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
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...
A Hard X-Ray Power-Law Spectral Cutoff in Centaurus X-4
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 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...
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...
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.
The frequency distribution for several characteristics of a solar flare obeys a power law only above a certain threshold, below which there is an apparent loss of small scale events presumably caused by limited instrumental sensitivity and the corresponding event selection bias. It is also possible that this deviation in the power law can have a physical origin in the source. We propose two fitting models incorporating a power law distribution with a low count rate cutoff plus a noise component for the frequency distribution of the hard X-ray peak count rate of all solar flare samples obtained with HXRBS/SMM and BATSE/CGRO observations. Our new fitting method produces the same power-law index as previously developed methods, a low cutoff of the power-law function and its corresponding noise level, which is consistent with measurements of the actual noise level of the hard X-ray count rate. We found that the fitted low cutoff appears to be related to the noise level, i.e., flares are only recognized when their peak count rate is 3σ greater than noise. Therefore, the fitted low cutoff, which is smaller than the aforementioned threshold, might be attributed to selection bias, and probably not to the actual count rate cutoff in flares at smaller scales. Whether or not the actual low cutoff physically exists needs to be checked by future observations with increased sensitivities
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
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,...
Power laws in Ising nanostripes
The results of high accuracy density-matrix renormalization-group calculations for infinite Ising stripes of finite widths 100 ≤ L ≤ 400 are presented. It is shown that in the presence of the small external magnetic field the infinite system critical power laws can be observed for L of order hundreds nm. The single power law describes the field dependence of the magnetization or the longitudinal correlation length only on the infinite system critical isotherm independently of the value of L. The approximate power law which describes how the magnetization varies with a distance from the infinite system critical point for several directions in the plane (temperature, external field) is also studied. (author)
Waves in plasmas with power-law distributions
Full text: Most theoretical studies of waves in plasmas assume a Maxwellian velocity distribution. However, often plasmas have a power-law distribution, with an excess of superthermal particles. Observations of power-law distributions are common in space, and they are also observed in the laboratory. Such velocity distributions may be modelled by a generalized Lorentzian distribution, often called a kappa-distribution. For high-energy particles this family of distributions has a power-law form, the real-valued parameter kappa allowing for fitting to the actual distribution. While kappa tending to infinity yields the Maxwellian, a low value of kappa describes a strongly accelerated, hard spectrum. Thus a wide range of distributions is represented. In particular it should be noted that observations are often fitted by a distribution with a fairly low value of kappa. A plasma dispersion function for electrostatic waves, introduced by Summers and Thorne for distributions having integer kappa, was generalized to distributions with arbitrary real kappa by Mace and Hellberg, and expressed in terms of a hypergeometric function. This representation allows for ease of application to wave studies. In the limit of kappa tending to infinity, it reduces to the usual Z-function of Fried and Conte. We discuss recent studies of waves in kappa-distribution plasmas, emphasizing in particular the effects of the non-Maxwellian nature of low-kappa distributions. Both dispersion and damping/growth of waves may differ significantly from the behaviour found for Maxwellian plasmas, as observed both in space and laboratory plasmas. In addition to considering electron plasma waves, we describe applications to a laboratory study of electron-acoustic waves and to a satellite-based observation of a whistler instability, using a bi-Lorentzian distribution
Hong, B H; Lee, J W; Hong, Byoung Hee; Lee, Kyoung Eun; Lee, Jae Woo
2007-01-01
We consider the scaling behaviors for fluctuations of the number of Korean firms bankrupted in the period from August 1 2002 to October 28 2003. We observe a power law for the distribution of the number of the bankrupted firms. The Pareto exponent is close to unity. We also consider the daily increments of the number of firms bankrupted. The probability distribution of the daily increments for the firms bankrupted follows the Gaussian distribution in central part and has a fat tail. The tail parts of the probability distribution of the daily increments for the firms bankrupted follow a power law.
Hong, Byoung Hee; Lee, Kyoung Eun; Lee, Jae Woo
2007-01-01
We consider the scaling behaviors for fluctuations of the number of Korean firms bankrupted in the period from 1 August 2002 to 28 October 2003. We observe a power law for the distribution of the number of the bankrupted firms. The Pareto exponent is close to unity. We also consider the daily increments of the number of firms bankrupted. The probability distribution of the daily increments for the firms bankrupted follows the Gaussian distribution in central part and has a fat tail. The tail parts of the probability distribution of the daily increments for the firms bankrupted follow a power law.
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
Addition to the methodology of research into permanent teeth hardness
Gnjato Sanja
2010-01-01
Full Text Available This paper examines permanent teeth hardness (microhardness using the Vickers method. An original methodology was developed and adopted for preparing the experimental material, i.e. the cross sections into four characteristic locations on the tooth: corona dentis, cervix dentis, pars medialis radicis dentis and apex radicis dentis. A new 'hardness profile' was introduced, which connects hardness and location along the cross section of the tooth. Hardness was measured 664 times on experimental cross sections with total a average hardness of 73.17 HV according to Vickers and a standard deviation of 55.68 HV. The derived descriptive statistical indicators of tooth hardness were calculated for equivalent cross sections, individual teeth, teeth groups and tooth localizations. Two algorithms were developed for determining the rank of tooth hardness - one for estimating the rank of arithmetic mean of the hardness of the cross sections of the teeth, and the other for estimating the rank of hardness for individual teeth. .
