqrt{eta }}{2}r^q} _pF_1 ( -n,a_2,ldots ,a_p;gamma;sqrt {eta } r^q, $$ for $eta, q,gamma >0$ to obtain the matrix elements for $hat H$. These formulas are then optimized with respect to variational parameters $eta ,q$ and $gamma $ to obtain accurate upper bounds for the given nonsolvable eigenvalue problem in quantum mechanics. Moreover, we write the matrix elements in terms of the generalized hypergeomtric functions. These results are generalization of those found earlier in [2], [8-16] for power-law potentials. Applications and comparisons with earlier work are presented.
Universal correlations and power-law tails in financial covariance matrices
Akemann, G.; Fischmann, J.; Vivo, P.
2010-07-01
We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.
Pressure falloff behavior in vertically fractured wells: Non-Newtonian power-law fluids
Energy Technology Data Exchange (ETDEWEB)
Vongvuthipornchai, S.; Raghauan, R.; Reynolds, A.C.
1984-09-01
This paper examines pressure falloff behavior in fractured wells following the injection of a non-Newtonian power-law fluid. Results are presented in a form suitable for field application. Responses at wells intercepting infinite-conductivity and uniformflux fractures are considered. Procedures to identify flow regimes are discussed. The solutions presented here are new and to our knowledge not available in the literature. The consequences of neglecting the non-Newtonian characteristics of the injected fluid are examined. The results of this work were obtained by a finite difference model. Procedures to compute the apparent viscosity of power-law fluids for twodimensional flow through porous media are discussed. The formulation given here avoids numerical problems (multiple solutions, cross over, etc.) reported in other studies. Although, the main objective of the work is to examine pressure falloff behavior at fractured wells, the authors also examine responses at unfractured wells. The main objective of this part of a study is to examine the validity of using the superposition principle to analyze pressure falloff data. (The pressure distribution for this problem is governed by a nonlinear partial differential equation.) If the solutions given in the literature are used, then correction factors are needed to analyze pressure falloff data. The results of this phase of the work can also be used to analyze data in fractured wells provided that pseudoradial flow conditions exist.
Supernova-blast waves in wind-blown bubbles, turbulent, and power-law ambient media
Haid, Sebastian; Naab, Thorsten; Seifried, Daniel; Mackey, Jonathan; Gatto, Andrea
2016-01-01
Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media with uniform (and with stellar wind blown bubbles), power-law, and turbulent density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with $n(r) \\sim$ $r^{-2}$ (for $n(r) > n_{_{\\rm floor}}$) the amount of momentum injection is solely r...
THE STRUCTURAL FLOW IN PIPE CONTAINING POROUS MEDIUM SATURATED WITH POWER-LAW FLUID
Institute of Scientific and Technical Information of China (English)
ZHOU Xiao-jun; YU Min-chao
2012-01-01
In this article,the method of volume averaging of flow in porous media and averaging theorem was employed to the Navier-Stokes equations.The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure (i.e.,the Darcy resistance) and the resistance due to the inertia force (i.e.,the Forchheimer resistance),then the Brinkman-Forchheimer extended Darcy model was obtained from average momentum equation.The structural flow in a pipe containing porous medium saturated with power law fluid was applied in the present study.A new theoretical analysis of fully developed non-Darcy flow in a pipe containing a fibrous medium saturated with power law fluid was conducted.Using the integration method,the boundary layer solutions were obtained for flow core velocity and its radius.These theoretical solutions were used to analyze the effects of the Darcy number and inertia parameter on the axial velocity profile in the porous medium pipe.
Double power-law spectra of energetic electrons in the Earth magnetotail
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A. V. Artemyev
2013-01-01
Full Text Available In this paper, we consider electron acceleration in the vicinity of X-line and corresponding formation of energy spectra. We develop an analytical model including the effect of the electron trapping by electrostatic fields and surfing acceleration. Speiser, Fermi and betatron mechanisms of acceleration are also taken into account. Analytical estimates are verified by the numerical integration of electron trajectories. The surfing mechanism and adiabatic heating are responsible for the formation of the double power-law spectrum in agreement with the previous studies. The energy of the spectrum knee is about ~150 keV for typical conditions of the Earth magnetotail. We compare theoretical results with the spacecraft observations of electron double power-law spectra in the magnetotail and demonstrate that the theory is able to describe typical energy of the spectra knee. We also estimate the role of relativistic effects and magnetic field fluctuations on the electron acceleration: the acceleration is more stable for relativistic electrons, while fluctuations of the magnetic field cannot significantly decrease the gained energy for typical magnetospheric conditions.
Pandya, Alex; Zhang, Zhaowei; Chandra, Mani; Gammie, Charles F.
2016-05-01
Synchrotron emission and absorption determine the observational appearances of many astronomical systems. In this paper, we describe a numerical scheme for calculating synchrotron emissivities and absorptivities in all four Stokes parameters for arbitrary gyrotropic electron distribution functions, building on earlier work by Leung, Gammie, and Noble. We use this technique to evaluate the emissivities and the absorptivities for a thermal (Maxwell–Jüttner), isotropic power-law, and an isotropic kappa distribution function. The latter contains a power-law tail at high particle energies that smoothly merges with a thermal core at low energies, as is characteristic of observed particle spectra in collisionless plasmas. We provide fitting formulae and error bounds on the fitting formulae for use in codes that solve the radiative transfer equation. The numerical method and the fitting formulae are implemented in a compact C library called symphony. We find that the kappa distribution has a source function that is indistinguishable from a thermal spectrum at low frequency and transitions to the characteristic self-absorbed synchrotron spectrum, \\propto {ν }5/2, at high frequency; the linear polarization fraction for a thermal spectrum is near unity at high frequency; and all distributions produce O(10%) circular polarization at low frequency for lines of sight sufficiently close to the magnetic field vector.
Power-law optical conductivity from unparticles: Application to the cuprates
Limtragool, Kridsanaphong; Phillips, Philip
2015-10-01
We calculate the optical conductivity by using several models for unparticle or scale-invariant matter. Within a Gaussian action for unparticles that is gauged with Wilson lines, we find that the conductivity computed from the Kubo formalism with vertex corrections yields no nontrivial deviation from the free-theory result. This result obtains because, at the Gaussian level, unparticles are just a superposition of particle fields and hence any transport property must be consistent with free theory. Beyond the Gaussian approach, we adopt the continuous-mass formulation of unparticles and calculate the Drude conductivity directly. We show that unparticles in this context can be tailored to yield an algebraic conductivity that scales as ω-2 /3 with the associated phase angle between the imaginary and real parts of arctanσ/2σ1=60∘ , as is seen in the cuprates. Given the recent results [J. High Energy Phys. 4, 40 (2014), 10.1007/JHEP04(2014)040; J. High Energy Phys. 7, 24 (2015), 10.1007/JHEP07(2015)024; arXiv:1506.06769] that gravitational crystals lack a power-law optical conductivity, this constitutes the first consistent account of the ω-2 /3 conductivity and the phase angle seen in optimally doped cuprates. Our results indicate that, at each frequency in the scaling regime, excitations on all energy scales contribute. Hence, incoherence is at the heart of the power law in the optical conductivity in strongly correlated systems such as the cuprates.
Directory of Open Access Journals (Sweden)
Taro Ueno
Full Text Available We analyzed the effects of dopamine signaling on the temporal organization of rest and activity in Drosophila melanogaster. Locomotor behaviors were recorded using a video-monitoring system, and the amounts of movements were quantified by using an image processing program. We, first, confirmed that rest bout durations followed long-tailed (i.e., power-law distributions, whereas activity bout durations did not with a strict method described by Clauset et al. We also studied the effects of circadian rhythm and ambient temperature on rest bouts and activity bouts. The fraction of activity significantly increased during subjective day and at high temperature, but the power-law exponent of the rest bout distribution was not affected. The reduction in rest was realized by reduction in long rest bouts. The distribution of activity bouts did not change drastically under the above mentioned conditions. We then assessed the effects of dopamine. The distribution of rest bouts became less long-tailed and the time spent in activity significantly increased after the augmentation of dopamine signaling. Administration of a dopamine biosynthesis inhibitor yielded the opposite effects. However, the distribution of activity bouts did not contribute to the changes. These results suggest that the modulation of locomotor behavior by dopamine is predominantly controlled by changing the duration of rest bouts, rather than the duration of activity bouts.
Detection of two power-law tails in the probability distribution functions of massive GMCs
Schneider, N; Girichidis, P; Rayner, T; Motte, F; Andre, P; Russeil, D; Abergel, A; Anderson, L; Arzoumanian, D; Benedettini, M; Csengeri, T; Didelon, P; Francesco, J D; Griffin, M; Hill, T; Klessen, R S; Ossenkopf, V; Pezzuto, S; Rivera-Ingraham, A; Spinoglio, L; Tremblin, P; Zavagno, A
2015-01-01
We report the novel detection of complex high-column density tails in the probability distribution functions (PDFs) for three high-mass star-forming regions (CepOB3, MonR2, NGC6334), obtained from dust emission observed with Herschel. The low column density range can be fit with a lognormal distribution. A first power-law tail starts above an extinction (Av) of ~6-14. It has a slope of alpha=1.3-2 for the rho~r^-alpha profile for an equivalent density distribution (spherical or cylindrical geometry), and is thus consistent with free-fall gravitational collapse. Above Av~40, 60, and 140, we detect an excess that can be fitted by a flatter power law tail with alpha>2. It correlates with the central regions of the cloud (ridges/hubs) of size ~1 pc and densities above 10^4 cm^-3. This excess may be caused by physical processes that slow down collapse and reduce the flow of mass towards higher densities. Possible are: 1. rotation, which introduces an angular momentum barrier, 2. increasing optical depth and weaker...
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.
Numerical simulation of flow in swirl injector for power-law fluid
Institute of Scientific and Technical Information of China (English)
WANG Feng; FU Qing-fei; YANG Li-jun
2012-01-01
In order to investigate the flow characteristics of swirl injectors for gelled propellants,which actually behaved as non-Newtonian power-law fluid,a swirl axisymmetric model was established to solve Navier-Stokes equations and VOF（volume of fluid） equation,and the power-law constitutive equation was used to describe the rheology characteristics of the gelled propellants.The film thickness and velocity distribution in the swirl injector under different flow conditions were studied numerically.The simulation results show that the increased geometry characteristic parameter of the swirl injector contributes to the decrease of liquid film thickness.The liquid film thickness is almost independent of the pressure drop.The rheologic parameters have great influences on the inner flow of swirl injector： by increasing the fluid consistency index K and power index n,both the axial and the swirl velocities decrease dramatically;higher fluid consistency index K and power index n make the liquid film thickness increase.When the viscosity is large enough,the air core in the injector would vanish.
Fertility Heterogeneity as a Mechanism for Power Law Distributions of Recurrence Times
Saichev, A
2012-01-01
We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future events. Specifically, we analyze the impact of the power law distribution of fertilities with exponent \\alpha, where the fertility of an event is the number of aftershocks of first generation that it triggers, on the probability distribution function (pdf) f(\\tau) of the recurrence times \\tau between successive events. The other input of the model is an exponential Omori law quantifying the pdf of waiting times between an event and its first generation aftershocks, whose characteristic time scale is taken as our time unit. At short time scales, we discover two intermediate power law asymptotics, f(\\tau) ~ \\tau^{-(2-\\alpha)} for \\tau << \\tau_c and f(\\tau) ~ \\tau^{-\\alpha} for \\tau_c << \\tau << 1, where \\tau_c is associated with the self-excited cascades of aft...
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.
Birth and death of protein domains: A simple model of evolution explains power law behavior
Directory of Open Access Journals (Sweden)
Berezovskaya Faina S
2002-10-01
Full Text Available Abstract 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
From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies
Soesoo, Alvar; Bons, Paul D.
2015-07-01
Magma is generated by partial melting from micrometre-scale droplets at the source and may accumulate to form >100 km-scale plutons. Magma accumulation thus spans well over ten orders of magnitude in scale. Here we provide measurements of migmatitic leucosomes and granitic veins in drill cores from the Estonian Proterozoic basement and outcrops at Masku in SW Finland and Montemor-o-Novo, central Portugal. Despite the differences in size and number of measured leucosomes and magmatic veins, differences in host rock types and metamorphic grades, the cumulative width distribution of the studied magmatic leucosomes/veins follows a power law with exponents usually between 0.7 and 1.8. Published maps of the SE Australian Lachlan Fold Belt were used to investigate the distribution of granitoid pluton sizes. The granites occupy ca. 22 % of the 2.6 × 105 km2 area. The cumulative pluton area distributions show good power law distributions with exponents between 0.6 and 0.8 depending on pluton area group. Using the self-affine nature of pluton shapes, it is possible to estimate the total volume of magma that was expelled from the source in the 2.6 × 105 km2 map area, giving an estimated 0.8 km3 of magma per km2. It has been suggested in the literature that magma batches in the source merge to form ever-bigger batches in a self-organized way. This leads to a power law for the cumulative distribution of magma volumes, with an exponent m V between 1 for inefficient melt extraction, and 2/3 for maximum accumulation efficiency as most of the volume resides in the largest batches that can escape from the source. If m V ≥ 1, the mass of the magma is dominated by small batches; in case m = 2/3, about 50 % of all magma in the system is placed in a single largest batch. Our observations support the model that the crust develops a self-organized critical state during magma generation. In this state, magma batches accumulate in a non-continuous, step-wise manner to form ever
Power laws and self-organized criticality in theory and nature
International Nuclear Information System (INIS)
Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real
On the Power-Law Distributions of X-ray Fluxes from Solar Flares Observed with GOES
Li, You-ping; Zhang, Ping; Liu, Siming; Gan, Weiqun
2016-01-01
Power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system of self-organized criticality (SOC). In this paper, we first show that, so long as the shape of the normalized light curve is not correlated with the peak flux, the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the power-law frequency distribution of the peak flux, which may partially explain why power-law distributions are ubiquitous in the Universe. We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different: the higher energy channel has a harder distribution than the lower energy channel, which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES. The temperature ($T$) distribution, on the other hand, approaches a ...
Akiba, M.; Tsujino, K.
2016-08-01
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 its 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.
Evidence for power-law tail of the wealth distribution in India
Sinha, Sitabhra
2006-01-01
The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-2004. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year under analysis). This provides a comparison with previous studies of wealth distribution, which have all been confined to Western advanced capitalist economies. We conclude with a discussion on the appropriateness of multiplicative stochastic process as a model for asset accumulation, the relation between the wealth and income distributions (we estimate the Pareto exponent for the latter to be around 1.5 for India), as well as possible sources of error in measuring the Pareto exponent for wealth.
OBTAINING THE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINNING FOR POWER LAW POLYMER FLUIDS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning,and to determine the critical draw ratio for draw resonance.The results show that for shear thin fluids,the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning.When the power index approaches zero,the critical draw ratio points at unity,indicating no melt spinning can be processed stably for such fluids.For shear thick fluids.the critical draw ratio increases in a more rapid Way with increasing the power index.
Scalar Field Probes of Power-Law Space-Time Singularities
Blau, Matthias; Weiss, S; Blau, Matthias; Frank, Denis; Weiss, Sebastian
2006-01-01
We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
Liu, Chao; Li, Rong
2016-09-01
An evolutionary prisoner's dilemma game (PDG) with players located on Barabási-Albert scale-free networks is studied. The impact of players' heterogeneous temporal activity pattern on the evolution of cooperation is investigated. To this end, the normal procedure that players update their strategies immediately after a round of game is discarded. Instead, players update strategies according to their assigned reproduction time, which follows a power-law distribution. We find that the temporal heterogeneity of players' activities facilitates the prosperity of cooperation, indicating the important role of hubs in the maintenance of cooperation on scale-free networks. When the reproduction time is assigned to individuals negatively related to their degrees, a fluctuation of the cooperation level with the increase of the exponent β is observed.
Transport ac loss of elliptical thin strips with a power-law E(J) relation
Jia, Chen-Xi; Chen, Du-Xing; Li, Shuo; Fang, Jin
2015-10-01
The transport ac loss Q of an elliptical thin strip of critical current I c with a power-law relation E\\propto {J}n is accurately computed as a function of current amplitude I m and frequency f. The resulting Q({I}m) is normalized to q({i}m) following the Norris critical-state formula, and converted to {q}*({i}m*) at a critical frequency f c based on a transport scaling law. Having a set of {q}*({i}m*) at several values of n as a base, a general expression of {q}*({i}m*,n) is obtained, which can be used to easily calculate q({i}m) for any practical purposes.
Power-law entropy-corrected new holographic dark energy in Horava-Lifshitz cosmology
Borah, Bharat; Ansari, M.
2014-12-01
Purpose of this paper is to study power-law entropy-corrected holographic dark energy (PLECHDE) in the frame work of Horava-Lifshitz cosmology with Granda-Oliveros (G-O) IR-cutoff. Considering interacting and non-interacting scenario of PLECHDE with dark matter in a spatially non-flat universe, we investigate the cosmological implications of this model in detail. We obtain equation of state parameter, deceleration parameter and the evolution of dark energy density to explain the expansion of the universe. We also find out these parameters for Ricci scale. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for law red-shifts.
Particle capture in axial magnetic filters with power law flow model
Abbasov, T; Koksal, M
1999-01-01
A theory of capture of magnetic particle carried by laminar flow of viscous non-Newtonian (power law) fluid in axially ordered filters is presented. The velocity profile of the fluid flow is determined by the Kuwabara-Happel cell model. For the trajectory of the particle, the capture area and the filter performance simple analytical expressions are obtained. These expressions are valid for particle capture processes from both Newtonian and non-Newtonian fluids. For this reason the obtained theoretical results make it possible to widen the application of high-gradient magnetic filtration (HGMF) to other industrial areas. For Newtonian fluids the theoretical results are shown to be in good agreement with the experimental ones reported in the literature. (author)
Critical Scaling of Extended Power Law Ⅰ-Ⅴ Isotherms near Vortex Glass Transition
Institute of Scientific and Technical Information of China (English)
HU Xiang; LI Chuan-Yi; YIN Dao-Le; HE Li; NING Zhen-Hua; CHEN Kai-Xuan; YIN Lan; LU Guo; XU Xiao-Lin; GUO Jian-Dong; WANG Fu-Ren
2006-01-01
In view of the question about the vortex glass theory of the freezing of disordered vortex matter raised by recent experimental observations, we reinvestigate the critical scaling of high Tc superconductors. It is found that the dc current-voltage characteristic of mixed state superconductors has a general form of extended power law which is based on the Ginzburg-Landau (GL) functional in the similar way as the vortex glass theory. Isotherms simulated from this nonlinear equation fit the experimental I- V data of Strachan et al. [Phys. Rev. Lett. 87 (2001) 067007].The puzzling question of the deriwtive plot for the I - V curves and the controversy surrounding the values of critical exponents are discussed.
Power-Law Behavior in Signal Scattering Process in Vertical Granular Chain with Light Impurities
Institute of Scientific and Technical Information of China (English)
XU Ai-Guo
2001-01-01
We investigate the scattering process of impulse in vertical granular chain with light impurities. When the perturbation is weak, the quantities describing the reflection rate exhibit power-law behavior with the impurity depth. The exponent is nearly independent of vi. When the perturbation is very strong, the vertical chain shows similar behavior to that of the horizontal chain, so the exponent is nearly zero. Our numerical investigation begins from the weak perturbation region and extends to the nonlinear region and found a peak of the exponent. The difficulty in extending the numerical investigation to a stronger perturbation region is analyzed.PACS numbers: 45.70.-n, 43.25.+y, 46.40.Cd
Mass transport in a thin layer of power-law fluid in an Eulerian coordinate system
Institute of Scientific and Technical Information of China (English)
刘洁; 白玉川
2016-01-01
The mass transport velocity in a thin layer of muddy fluid is studied theoretically. The mud motion is driven by a periodic pressure load on the free surface, and the mud is described by a power-law model. Based on the key assumptions of the shallowness and the small deformation, a perturbation analysis is conducted up to the second order to find the mean Eulerian velocity in an Eulerian coordinate system. The numerical iteration method is adopted to solve these non-linear equations of the leading order. From the numerical results, both the first-order flow fields and the second-order mass transport velocities are examined. The verifications are made by comparing the numerical results with experimental results in the literature, and a good agreement is confirmed.
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.
Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions
Directory of Open Access Journals (Sweden)
Giorgio Kaniadakis
2013-09-01
Full Text Available We present the main features of the mathematical theory generated by the √ κ-deformed exponential function expκ(x = ( 1 + κ2x2 + κx1/κ, with 0 ≤ κ < 1, developed in the last twelve years, which turns out to be a continuous one parameter deformation of the ordinary mathematics generated by the Euler exponential function. The κ-mathematics has its roots in special relativity and furnishes the theoretical foundations of the κ-statistical mechanics predicting power law tailed statistical distributions, which have been observed experimentally in many physical, natural and artificial systems. After introducing the κ-algebra, we present the associated κ-differential and κ-integral calculus. Then, we obtain the corresponding κ-exponential and κ-logarithm functions and give the κ-version of the main functions of the ordinary mathematics.
A comment on power-law inflation with a dark radiation component
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.
A comment on power-law inflation with a dark radiation component
Di Valentino, Eleonora
2016-01-01
Tram et al. 2016 recently pointed out that power-law inflation in presence of a dark radiation component may relieve the 3.3 sigma tension which exists within standard LCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) and the value derived from CMB anisotropy data by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the $\\sigma_8$ 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 are included in the analysis, the $H_0$ tension reappears and this scenario looses appeal.
Sudden expansion of a one-dimensional bose gas from power-law traps.
Campbell, A S; Gangardt, D M; Kheruntsyan, K V
2015-03-27
We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.
The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics
Sinha, S; Sinha, Sitabhra; Pan, Raj Kumar
2006-01-01
The nature of fluctuations in the Indian financial market is analyzed in this paper. We have looked at the price returns of individual stocks, with tick-by-tick data from the National Stock Exchange (NSE) and daily closing price data from both NSE and the Bombay Stock Exchange (BSE), the two largest exchanges in India. We find that the price returns in Indian markets follow a fat-tailed cumulative distribution, consistent with a power law having exponent $\\alpha \\sim 3$, similar to that observed in developed markets. However, the distributions of trading volume and the number of trades have a different nature than that seen in the New York Stock Exchange (NYSE). Further, the price movement of different stocks are highly correlated in Indian markets.
Biswas, Sunil Kumar; Ghosh, Amar Chandra Das; Bhattacharyya, Subrata; 10.4236/ojm.2012.21001
2012-01-01
Studies on `strange' particle production have always occupied a very important space in the domain of Particle Physics. This was and is so, just because of some conjectures about specially abundant or excess production of `strange' particles, at certain stages and under certain conditions arising out of what goes by the name of `Standard' model in Particle Physics. With the help of Hagedornian power laws we have attempted to understand and interpret here the nature of the $p_T$-spectra for the strange particle production in a few high energy nuclear collisions, some interesting ratio-behaviours and the characteristics of the nuclear modification factors that are measured in laboratory experiments. After obtaining and analysing the final results we do not confront any peculiarities or oddities or extraneous excesses in the properties of the relevant observables with no left-over problems or puzzles. The model(s) used by us work(s) quite well for explaining the measured data.
On energy boundary layer equations in power law non-Newtonian fluids
Institute of Scientific and Technical Information of China (English)
郑连存; 张欣欣
2008-01-01
The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.
Architectures engender crises: The emergence of power laws in social networks
Tohmé, Fernando; Larrosa, Juan M. C.
2016-05-01
Recent financial crises posed a number of questions. The most salient were related to the cogency of derivatives and other sophisticated hedging instruments. One claim is that all those instruments rely heavily on the assumption that events in the world are guided by normal distributions while, instead, all the evidence shows that they actually follow fat-tailed power laws. Our conjecture is that it is the very financial architecture that engenders extreme events. Not on purpose but just because of its complexity. That is, the system has an internal connection structure that is able to propagate and enhance initially small disturbances. The final outcome ends up not being correlated with its triggering event. To support this claim, we appeal to the intuition drawn from the behavior of social networks. Most of the interesting cases constitute scale-free structures. In particular, we contend, those that arise from strategic decisions of the agents.
Evolutionary implications of a power-law distribution of protein family sizes
Bader, J S
1999-01-01
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in a family can grow over time as genetic information is duplicated through evolution. We explore how evolution directs the size distribution of these families. Theoretical predictions for family sizes are obtained from two models, one in which individual genes duplicate and a second in which the entire genome duplicates. Predictions from these models are compared with the family size distributions for several organisms whose complete genome sequence is known. We find that protein family size distributions in nature follow a power-law distribution. Comparing these results to the model systems, we conclude that genome duplication is the dominant mechanism leading to increased genetic material in the species considered.
Deschanel, S.; Vanel, L.; Godin, N.; Vigier, G.; Ciliberto, S.
2009-01-01
We discuss the results of a series of experiments performed on heterogeneous materials where we have measured the acoustic emission (AE) signals preceding macroscopic failure that correspond to precursory rupture events. We mainly focus on polyurethane foams whose heterogeneities (pores) constitute arrest points for microcracks. The released AE energy is always power law distributed independently of the material porosity, the loading history (creep and tensile) and the mechanical properties (from brittle to ductile with increasing temperature). This is also the case for time intervals between events except in tensile tests when the material is brittle. We also highlight two key physical behaviors. The first is the occurrence of a unique behavior for a cumulative number of events and the cumulative energy in creep tests. The second is that the statistical properties are more influenced by the mechanical behavior than the microstructure of the material. Finally we discuss the problems which are still open for connecting these results with theoretical modeling of AE.
On the Power-Law Tails of Vote Distributions in Proportional Elections
Palombi, Filippo
2016-01-01
In proportional elections with open lists the excess of preferences received by candidates with respect to the list average is known to follow a universal lognormal distribution. We show that lognormality is broken provided preferences are conditioned to lists with many candidates. In this limit power-law tails emerge. We study the large-list limit in the framework of a quenched approximation of the word-of-mouth model introduced by Fortunato and Castellano (Phys.Rev.Lett.99(13):138701,2007), where the activism of the agents is mitigated and the noise of the agent-agent interactions is averaged out. Then we argue that our analysis applies mutatis mutandis to the original model as well.
Elastic-plastic growth of plane stress mode II cracks in power law hardening solids
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The asymptotic analysis of near tip field of plane stress mode II cracks growing quasi-statically in steadiness in power law hardening solids has been performed. Attention was focused on the behavior of the asymptotic solutions as hardening exponent n→∞. Analytical expressions of the dominant terms of velocities and flow factor in centered fan sectors were obtained by expanding them in series of the small parameter s=2/(n-1). Results show that, as n→∞, all the expressions of dominant terms of quantities in near tip field tend to their corresponding ones for elastic-perfectly plastic materials. The effect of hardening exponent n on the angular variations of stresses in near tip field is very weak. Analysis and discussion that related to plane stress mode I crack problem is given in appendix for comparison with results for mode II.
An optimized framework for degree distribution in LT codes based on power law
Institute of Scientific and Technical Information of China (English)
Asim; Muhammad; Choi; GoangSeog
2013-01-01
LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)k number of encoded symbols to recover the original information. The degree distribution function in the LT codes helps to generate a random graph also referred as tanner graph. The artifact of tanner graph is responsible for computational complexity and overhead in the LT codes. Intuitively, a well designed degree distribution can be used for an efficient implementation of LT codes. The degree distribution function is studied as a function of power law, and LT codes are classified into two different categories: SFLT and RLT codes. Also, two different degree distributions are proposed and analyzed for SFLT codes which guarantee optimal performance in terms of computational complexity and overhead.
Modified Anderson orthogonality catastrophe power law in the presence of shell structure
Bandopadhyay, Swarnali; Hentschel, Martina
2011-01-01
We study Anderson orthogonality catastrophe (AOC) for parabolic quantum dots and focus on the effects of degeneracies, realized through the inherent shell structure of their energy levels that can be lifted through an external magnetic field, on the Anderson overlap. We find rich and interesting behaviors as a function of the strength and position of the perturbation, the system size, and the applied magnetic field. In particular, even for weak perturbations, we observe a pronounced AOC that is related to the degeneracy of energy levels. Most importantly, the power-law decay of the Anderson overlap as a function of the number of particles is modified in comparison to the metallic case due to the rearrangement of the energy-level shell structure. We support our analytical results by numerical calculations and also study the distribution of Anderson overlaps.
Earthquake Size Distribution: Power-Law with Exponent Beta = 1/2 ?
Kagan, Yan Y
2009-01-01
We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are confirmed by recent investigations of the seismic moment distribution in global earthquake catalogs and by the results on the distribution in crystals of dislocation avalanche sizes. We consider possible systematic and random errors in determining earthquake size, especially its seismic moment. These effects increase the estimate of the parameter beta of the power-law distribution of earthquake sizes. In particular we find that the decrease in relative moment uncertainties with earthquake size causes inflation in the beta-value by about 1-3%. Moreover, earthquake clustering greatly influences the beta-parameter. If clusters (aftershock sequences) are taken as the entity to be studied, then the exponent value for their size distribution would decrease by 5-10%. The complexity ...
Anomalous Power Law Distribution of Total Lifetimes of Branching Processes Relevant to Earthquakes
Saichev, A
2004-01-01
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (``productivity'' or ``fertility''), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities $\\mu$ is characterized by a power law $\\sim 1/\\mu^{1+\\gamma}$ and the bare Omori law for the memory of previous triggering mothers decays slowly as $\\sim 1/t^{1+\\theta}$, with $0 < \\theta <1$ relevant for earthquakes. Using the tool of generating probability functions and a quasistatic approximation which is shown to be exact asymptotically for large durations, we show that the density distribution of to...
A Closed-Form Method for LRU Replacement under Generalized Power-Law Demand
Laoutaris, Nikolaos
2007-01-01
We consider the well known \\emph{Least Recently Used} (LRU) replacement algorithm and analyze it under the independent reference model and generalized power-law demand. For this extensive family of demand distributions we derive a closed-form expression for the per object steady-state hit ratio. To the best of our knowledge, this is the first analytic derivation of the per object hit ratio of LRU that can be obtained in constant time without requiring laborious numeric computations or simulation. Since most applications of replacement algorithms include (at least) some scenarios under i.i.d. requests, our method has substantial practical value, especially when having to analyze multiple caches, where existing numeric methods and simulation become too time consuming.
The flow of power law fluids in elastic networks and porous media
Sochi, Taha
2015-01-01
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 non-linearity 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...
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.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
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.
Supernova blast waves in wind-blown bubbles, turbulent, and power-law ambient media
Haid, S.; Walch, S.; Naab, T.; Seifried, D.; Mackey, J.; Gatto, A.
2016-08-01
Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media (densities of 0.1 ≥ n0 [cm- 3] ≥ 100) with uniform (and with stellar wind blown bubbles), power-law, and turbulent (Mach numbers M from 1to100) density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with n(r) ˜ r-2 (for n(r) > nfloor) the amount of momentum injection is solely regulated by the background density nfloor and compares to nuni = nfloor. However, in turbulent ambient media with lognormal density distributions the momentum input can increase by a factor of 2 (compared to the homogeneous case) for high Mach numbers. The average momentum boost can be approximated as p_{turb}/{p_{{0}}} =23.07 (n_{{0,turb}}/1 cm^{-3})^{-0.12} + 0.82 (ln (1+b2{M}2))^{1.49}(n_{{0,turb}}/1 cm^{-3})^{-1.6}. The velocity distributions are broad as gas can be accelerated to high velocities in low-density channels. The model values agree with results from recent, computationally expensive, three-dimensional simulations of SN explosions in turbulent media.
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
Directory of Open Access Journals (Sweden)
Sami El Boustani
2009-09-01
Full Text Available 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
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
Supernova-blast waves in wind-blown bubbles, turbulent, and power-law ambient media
Haid, S.; Walch, S.; Naab, T.; Seifried, D.; Mackey, J.; Gatto, A.
2016-05-01
Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media (densities of 0.1 ≥ n0 [cm-3 ≥ 100) with uniform (and with stellar wind blown bubbles), power-law, and turbulent (Mach numbers M from 1 - 100) density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with n(r) ˜ r-2 (for n(r) > nfloor) the amount of momentum injection is solely regulated by the background density nfloor and compares to nuni = nfloor. However, in turbulent ambient media with log-normal density distributions the momentum input can increase by a factor of 2 (compared to the homogeneous case) for high Mach numbers. The average momentum boost can be approximated as p_{_turb}/p_{0} =23.07 (n_{_{0,turb}}/1 cm^{-3})^{-0.12} + 0.82 (ln (1+b2M2))^{1.49}(n_{_{0,turb}}/1 cm^{-3})^{-1.6}. The velocity distributions are broad as gas can be accelerated to high velocities in low-density channels. The model values agree with results from recent, computationally expensive, three-dimensional simulations of SN explosions in turbulent media.
Saichev, A; Sornette, D
2004-10-01
We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes ("aftershocks"). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake ("productivity" or "fertility"), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities mu is characterized by a power law approximately 1/ mu(1+gamma) and the bare Omori law for the memory of previous triggering mothers decays slowly as approximately 1/ t(1+theta;) , with 0aftershock lifetimes scales as approximately 1/ t(1+theta;/gamma) when the average branching ratio is critical (n=1) . The coefficient 1aftershocks with mainshock magnitude m (productivity), with 0.5
From the Cover: Musical rhythm spectra from Bach to Joplin obey a 1/f power law
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.
Takahashi, Ryosuke; Okajima, Takaharu
2016-08-01
We investigated how stress relaxation mapping is quantified compared with the force modulation mapping of confluent epithelial cells using atomic force microscopy (AFM). Using a multi-frequency AFM technique, we estimated the power-law rheological behaviors of cells simultaneously in time and frequency domains. When the power-law exponent α was low ( 0.1), α in the time domain was underestimated relative to that in the frequency domain, and the difference increased with α, whereas the cell modulus was overestimated in the time domain. These results indicate that power-law rheological parameters estimated by stress relaxation are sensitive to lag time during initial indentation, which is inevitable in time-domain AFM experiments.
Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field
Zangeneh, M Kord; Sheykhi, A
2015-01-01
In this paper, we present a new class of higher dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserv...
Sensitivity of the power-law exponent in gene expression distribution to mRNA decay rate
International Nuclear Information System (INIS)
Large-scale acquisition technologies in mRNA abundance (gene expression) have provided new opportunities to better understand many complex biological processes. Lately, it has been reported that the observed gene expression data in several organisms significantly deviates from a Poisson distribution and follows a power-law or fat-tailed distribution. Here, we show that a simple stochastic model of gene expression with intrinsic and extrinsic noise derives the stationary power-law distribution using the Stratonovich calculus. Furthermore, we connect the experimental measure of the power-law exponent with the value of the mRNA decay. Finally, we compare the results with other models where stochastic equations were used within the Ito interpretation
Inglis, A R; Dominique, M
2014-01-01
The nature of quasi-periodic pulsations in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra, also referred to as 'red' noise processes, 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 QPP is needed. Here we adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power law properties of flare signals. Using data from the PROBA2/LYRA, Fermi/GBM, Nobeyama Radioheliograph and Yohkoh/HXT instruments, we study a selection of flares from the literature 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 in order to explain the observations. Instead, the flare signals are adequately descri...
Effect of buoyancy-assisted flow on convection from an isothermal spheroid in power-law fluids
Gupta, Anoop K.; Chhabra, Rajendra Prasad
2016-05-01
In this work, the coupled momentum and energy equations have been solved to elucidate the effect of aiding-buoyancy on the laminar mixed-convection from a spheroidal particle in power-law media over wide ranges of the pertinent parameters: Richardson number, 0≤ Ri≤5; Reynolds number, 1≤ Re≤100; Prandtl number, 1≤ Pr≤100; power-law index, 0.3≤ n≤1.8, and aspect ratio, 0.2≤ e≤5 for the case of constant thermo-physical properties. New results for the velocity and temperature fields are discussed in terms of the streamline and isotherm contours, surface pressure and vorticity contours, drag coefficient, local and surface averaged Nusselt number. The effect of particle shape on the flow is seen to be more pronounced in the case of oblates ( e 1). The propensity for wake formation reduces with the rising values of power-law index, Richardson number and slenderness of the body shape ( e > 1). Also, the drag coefficient is seen to increase with the Richardson number and power-law index. All else being equal, the Nusselt number shows a positive dependence on the Richardson number and Reynolds number and an inverse dependence on the power-law index and aspect ratio of the spheroid. Limited results were also obtained by considering the exponential temperature dependence of the power-law consistency index. This factor can increase the values of the average Nusselt number by up to ~10-12% with reference to the corresponding values for the case of the constant thermo-physical properties under otherwise identical conditions. Finally, the present values of the Nusselt number have been consolidated in the form of Colburn j-factor as a function of the modified Reynolds and Prandtl numbers for each value of the aspect ratio ( e). The effect of the temperature dependent viscosity is included in this correlation in terms of a multiplication factor.
Spectro-timing study of GX 339-4 in a hard intermediate state
Fuerst, F; Tomsick, J A; Bachetti, M; Boggs, S E; Brightman, M; Christensen, F E; Craig, W W; Gandhi, P; Grefenstette, B; Hailey, C J; Harrison, F A; Madsen, K K; Parker, M L; Pottschmidt, K; Stern, D; Walton, D J; Wilms, J; Zhang, W W
2016-01-01
We present an analysis of NuSTAR energy and power spectra of the transient accreting black hole GX 339-4 taken in January 2015. The observations took place during a hard intermediate state and the source softened significantly over the course of the 1.3 d-long observation. We perform time-resolved spectral analysis by splitting the data into 21 sub-sets and find that the energy 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 ~1.69 to ~1.77 over the course of the observation. We find that the best-fit model requires a harder power-law incident on the reflector than that observed as primary continuum. The accretion disk is truncated at around 9 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 changes in frequency from ~0.68 to ~1.05 Hz over the course of the observation. Th...
Discovery of Power-Law Growth in the Self-Renewal of Heterogeneous Glioma Stem Cell Populations.
Directory of Open Access Journals (Sweden)
Michiya Sugimori
Full Text Available Accumulating evidence indicates that cancer stem cells (CSCs drive tumorigenesis. This suggests that CSCs should make ideal therapeutic targets. However, because CSC populations in tumors appear heterogeneous, it remains unclear how CSCs might be effectively targeted. To investigate the mechanisms by which CSC populations maintain heterogeneity during self-renewal, we established a glioma sphere (GS forming model, to generate a population in which glioma stem cells (GSCs become enriched. We hypothesized, based on the clonal evolution concept, that with each passage in culture, heterogeneous clonal sublines of GSs are generated that progressively show increased proliferative ability.To test this hypothesis, we determined whether, with each passage, glioma neurosphere culture generated from four different glioma cell lines become progressively proliferative (i.e., enriched in large spheres. Rather than monitoring self-renewal, we measured heterogeneity based on neurosphere clone sizes (#cells/clone. Log-log plots of distributions of clone sizes yielded a good fit (r>0.90 to a straight line (log(% total clones = k*log(#cells/clone indicating that the system follows a power-law (y = xk with a specific degree exponent (k = -1.42. Repeated passaging of the total GS population showed that the same power-law was maintained over six passages (CV = -1.01 to -1.17. Surprisingly, passage of either isolated small or large subclones generated fully heterogeneous populations that retained the original power-law-dependent heterogeneity. The anti-GSC agent Temozolomide, which is well known as a standard therapy for glioblastoma multiforme (GBM, suppressed the self-renewal of clones, but it never disrupted the power-law behavior of a GS population.Although the data above did not support the stated hypothesis, they did strongly suggest a novel mechanism that underlies CSC heterogeneity. They indicate that power-law growth governs the self-renewal of heterogeneous
Mo, Jie-Xiong; Li, Gu-Qiang; Xu, Xiao-Bao
2016-04-01
The effects of a power-law Maxwell field on the critical phenomena of higher dimensional dilaton black holes are probed in detail. We successfully derive the analytic solutions of the critical point and carry out some checks to ensure that these critical quantities are positive. It is shown that the constraint on the parameter α describing the strength of the coupling of the electromagnetic field and the scalar field turns out to be 0 affected by the power-law Maxwell field. Moreover, critical exponents are found to coincide with those of other anti-de Sitter black holes, showing the powerful influence of mean field theory.
Du, Jiulin
2006-01-01
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established between the nonextensive paramet...
A simple marriage model for the power-law behaviour in the frequency distributions of family names
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.
Cusp-latitude Pc3 spectra: band-limited and power-law components
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P. V. Ponomarenko
Full Text Available This work attempts to fill a gap in comparative studies of upstream-generated Pc3–4 waves and broad band ULF noise observed at cusp latitudes. We performed a statistical analysis of the spectral properties of three years of cusp-latitude ground magnetometer data, finding that the average daytime Pc3–4 spectra are characterized by two principal components: an upstream-related band-limited enhancement (‘signal’ and a power-law background (‘noise’ with S(f a f ^{-4} . Based on this information we developed an algorithm allowing for the deconvolution of these two components in the spectral domain. The frequency of the signal enhancement increases linearly with IMF magnitude as f [mHz] ~ 4.4 | B_{IMF} | [nT], and its power maximizes around IMF cone angles q_{xB} ~ 20 and 160° and at 10:30–11:00 MLT. Both spectral components exhibit similar semiannual variations with equinoctial maxima. The back-ground noise power grows with increasing southward B_{z} and remains nearly constant for northward B_{z} . Its diurnal variation resembles that of Pc5 field-line resonance power, with a maximum near 09:00 MLT. Both the band-limited signal and broad band noise components show power-law growth with solar wind velocity a V ^{5.71}_{sw} and a V ^{4.12}_{sw}, respectively. Thus, the effective signal-to-noise ratio increases with in-creasing V_{sw}. The observations suggest that the noise generation is associated with reconnection processes.
Key words. Magnetospheric physics (magnetopause, cusp, and boundary layers; MHD waves and instabilities; solar wind magnetosphere interactions
Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Suvodip; Das, Santanu; Souradeep, Tarun [Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune-411007 (India); Joy, Minu, E-mail: suvodip@iucaa.ernet.in, E-mail: santanud@iucaa.ernet.in, E-mail: minujoy@gmail.com, E-mail: tarun@iucaa.ernet.in [Dept. of Physics, Alphonsa College, Pala, 686574 India (India)
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 independent 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.
Power-law modulation of the scalar power spectrum from a heavy field with a monomial potential
Huang, Qing-Guo
2016-01-01
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)~\\phi^n. In general the modulation is characterized by a power-law oscillation which is reduced to the logarithmic oscillation in the case of n=2.
EVIDENCE FOR DEPARTURE FROM A POWER-LAW FLARE SIZE DISTRIBUTION FOR A SMALL SOLAR ACTIVE REGION
International Nuclear Information System (INIS)
Active region 11029 was a small, highly flare-productive solar active region observed at a time of extremely low solar activity. The region produced only small flares: the largest of the >70 Geostationary Observational Environmental Satellite (GOES) events for the region has a peak 1-8 A flux of 2.2 x 10-6 W m-2 (GOES C2.2). The background-subtracted GOES peak-flux distribution suggests departure from power-law behavior above 10-6 W m-2, and a Bayesian model comparison strongly favors a power-law plus rollover model for the distribution over a simple power-law model. The departure from the power law is attributed to this small active region having a finite amount of energy. The rate of flaring in the region varies with time, becoming very high for 2 days coinciding with the onset of an increase in complexity of the photospheric magnetic field. The observed waiting-time distribution for events is consistent with a piecewise-constant Poisson model. These results present challenges for models of flare statistics and of energy balance in solar active regions.
Evidence for departure from a power-law flare size distribution for a small solar active region
Wheatland, M S
2010-01-01
Active region 11029 was a small, highly flare-productive solar active region observed at a time of extremely low solar activity. The region produced only small flares: the largest of the $>70$ Geostationary Observational Environmental Satellite (GOES) events for the region has a peak 1--$8{\\AA}$ flux of $2.2\\times 10^{-6} {\\rm W} {\\rm m}^{-2}$ (GOES C2.2). The background-subtracted GOES peak-flux distribution suggests departure from power-law behavior above $10^{-6} {\\rm W} {\\rm m}^{-2}$, and a Bayesian model comparison strongly favors a power-law plus rollover model for the distribution over a simple power-law model. The departure from the power law is attributed to this small active region having a finite amount of energy. The rate of flaring in the region varies with time, becoming very high for two days coinciding with the onset of an increase in complexity of the photospheric magnetic field. The observed waiting-time distribution for events is consistent with a piecewise-constant Poisson model. These res...
DEFF Research Database (Denmark)
Jørgensen, Bent; Demétrio, Clarice G.B.; Kristensen, Erik;
2011-01-01
Estimation of Taylor’s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating...
In-Degree and PageRank of web pages: why do they follow similar power laws?
Litvak, N.; Scheinhardt, W.R.W.; Volkovich, Y.V.
2009-01-01
PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is mo
International Nuclear Information System (INIS)
The power law suggests that the spin is varied with non integer spin more appropriately than other energy expressions. The PL gives the better fit of the energy because the RMSD is very smaller in comparison to SRF for Nd nuclei
Arata, Yukinobu; Takagi, Hiroaki; Sako, Yasushi; Sawa, Hitoshi
2014-01-01
Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and power law relationship is conserved in Xenopus and C. elegans, while the absolute powers in C. elegans were different from that in Xenopus. Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic C. elegans cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures.
Power-law creep of powder-metallurgy grade molybdenum sheet
Energy Technology Data Exchange (ETDEWEB)
Ciulik, J. [University of Texas at Austin, Mechanical Engineering Department, 1 University Station, C2200, Austin, TX 78712-0292 (United States)], E-mail: jciulik@mail.utexas.edu; Taleff, E.M. [University of Texas at Austin, Mechanical Engineering Department, 1 University Station, C2200, Austin, TX 78712-0292 (United States)
2007-08-15
Creep behavior of commercial-purity, powder-metallurgy grade molybdenum (Mo) sheet has been investigated at temperatures between 1300 and 1600 deg. C (0.56-0.63 T{sub m}) using tensile testing at controlled strain rates. Strain-rate-change tests were performed at constant-temperatures over true-strain rates from 1.0 x 10{sup -6} to 5.0 x 10{sup -4} s{sup -1}. Results agree with previously published data indicating that Mo follows power-law creep with a stress exponent of about 5; however, the present results address a temperature range not previously documented. The activation energy for creep was determined to be 240 kJ/mol within this temperature range, which is lower than previously published values and approximately half the value reported for self-diffusion, indicating that diffusion mechanisms faster than lattice diffusion are active. It is shown that Mo creep data from a variety of investigations converge closely to a single line on a master plot of strain rate normalized using an activation energy of 240 kJ/mol when plotted against stress normalized by the temperature-dependent elastic modulus. This activation energy for creep is attributed to an effective diffusivity that fits the creep data obtained during this study as well as from previously published creep data from commercial-purity molybdenum.
Power-law entropy-corrected Ricci dark energy and dynamics of scalar fields
Pasqua, Antonio; Jamil, Mubasher; Myrzakulov, Ratbay; Majeed, Bushra
2012-10-01
Motivated by the holographic principle, it has previously been suggested that the dark energy (DE) density can be inversely proportional to the area A of the event horizon of the Universe. However, this kind of model would have a casuality problem. In this work, we study the power-law entropy-corrected holographic DE (PLECHDE) model in the non-flat Friedmann-Robertson-Walker universe, with the future event horizon replaced by the average radius of the Ricci scalar curvature. We derive the equation of state parameter ωΛ, the deceleration parameter q and the evolution of energy density parameter ΩD‧ in the presence of interaction between DE and dark matter. We consider the correspondence between our Ricci-PLECHDE model and the modified Chaplygin gas and the tachyon, K-essence, dilaton and quintessence scalar fields. The potential and dynamics of the scalar field models have been reconstructed according to the evolutionary behaviour of the interacting entropy-corrected holographic DE model.
Power-Law Entropy Corrected Ricci Dark Energy and Dynamics of Scalar Fields
Pasqua, Antonio; Myrzakulov, Ratbay; Majeed, Bushra; 10.1088/0031-8949/86/04/045004
2012-01-01
Motivated by the holographic principle, it has been suggested that the Dark Energy (DE) density can be inversely proportional to the area $A$ of the event horizon of the universe. However, this kind of model would have a casuality problem. In this work, we study the power-law entropy corrected holographic DE (PLECHDE) model in the non-flat Friedmann-Robertson-Walker universe, with the future event horizon replaced by the average radius of the Ricci scalar curvature. We derive the equation of state parameter $\\omega_{\\Lambda}$, the deceleration parameter $q$ and the evolution of energy density parameter $\\Omega_D'$ in presence of interaction between DE and Dark Matter (DM). We consider the correspondence between our Ricci-PLECHDE model and the Modified Chaplygin Gas (MCG) and the tachyon, K-essence, dilaton and quintessence scalar fields. The potential and the dynamics of the scalar field models have been reconstructed according to the evolutionary behaviour of the interacting entropy-corrected holographic DE ...
Power-law entropy-corrected Ricci dark energy and dynamics of scalar fields
International Nuclear Information System (INIS)
Motivated by the holographic principle, it has previously been suggested that the dark energy (DE) density can be inversely proportional to the area A of the event horizon of the Universe. However, this kind of model would have a casuality problem. In this work, we study the power-law entropy-corrected holographic DE (PLECHDE) model in the non-flat Friedmann-Robertson-Walker universe, with the future event horizon replaced by the average radius of the Ricci scalar curvature. We derive the equation of state parameter ωΛ, the deceleration parameter q and the evolution of energy density parameter ΩD′ in the presence of interaction between DE and dark matter. We consider the correspondence between our Ricci-PLECHDE model and the modified Chaplygin gas and the tachyon, K-essence, dilaton and quintessence scalar fields. The potential and dynamics of the scalar field models have been reconstructed according to the evolutionary behaviour of the interacting entropy-corrected holographic DE model.
Robust Statistical Tests of Dragon-Kings beyond Power Law Distributions
Pisarenko, V F
2011-01-01
We ask the question whether it is possible to diagnose the existence of "Dragon-Kings" (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in Ger...
Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
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.
Adjustment to subtle time constraints and power law learning in rapid serial visual presentation
Directory of Open Access Journals (Sweden)
Jacqueline Chakyung Shin
2015-11-01
Full Text Available We investigated whether attention could be modulated through the implicit learning of temporal information in a rapid serial visual presentation (RSVP task. Participants identified two target letters among numeral distractors. The stimulus-onset asynchrony immediately following the first target (SOA1 varied at three levels (70, 98, and 126 ms randomly between trials or fixed within blocks of trials. Practice over three consecutive days resulted in a continuous improvement in the identification rate for both targets and attenuation of the attentional blink (AB, a decrement in target (T2 identification when presented 200-400 ms after another target (T1. Blocked SOA1s led to a faster rate of improvement in RSVP performance and more target order reversals relative to random SOA1s, suggesting that the implicit learning of SOA1 positively affected performance. The results also reveal power law learning curves for individual target identification as well as the reduction in the AB decrement. These learning curves reflect the spontaneous emergence of skill through subtle attentional modulations rather than general attentional distribution. Together, the results indicate that implicit temporal learning could improve high level and rapid cognitive processing and highlights the sensitivity and adaptability of the attentional system to subtle constraints in stimulus timing.
Two-dimensional magnetic cluster growth with a power-law interaction
Energy Technology Data Exchange (ETDEWEB)
Xu Xiaojun [Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310032 (China)], E-mail: xxj@zjut.edu.cn; Wu Yiqi [Wenzhou University Oujiang College, Wenzhou 325027 (China); Department of Physics, Zhejiang University, Hangzhou 310027 (China); Ye Gaoxiang [Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2008-03-30
A two-dimensional cluster model in which the morphology of clusters depends on power-law magnetic interactions that decay with distance r as a r{sup -{alpha}} law is introduced. The growth algorithm is a generalization of diffusion-limited aggregation (DLA) model. The particles with spin degree diffuse on a square lattice and each spin is allowed to flip under a Monte Carlo probability. The simulation shows that, for the antiferromagnetic coupling, the spins of the particles in clusters tend to be oriented alternately. For the ferromagnetic coupling, however, the spin distribution depends on the exponent {alpha}: for large value of {alpha}, domains with different sizes are observed in the clusters; while for small {alpha}, during the earlier stage of the growth process, the clusters exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the clusters, the spin states of all particles are similar. The magnetization and system energy of the clusters as well as their evolutions with the growth parameters are also studied in detail.
Two-dimensional magnetic cluster growth with a power law interaction
Xu, Xiaojun; Wu, Yiqi; Ye, Gaoxiang
2008-03-01
A two-dimensional cluster model in which the morphology of clusters depends on power-law magnetic interactions that decay with distance r as a r- α law is introduced. The growth algorithm is a generalization of diffusion-limited aggregation (DLA) model. The particles with spin degree diffuse on a square lattice and each spin is allowed to flip under a Monte Carlo probability. The simulation shows that, for the antiferromagnetic coupling, the spins of the particles in clusters tend to be oriented alternately. For the ferromagnetic coupling, however, the spin distribution depends on the exponent α: for large value of α, domains with different sizes are observed in the clusters; while for small α, during the earlier stage of the growth process, the clusters exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the clusters, the spin states of all particles are similar. The magnetization and system energy of the clusters as well as their evolutions with the growth parameters are also studied in detail.
Stochastic models with power-law tails the equation X = AX + B
Buraczewski, Dariusz; Mikosch, Thomas
2016-01-01
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the c...
HST Morphologies of z~2 Dust Obscured Galaxies I: Power-law Sources
Bussmann, R S; Lotz, J; Armus, L; Brand, K; Brown, M J I; Desai, V; Eisenhardt, P; Higdon, J; Higdon, S; Jannuzi, B T; Le Floc'h, E; Melbourne, J; Soifer, B T; Weedman, D
2008-01-01
We present high spatial resolution optical and near-infrared imaging obtained using the ACS, WFPC2 and NICMOS cameras aboard the Hubble Space Telescope of 31 24um--bright z~2 Dust Obscured Galaxies (DOGs) identified in the Bootes Field of the NOAO Deep Wide-Field Survey. Although this subset of DOGs have mid-IR spectral energy distributions dominated by a power-law component suggestive of an AGN, all but one of the galaxies are spatially extended and not dominated by an unresolved component at rest-frame UV or optical wavelengths. The observed V-H and I-H colors of the extended components are 0.2-3 magnitudes redder than normal star-forming galaxies. All but 1 have axial ratios >0.3, making it unlikely that DOGs are composed of an edge-on star-forming disk. We model the spatially extended component of the surface brightness distributions of the DOGs with a Sersic profile and find effective radii of 1-6 kpc. This sample of DOGs is smaller than most sub-millimeter galaxies (SMGs), but larger than quiescent high...
Transport ac loss in a rectangular thin strip with power-law E(J) relation
Energy Technology Data Exchange (ETDEWEB)
Li, Shuo [School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044 (China); Chen, Du-Xing, E-mail: chendx3008@hotmail.com [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); Fan, Yu; Fang, Jin [School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044 (China)
2015-01-15
Highlights: • Transport ac loss in a thin strip with power-law E(J) is systematically computed. • The scaled results can be accurately used for strips with any critical current and frequency. • Experiments may be unambiguously compared with modeling results at a critical frequency. - Abstract: Transport ac losses of a rectangular thin strip obeying relation E/E{sub c}=(J/J{sub c}){sup n} with a fixed critical current I{sub c} and n=5,10,20,30, and 40 are accurately computed at a fixed frequency f as functions of the current amplitude I{sub m}. The results may be interpolated and scaled to those at any values of I{sub c},f, and 5⩽n⩽40. Normalized in the same way as that in Norris’ analytical formula derived from the critical-state model and converting f to a critical frequency f{sub c}, the modeling results may be better compared with the Norris formula and experimental data. A complete set of calculated modeling data are given with necessary formulas to be easily used by experimentalists in any particular case.
Thermodynamics of charged rotating dilaton black branes with power-law Maxwell field
Energy Technology Data Exchange (ETDEWEB)
Zangeneh, M.K. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Sheykhi, A.; Dehghani, M.H. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O.Box 55134-441, Maragha (Iran, Islamic Republic of)
2015-10-15
In this paper, we construct a new class of charged rotating dilaton black brane solutions, with a complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime, such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both the canonical and the grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of the Maxwell field on the thermal stability of the solutions. We find that, for α ≤ 1, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For α > 1, the solutions can encounter an unstable phase depending on the metric parameters. (orig.)
Breakup characteristics of power-law liquid sheets formed by two impinging jets
Energy Technology Data Exchange (ETDEWEB)
Bai, Fuqiang; Diao, Hai; Chang, Qing; Wang, Endong; Du, Qing [State Key Laboratory of Engines, Tianjin University, Tianjin, 300072, People’s Republic of China (China); Zhang, Mengzheng, E-mail: duqing@tju.edu.cn [Xi’an Aerospace Propulsion Institute, Xi’an, 710100, People’s Republic of China (China)
2014-10-01
The breakup characteristics of the shear-thinning power-law liquid sheets formed by two impinging jets have been investigated with the shadowgraph technique. This paper focuses on the effects of spray parameters (jet velocity), physical parameters (viscosity) and geometry parameters (impinging angle and nozzle cross-sectional shape) on the breakup behaviors of liquid sheets. The breakup mode, sheet length and expansion angle of the sheet are extracted from the spray images obtained by a high speed camera. Impinging angle and Weber number play the similar roles in promoting the breakup of liquid sheets. With the increase of jet velocity, five different breakup modes are observed and the expansion angle increases consistently after the closed-rim mode while the sheet length first increases and then decreases. But there exists a concave consisting of a fierce drop and a second rising process on the sheet length curve for the fluid with smaller viscosity. Different nozzle cross-sectional shapes emphasize significant effects on the sheet length and expansion angle of liquid sheets. At a fixed Weber number, the liquid sheet with greater viscosity has a greater sheet length and a smaller expansion angle due to the damping effect of viscosity. (papers)
Common origin of power-law tails in income distributions and relativistic gases
Modanese, G.
2016-01-01
Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms ("saving propensity") which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the macroscopic distribution for the income or respectively for the energy.
Common Origin of Power-law Tails in Income Distributions and Relativistic Gases
Modanese, G
2016-01-01
Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms ("saving propensity") which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the m...
Directory of Open Access Journals (Sweden)
Tamás Sándor Biró
2014-12-01
Full Text Available Certain fluctuations in particle number, \\(n\\, at fixed total energy, \\(E\\, lead exactly to a cut-power law distribution in the one-particle energy, \\(\\omega\\, via the induced fluctuations in the phase-space volume ratio, \\(\\Omega_n(E-\\omega/\\Omega_n(E=(1-\\omega/E^n\\. The only parameters are \\(1/T=\\langle \\beta \\rangle=\\langle n \\rangle/E\\ and \\(q=1-1/\\langle n \\rangle + \\Delta n^2/\\langle n \\rangle^2\\. For the binomial distribution of \\(n\\ one obtains \\(q=1-1/k\\, for the negative binomial \\(q=1+1/(k+1\\. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion \\(\\omega \\ll E\\. For general systems the average phase-space volume ratio \\(\\langle e^{S(E-\\omega}/e^{S(E}\\rangle\\ to second order delivers \\(q=1-1/C+\\Delta \\beta^2/\\langle \\beta \\rangle^2\\ with \\(\\beta=S^{\\prime}(E\\ and \\(C=dE/dT\\ heat capacity. However, \\(q \
Study of the Power-Law Fluctuations in the Email Size
Matsubara, Yoshitsugu
2016-01-01
In a previous study, we investigated the frequency distribution of the email size in the system log data of the main email server for the staff on a campus network. We found that the frequencies of email sizes followed a power-law distribution and discovered two inflection points in the distribution. After analyzing these results, we collected new system log data for both staff and students for the period from April 1, 2009 to March 31, 2015 and analyzed the frequency distributions per academic year. The results of the earlier investigation were replicated for each of these distributions. Then, we disaggregated the system log data for the staff for the period from May 1, 2015 to July 31, 2015 using the email header "Content-Type" and created four subdistributions. Frequency distributions were calculated for the disaggregated data. We then proposed and evaluated a model to explain the overall frequency distribution as a sum of the four subdistributions. The correlation coefficient between the observed frequenc...
Analysis of log-periodic power law singularity patterns in time series related to credit risk
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.
Can log-periodic power law structures arise from random fluctuations?
Wosnitza, Jan Henrik; Leker, Jens
2014-05-01
Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable LPPL structures. To this end, we first estimate the stochastic process underlying the DAX log-returns during the period from mid-1997 until end-2003. The employed data set contains about 3.93ṡ106 intraday DAX quotes at a sampling rate of 15 s. Our results indicate that the DAX log-returns can be described as a Markov process. As a consequence, a Langevin equation is derived. Based on this model equation, we run extensive simulations in order to generate 100 synthetic DAX trajectories each covering 3000 trading days. We find LPPL behavior in ten artificial time series. Moreover, we can establish a link between LPPL patterns and ensuing bubble bursts in seven synthetic 600-week windows. However, the LPPL components in most synthetic trajectories differ fundamentally from those LPPL structures that have previously been detected in real financial time series. Summarized, this paper demonstrates that LPPL structures are not necessarily the signature of imitative behavior among investors but can also stem from noise, even though the likelihood of this is extremely low. Thus, our findings confirm with high statistical confidence that the LPPL structures in the DAX development are rooted deeper than only in the random fluctuations of the German stock market.
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.
Two Power-Law States of the Ultraluminous X-ray Source IC342 X-1
Yoshida, Tessei; Mineshige, Shin; Kubota, Aya; Mizuno, Tsunefumi; Saitou, Kei
2012-01-01
In order to elucidate the emission properties of ultraluminous X-ray sources (ULXs) during their power-law (PL) state, we examined long-term X-ray spectral data of IC342 X-1 during its PL state by using our own Suzaku data and the archival data by XMM-Newton, Chandra, and Swift observations. The PL state of this source seems to be classified into two sub-states in terms of the X-ray luminosities in 0.5-10 keV: the low luminosity PL state with 4-6*10^{39} erg/s and the high luminosity one with 1.1-1.4*10^{40} erg/s. During the Suzaku observations which were made in 2010 August and 2011 March, X-1 stayed in the low luminosity PL state. The observed X-ray luminosity (4.9-5.6*10^{39} erg/s) and the spectral shape (photon index = 1.67-1.83) slightly changed between the two observations. Using the Suzaku PIN detector, we for the first time confirmed a PL tail extending up to at least 20 keV with no signatures of a high-energy turnover in both of the Suzaku observations. In contrast, a turnover at about 6 keV was ob...
A unified econophysics explanation for the power-law exponents of stock market activity
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.
Friction losses in valves and fittings for power-law fluids
Directory of Open Access Journals (Sweden)
Polizelli M.A.
2003-01-01
Full Text Available Data on pressure drop were obtained in stainless steel, sanitary fittings and valves during laminar and turbulent flow of aqueous solutions of sucrose and xanthan gum, which were selected as model fluids. The rheological properties of these solutions were determined and the power-law model provided the best fit for experimental data. Friction losses were measured in fully and partially open butterfly and plug valves, bends and unions. Values of loss coefficients (k f were calculated and correlated as a function of the generalized Reynolds number by the two-k method. The model adjustment was satisfactory and was better in the laminar flow range (0.976 < r² < 0.999 than in the turbulent flow range (0.774 < r² < 0.989. In order to test the adequacy of the results for predicting loss coefficients during flow of real fluids, experiments were conducted with coffee extract. Comparison between experimental and predicted loss coefficients showed very good agreement.
Electroosmotic Flow of Power-Law Fluids in a Cylindrical Microcapillary
Saidi, M. H.; Babaie, Ashkan; Sadeghi, Arman; Center of Excellence in Energy Conversion Team
2012-11-01
In biological applications where most fluids are considered to be non-Newtonian, Newtonian law of viscosity looks insufficient for describing the flow characteristics. In the present work, the electroosmotic flow of power-law fluids in a circular micro tube is investigated. The Poisson-Boltzmann equation for electrical potential is solved numerically in the complete form without using the Debye-Hückel approximation. The physical model includes the Joule heating and viscous dissipation effects. Once the momentum and energy equations are solved numerically, a parametric study is done to investigate the effects of different parameters such as flow behavior index, wall zeta potential and the Debye-Hückel parameter on thermal and hydrodynamic characteristics of the flow. Results show that based on the value of viscous dissipation and the Debye-Hückel parameter the non-Newtonian characteristics of the flow can lead to significant changes regarding to Newtonian behaviors. The provided results in this study would lead to accurate prediction of temperature of biofluids in Lab-on-a-chip devices which is vital for retaining samples in a healthy condition.
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids
Banik, Indranil
2013-01-01
We attempt to better understand the flow of marine ice sheets. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases - the presence or absence of contact with sidewalls. Most real-world situations fall somewhere between the two extreme cases considered. When sidewalls are absent, we obtain the equilibrium grounding line thickness using a simple computer model and have an analytic approximation. For shelves in contact with sidewalls, we obtain an asymptotic theory, valid for long shelves. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We determine when this is. We conducted experiments using a laboratory model for ice. This was a suspension of xanthan in water, at a concentration of 0.5% by mass. The lab model has $n \\approx 3.8$ (similar to that of ice). The experiments agreed extremely well with our theories for all relevant p...
Thermodynamics of charged rotating dilaton black branes with power-law Maxwell field
International Nuclear Information System (INIS)
In this paper, we construct a new class of charged rotating dilaton black brane solutions, with a complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime, such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both the canonical and the grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of the Maxwell field on the thermal stability of the solutions. We find that, for α ≤ 1, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For α > 1, the solutions can encounter an unstable phase depending on the metric parameters. (orig.)
Evidence for Power Law in the Spectrum of the Coronal Ly-alpha Line
Telloni, Daniele; Antonucci, Ester; Bruno, Roberto; D'Amicis, Raffaella
Long time series of the intensity of the hydrogen Lyα line revealed the existence of f-2 power spectra in the corona at low and mid latitudes and very close to the Sun, at 1.7 solar radii. These observations are performed with the UltraViolet Coronagraph Spectrometer (UVCS) on board the Solar and Heliospheric Observatory (SoHO). A preliminary analysis indicates that this scaling extends for more than a decade and terminates at higher frequencies with a flat spectrum indicating the presence of white-noise fluctuations. The frequency corresponding to the knee which separates these two different spectral regimes moves to lower and lower values for observations performed at higher and higher heliographic latitudes. Low-frequency power spectra with a f-2 dependence may be due rapid changes (jumps) in the time series. If these coherent structures are removed from the time series, hydrogen coronal intensity power spectra seem to show a power law following the f-1 scaling which would suggest that 1/f interplanetary noise originates in corona.
The self-similar laminar boundary layer of power law non-Newtonian fluids
International Nuclear Information System (INIS)
Many fluids of practical interest are non-Newtonian, which influences many aspects of their behaviour, particularly the structure and properties of the laminar boundary layer, that differs qualitatively and quantitatively from the classical solution of Prandtl. It is studied the problem for a power law rheology, that describes with fair accuracy the behaviour of many fluids in an important range of shear. Since this type of rheology depends on a single-dimensional parameter, the solution of the problem is self-similar and can be obtained by a generalization of the usual procedure for the case of Newtonian fluids. A phase-plane formalism is introduced and the solutions are obtained as a function of the rheological index. It is found that the boundary layer of a dilatant fluid is spatially localized, i.e. it ends abruptly at a finite distance from the wall; this is a consequence of the non-linear character of the vorticity diffusion of a non-Newtonian fluid. A very good analytical approximation is obtained for dilatant fluids
Navigation on Power-Law Small World Network with Incomplete Information
Institute of Scientific and Technical Information of China (English)
CHEN Jian-Zhen; ZHU Jian-Yang
2007-01-01
We investigate the navigation process on a variant of the Watts-Strogatz small-world network model with local information. In the network construction, each vertex of an N × N square lattice sends out a long-range link with probability p. The other end of the link falls on a randomly chosen vertex with probability proportional to r-α, where r is the lattice distance between the two vertices, and α ≥ 0. The average actual path length,i.e. the expected number of steps for passing messages between randomly chosen vertex pairs, is found to scale as a power-law function of the network size Nβ, except when α is close to a specific value αmin, which gives the highest efficiency of message navigation. For a finite network, the exponent β depends on both α and p, and αmin drops to zero at a critical value of p which depends on N. When the network size goes to infinity,β depends only on α, and αmin is equal to the network dimensionality.
DEFF Research Database (Denmark)
Tendulkar, Shriharsh P.; Bachetti, Matteo; Tomsick, J.;
2014-01-01
frequencies. The Lorentzian has a width of 2 Hz and a fractional rms of 25+/-3%. The hard power-law index, the high energy of the cutoff, and the level of variability all are consistent with properties expected for an accreting black hole in the hard state. While we cannot completely rule out the possibility...... of a low magnetic field neutron star, a black hole is more likely....
What if the power-law model did not apply for the prediction of very large rockfall events?
Rohmer, J.; Dewez, T.
2012-04-01
Extreme events are of primary importance for risk management in a variety of natural phenomena, and more particularly for landslides and rockfalls, because they might be associated with huge losses. Numerous research works have addressed this problem based on the same paradigm: if events exhibit the same statistical properties across a broad range of sizes, the probability of extreme events can be evaluated by extrapolating the frequency-size distribution. Considering landslides' areas or rockfalls' volumes, the frequency distribution has been found to be heavy-tailed and the well-known power law distribution has been proposed to model it. Yet, the vision of very large extreme event (catastrophic) frequency being an extrapolation of the power laws fitted on small and intermediate events has been challenged in various contexts, in particular by Sornette and co-authors, who proposed viewing such catastrophic events as "outliers" from the power-law model, i.e. they deviate by an abnormal large distance from the extrapolated prediction. In this study, we address such an issue considering a rockfall inventory, containing >8500 events spanning 8 orders of magnitudes of volume and collated from 2.5 years of high-accuracy repeated terrestrial laser scanning (TLS) surveys on a coastal chalk cliff in Normandy (France). This inventory contains a particularly large event of 70,949 m3 which occurred some time between February 1 and 7 April 2008. It is the second largest cliff failure reported in Normandy, and is larger than those collated in historical cliff failure inventories across various geological and geomorphological coastal settings. Is this event an outlier of the power-law volume-frequency distribution ? And if so, why? This largest event recorded appears to stand out of the rest of the sample. We use it to revisit the techniques to fit power-law distribution with robust techniques (robust weighted maximum likelihood estimator), rarely used in rockfall studies, and
Eracleous, M; Eracleous, Michael; Halpern, Jules P.
1998-01-01
We present the X-ray spectrum of the broad-line radio galaxy Pictor A as observed by ASCA in 1996. The main objective of the observation was to detect and study the profiles of the Fe~K$\\alpha$ lines. The motivation was the fact that the Balmer lines of this object show well-separated displaced peaks, suggesting an origin in an accretion disk. The 0.5-10 keV X-ray spectrum is described very well by a model consisting of a power law of photon index 1.77 modified by interstellar photoelectric absorption. We find evidence for neither a soft nor a hard (Compton reflection) excess. More importantly, we do not detect an Fe K-alpha line, in marked contrast with the spectra of typical Seyfert galaxies and other broad-line radio galaxies observed by ASCA. The 99%-confidence upper limit on the equivalent width of an unresolved line at a rest energy of 6.4 keV is 100 eV, while for a broad line (FWHM of approximately 60,000 km/s) the corresponding upper limit is 135 eV. We discuss several possible explanations for the we...
Bubble motion through a generalized power-law fluid flowing in a vertical tube.
Mukundakrishnan, Karthik; Eckmann, David M; Ayyaswamy, P S
2009-04-01
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
The origin of tablet boudinage: Results from experiments using power-law rock analogs
Zulauf, J.; Zulauf, G.; Kraus, R.; Gutiérrez-Alonso, G.; Zanella, F.
2011-10-01
We used power-law viscous plasticine ( n = ca. 7) as a rock analog to simulate boudinage of rocks undergoing dislocation creep and brittle fracture. A competent plasticine layer, oriented perpendicular to the main shortening direction, Z, underwent bulk pure flattening inside a less competent plasticine matrix. Computer tomographic analyses of the deformed samples revealed that boudinage results from an initial phase of viscous necking followed by tensile failure along the previously formed necks. The resulting boudins display a polygonal shape in plan-view and are referred to as 'tablet boudins' (in contrast to the square to rectangular shaped chocolate-tablet boudins). The ratio between the plan-view long and short axis, R, ranges from 1.2 to 2.6. The polygonal, non-isometric shape of the tablet boudins can be explained by the strong interaction of concentric and radial tensile fractures. With increasing layer thickness, Hi, the mean diameter of the boudin tablets, Wa, increases, while the number of boudins, N, decreases. Progressive finite strain results in a higher number of the boudins and a smaller mean diameter. The thickness of the boudins, Hf, is almost the same as the initial layer thickness, Hi, while the aspect ratio ( Wd = Wa / Hf) decreases with layer thickness and finite strain. The mean Wd values obtained from all experiments span from ca. 4 to ca. 11. Tablet boudins, described in the present paper, have yet not been described from natural outcrops. The reasons might be that pure flattening strain is not common in nature, and the characterization and evaluation of tablet boudins requires geometrical analysis in three dimensions, which is a difficult task when such structures occur in nature.
Directory of Open Access Journals (Sweden)
Anthony Papadopoulos
Full Text Available 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.
Power-law and logarithmic entropy-corrected Ricci viscous dark energy and dynamics of scalar fields
Pasqua, Antonio
2013-08-01
In this work, I consider the logarithmic-corrected and the power-law corrected versions of the holographic dark energy (HDE) model in the non-flat FRW universe filled with a viscous Dark Energy (DE) interacting with Dark Matter (DM). I propose to replace the infra-red cut-off with the inverse of the Ricci scalar curvature R. I obtain the equation of state (EoS) parameter ω Λ , the deceleration parameter q and the evolution of energy density parameter \\varOmegaD' in the presence of interaction between DE and DM for both corrections. I study the correspondence of the logarithmic entropy corrected Ricci Dark Dnergy (LECRDE) and power-law entropy corrected Ricci Dark Energy (PLECRDE) models with the the Modified Chaplygin Gas (MCG) and some scalar fields including tachyon, K-essence, dilaton and quintessence. I also make comparisons with previous results.
Power-Law and Logarithmic Entropy-Corrected Ricci Viscous Dark Energy and Dynamics of Scalar Fields
Pasqua, Antonio
2013-01-01
In this work, I consider the logarithmic-corrected and the power-law corrected versions of the holographic dark energy (HDE) model in the non-flat FRW universe filled with a viscous Dark Energy (DE) interacting with Dark Matter (DM). We propose to replace the infra-red cut-off with the inverse of the Ricci scalar curvature $R$. I obtain the equation of state (EoS) parameter $\\omega_{\\Lambda}$, the deceleration parameter $q$ and the evolution of energy density parameter $\\Omega_D'$ in the presence of interaction between DE and DM for both corrections. I study the correspondence of the logarithmic entropy corrected Ricci Dark Dnergy (LECRDE) and power-law entropy corrected Ricci Dark Energy (PLECRDE) models with the the Modified Chaplygin Gas (MCG) and some scalar fields including tachyon, K-essence, dilaton and quintessence. I also make comparisons with previous results.
Institute of Scientific and Technical Information of China (English)
唐立强; 李永东; 刘长海
2004-01-01
A mechanical model was established for mode Ⅱ interfacial crack static growing along an elastic-elastic power law creeping bimaterial interface. For two kinds of boundary conditions on crack faces, traction free and frictional contact, asymptotic solutions of the stress and strain near tip-crack were given. Results derived indicate that the stress and strain have the same singularity, there is not the oscillatory singularity in the field; the creep power-hardening index n and the ratio of Young' s module notably influence the cracktip field in region of elastic power law creeping material and n only influences distribution of stresses and strains in region of elastic material. When n is bigger, the creeping deformation is dominant and stress fields become steady, which does not change with n.Poisson ' s ratio does not affect the distributing of the crack- tip field.
A model for the non-universal power-law of the solar wind sub-ion scale magnetic spectrum
Passot, T
2015-01-01
A phenomenological turbulence model for kinetic Alfv\\'en waves in a magnetized collisionless plasma, able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere, is presented. Nonlocal interactions are retained, and critical balance, characteristic of a strong turbulence regime, establishes dynamically as the cascade proceeds. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically-balanced turbulence, whose exponent is in particular sensitive to the ratio between the Alfv\\'en wave period and the nonlinear timescale.
Energy Technology Data Exchange (ETDEWEB)
Takahashi, Ryosuke; Okajima, Takaharu, E-mail: okajima@ist.hokudai.ac.jp [Graduate School of Information Science and Technology, Hokkaido University, Kita-ku N14 W9, Sapporo 060-0814 (Japan)
2015-10-26
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 in 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.
A MODEL FOR THE NON-UNIVERSAL POWER LAW OF THE SOLAR WIND SUB-ION-SCALE MAGNETIC SPECTRUM
Energy Technology Data Exchange (ETDEWEB)
Passot, T.; Sulem, P. L., E-mail: passot@oca.eu, E-mail: sulem@oca.eu [Laboratoire Lagrange, Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, CS 34229, F-06304 Nice Cedex 4 (France)
2015-10-20
A phenomenological turbulence model for kinetic Alfvén waves in a magnetized collisionless plasma that is able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere is presented. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition from large-scale weak turbulence to smaller scale strong turbulence is captured and nonlocal interactions, relevant in the case of steep spectra, are accounted for.
International Nuclear Information System (INIS)
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*. 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 in 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
Michelitsch, Thomas; Riascos, Alejandro; Nowakowski, Andrzej F; Nicolleau, Franck C G A
2016-01-01
We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law matrix functions of the simple local Bornvon Karman Laplacian. The fractional Laplacian matrices are well defined on periodic and infinite lattices in $n=1,2,3,..$ dimensions. The present approach generalizes the central symmetric second differenceoperator (Born von Karman Laplacian) to its fractional central symmetric counterpart (Fractional Laplacian matrix).For non-integer powers of the Born von Karman Laplacian, the fractional Laplacian matrix is nondiagonal with nonzero matrix elements everywhere, corresponding to nonlocal behavior: For large lattices the matrix elements far from the diagonal expose power law asymptotics leading to continuum limit kernels of Riesz fractional derivative type. We present explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractio...
Control of Beam Halo-Chaos by Fraction Power-Law Function in Hackle Periodic-Focusing Channel
Institute of Scientific and Technical Information of China (English)
YU Hai-Jun; BAI Long; WENG Jia-Qiang; LUO Xiao-Shu; FANG Jin-Qing
2008-01-01
The Kapehinsky-Vladimirsky (K-V) beam through a hackle periodic-focusing magnetic field is studied using the particle-core model. The beam halo-chaos is found, and an idea of fraction power-law function controller is proposed based on the mechanism of halo formation and the strategy of controlling halo-chaos. The method is applied to the multi-particle simulation to control the halo. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively by using the fraction power-law function control method. At the same time, the radial particle density is uniform at the beam's center as long as the control method and appropriate parameter are chosen.
DEFF Research Database (Denmark)
Freltoft, T.; Kjems, Jørgen; Sinha, S. K.
1986-01-01
Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/cm3. Assuming power-law correlations between particles and a finite correlation length ξ......, the authors derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension df corresponding to the power-law correlation was 2.61±0.1 for all dry samples, and 2.......34±0.1 for the water-suspended samples. The intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system...
Institute of Scientific and Technical Information of China (English)
A H Bokhari; F D Zaman; K Fakhar; A H Kara
2011-01-01
@@ First,we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation.The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.%First, we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved Bows.
Suzaku observations of the hard X-ray spectrum of Vela Jr. (SNR RX J0852.0-4622)
Takeda, Sawako; Bamba, Aya; Terada, Yukikatsu; Tashiro, Makoto S.; Katsuda, Satoru; Yamazaki, Ryo; Ohira, Yutaka; Iwakiri, Wataru
2016-06-01
We report the results of Suzaku observations of the young supernova remnant, Vela Jr. (RX J0852.0-4622), which is known to emit synchrotron X-rays, as well as TeV gamma-rays. Utilizing 39 Suzaku mapping observation data from Vela Jr., a significant hard X-ray emission is detected with the hard X-ray detector (HXD) from the northwest TeV-emitting region. The X-ray spectrum is reproduced well by a single power-law model with a photon index of 3.15^{+1.18}_{-1.14} in the 12-22 keV band. Compiling this hard X-ray spectrum with the soft X-ray spectrum simultaneously observed with the X-ray imaging spectrometer (XIS) onboard Suzaku, we find that the wide-band X-ray spectrum in the 2-22 keV band is reproduced with a single power-law or concave broken power-law model, which are statistically consistent with each other. Whichever of the two models, single or broken power-law, is appropriate, clearly the spectrum has no roll-off structure. Applying this result to the method introduced in Yamazaki et al. (2014, Res. Astron. Astrophys., 14, 165), we find that a one-zone synchrotron model with electron spectrum having a power-law plus exponential cut-off may not be applicable to Vela Jr.
Wang, Zebin; Narsimhan, Ganesan
2006-08-01
A model for drainage of a power-law fluid through a Plateau border is proposed which accounts for the actual Plateau border geometry and interfacial mobility. The non-dimensionalized Navier-Stokes equations have been solved using finite element method to obtain the contours of velocity within the Plateau border cross section and average Plateau border velocity in terms of dimensionless inverse surface viscosity and power-law rheological parameters. The velocity coefficient, the correction for the average velocity through a Plateau border of actual geometry compared to that for a simplified circular geometry of the same area of cross section, was expressed as a function of dimensionless inverse surface viscosity and flow behavior index of the power-law fluid. The results of this improved model for Plateau border drainage were then incorporated in a previously developed foam drainage model [G. Narsimhan, J. Food Eng. 14 (1991) 139] to predict the evolution of liquid holdup profiles in a standing foam. Foam drainage was found to be slower for actual Plateau border cross section compared to circular geometry and faster for higher interfacial mobility and larger bubble size. Evolution of liquid holdup profiles in a standing foam formed by whipping and stabilized by 0.1% beta-lactoglobulin in the presence of xanthan gum when subjected to 16g and 45g centrifugal force fields was measured using magnetic resonance imaging for different xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Measured bubble size, surface shear viscosity of beta-lactoglobulin solutions and literature values of power-law parameters of xanthan gum solution were employed in the current model to predict the evolution of liquid holdup profile which compared well with the experimental data. Newtonian model for foam drainage for zero shear viscosity underpredicted drainage rates and did not agree with the experimental data. PMID
Cao, Shuo; Yao, Meng; Zhu, Zong-Hong
2016-01-01
We use 118 strong gravitational lenses observed by the SLACS, 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 $z \\sim 1$. Assuming power-law density profiles for the total mass density, $\\rho=\\rho_0(r/r_0)^{-\\alpha}$, and luminosity density, $\
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.
An Envelope Soliton in a Nonlinear Chain with the Power-Law Dependence of Long-Range Interaction
Institute of Scientific and Technical Information of China (English)
王登龙; 颜晓红; 唐翌
2003-01-01
We study the Fermi-Pasta-Ulam lattice model in the presence ora power-law dependence of long-range interaction by virtue of the method of multiple scales. Our results show that an envelope soliton still appears, but it is of different property for the group velocity compared with that of the soliton in the model when long-range interaction is absent.
Directory of Open Access Journals (Sweden)
Krishna Lal
1970-01-01
Full Text Available The motion of a power law fluid past a suddenly accelerated wall which moves with a constant velocity U (t parallel to the wall has been considered for the similarity analysis. Recently this problem has been discussed and two possible group of transformation have been used by T.Y. Na/sup 1/. In this paper the third possible transformation has been found. The variation of the wall velocity U (t with time, t, has been worked out.
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
Capillary force between a probe tip with a power-law profile and a surface or a nanoparticle
International Nuclear Information System (INIS)
This paper presents a method to exactly calculate the capillary bridge profile and capillary force between a probe tip with a power-law profile and a surface or nanoparticle at various humidities. The shape of the probe tip is denoted by a power-law profile including a shape index, which is a general extension of the usual parabolids. The accuracy of the usual circular approximation of the capillary bridge is investigated, and it is found that great deviations may occur for capillary bridges and capillary forces at nanoscales, especially for the probe tip with a small shape index. The proportion of the capillary pressure force and the surface tension force which constitute the capillary force is also considered. The results show that the surface tension force can even be dominant at nanoscales. The influences of various parameters, including the shape index, equivalent radius of the tip, relative humidity, contact angles and separation distances, on the capillary force between a probe tip with a power-law profile and a surface or nanoparticle are studied. The rupture distances of the liquid bridges at condensation equilibrium and constant volume conditions are also compared. (paper)
Power-law versus log-law in wall-bounded turbulence: A large-eddy simulation perspective
Cheng, W.
2014-01-29
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 Re θ 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.
Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field
Zangeneh, M. Kord; Dehghani, M. H.; Sheykhi, A.
2015-11-01
In this paper, we present a new class of higher-dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon.
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.
Beskardes, G. D.; Weiss, C. J.; Everett, M. E.
2013-12-01
Electromagnetic methods of geophysical exploration are a reflection of the spatio-temporal variability in ground conductivity, a macroscopic physical property that is a function of lithology, pore-scale surface chemistry, fracture networks, and the presence and distribution of fluids and partial melts. As such, the bulk electrical properties of some representative elementary volume within the subsurface derive from the macroscopic effect of charge buildup and current pathways across a range of length scales within. Quantifying this relationship between multiscale electrical properties and the observed geophysical data is a critical step toward meaningful geologic interpretation. Previously we presented evidence of near-surface electromagnetic data whose small scale fluctuations are both repeatable and fractally distributed -- an observation that supports the notion of a spatially hierarchical Earth. Bounded by the end member cases from homogenized isotropic and anisotropic media, we present numerical modeling results from textured and spatially-correlated, stochastic geologic media, demonstrating that the electromagnetic response is a power law distribution similar to that seen in the earlier observational data, rather than a smooth response polluted with Gaussian noise as is commonly assumed. Furthermore, we show that such power law behavior is dependent on correlation length within the medium and that the power law distribution of Earth conductivity can be estimated from that of the observed electromagnetic data.
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Dimitris Polychronopoulos
Full Text Available Conserved, ultraconserved and other classes of constrained elements (collectively referred as CNEs here, identified by comparative genomics in a wide variety of genomes, are non-randomly distributed across chromosomes. These elements are defined using various degrees of conservation between organisms and several thresholds of minimal length. We here investigate the chromosomal distribution of CNEs by studying the statistical properties of distances between consecutive CNEs. We find widespread power-law-like distributions, i.e. linearity in double logarithmic scale, in the inter-CNE distances, a feature which is connected with fractality and self-similarity. Given that CNEs are often found to be spatially associated with genes, especially with those that regulate developmental processes, we verify by appropriate gene masking that a power-law-like pattern emerges irrespectively of whether elements found close or inside genes are excluded or not. An evolutionary model is put forward for the understanding of these findings that includes segmental or whole genome duplication events and eliminations (loss of most of the duplicated CNEs. Simulations reproduce the main features of the observed size distributions. Power-law-like patterns in the genomic distributions of CNEs are in accordance with current knowledge about their evolutionary history in several genomes.