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
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 inflation with electromagnetism
We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (Mn+1,g-hat, ϕ-hat) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in Ringström (2009) [11]) we focus on pairs of relatively scaled open sets UR0⊂U4R0 on an initial slice of (Mn+1,g-hat), and if we choose a set of perturbed data which on U4R0 is sufficiently close to that of (Mn+1,g-hat,ϕ-hat, A-hat = 0), then in the maximal globally hyperbolic spacetime development (Mn+1,g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from UR0 are future complete (just as in (Mn+1,g-hat)). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (Mn+1,g-hat, ϕ-hat, A-hat = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results
Power laws from linear neuronal cable theory
Pettersen, Klas H; Lindén, Henrik Anders; Tetzlaff, Tom;
2014-01-01
Power laws, that is, power spectral densities (PSDs) exhibiting [Formula: see text] behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been ...... channels. The significance of this finding goes beyond neuroscience as it demonstrates how [Formula: see text] power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation....... suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general...
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 Distributions in Two Community Currencies
Kichiji, N.; Nishibe, M.
2007-07-01
The purpose of this paper is to highlight certain newly discovered social phenomena that accord with Zipf's law, in addition to the famous natural and social phenomena including word frequencies, earthquake magnitude, city size, income1 etc. that are already known to follow it. These phenomena have recently been discovered within the transaction amount (payments or receipts) distributions within two different Community Currencies (CC) that had been initiated as social experiments. One is a local CC circulating in a specific geographical area, such as a town. The other is a virtual CC used among members who belong to a certain community of interest (COI) on the Internet. We conducted two empirical studies to estimate the economic vitalization effects they had on their respective local economies. The results we found were that the amount of transactions (payments and receipts) of the two CCs was distributed according to a power-law distribution with a unity rank exponent. In addition, we found differences between the two CCs with regard to the shapes of their distribution over a low-transaction range. The result may originate from the difference in methods of issuing CCs or in the magnitudes of the minimum-value unit; however, this result calls for further investigation.
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.
Hierarchical networks, power laws, and neuronal avalanches.
Friedman, Eric J; Landsberg, Adam S
2013-03-01
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws. PMID:23556972
Memory Constraints for Power-Law Series
Guo, Fangjian; Zhao, Zhi-Dan; Zhou, Tao
2015-01-01
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents $\\alpha$. By permuting the independently drawn samples from a power-law distribution, we present non-trivial bounds on the memory (1st-order autocorrelation) as a function of $\\alpha$, which are markedly different from the ordinary $\\pm 1$ bounds for Gaussian or uniform distributions. When $1 3$, the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the ratings of MovieLens and posts in Twitter, we also find that empirical power-law distributed data produced by human activities conform to such constraints.
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.
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...
Power law analysis of the human microbiome.
Ma, Zhanshan Sam
2015-11-01
Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs. PMID:26407082
Instabilities in power law gradient hardening materials
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 of grad...... gradient hardening are found to delay the onset of localization under plane strain tension, and significantly reduce strain gradients in the localized zone. For plane strain compression gradient hardening is found to increase the load-carrying capacity significantly.......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 of...
Zipf's law, power laws and maximum entropy
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. (paper)
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.
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.
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.
Variational principle for the Pareto power law.
Chakraborti, Anirban; Patriarca, Marco
2009-11-27
A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system. PMID:20366128
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.
The power-law reaction rate coefficient for barrierless reactions
Yin, Cangtao; Du, Jiulin
2014-01-01
The power-law reaction rate coefficient for the barrierless reactions is studied if the reactions take place in systems with power-law distributions, and a generalized rate formula for the barrierless reactions in Gorin model is derived. We show that due to barrierless, different from those for bimolecular and unimolcular reactions, the power-law rate coefficient for the barrierless reactions does not have the factor of power-law distribution function and thus it is not very strongly dependen...
Power Law Analysis of Financial Index Dynamics
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.
A universal power law for metallic glasses
We report a universal power law between bulk modulus and molar volume that holds for metallic glasses (MGs) and most polycrystalline metals, which demonstrates that the volumetric derivative of energy minima can be determined by the average atomic volume. Our findings reveal a characteristic size rang of the short-range order of 0.23–0.32 nm in MGs that is closest to that in face-centered cubic metals. More interestingly, the short-range order in noncrystalline and crystalline metals seem to be self-similar from a viewpoint of the compressibility
Influence of probiotic cultures addition on the properties of semi-hard ewe’s cheese
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.
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.
Long-term power-law fluctuation in Internet traffic
Tadaki, Shin-ichi
2006-01-01
Power-law fluctuation in observed Internet packet flow are discussed. The data is obtained by a multi router traffic grapher (MRTG) system for 9 months. The internet packet flow is analyzed using the detrended fluctuation analysis. By extracting the average daily trend, the data shows clear power-law fluctuations. The exponents of the fluctuation for the incoming and outgoing flow are almost unity. Internet traffic can be understood as a daily periodic flow with power-law fluctuations.
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...
Influence of probiotic cultures addition on the properties of semi-hard ewe’s cheese
Blaženka Kos; Marijana Blažić; Zalazar, Carlos A.; Susana Bernal; Carlos Meinardi; Bojan Matijević
2011-01-01
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 hu...
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. PMID:24822039
Power law scaling in synchronization of brain signals depends on cognitive load
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.
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...
Critical point calculation for binary mixtures of symmetric non-additive hard disks
W.T. Gózdz
2016-02-01
Full Text Available We have calculated the values of critical packing fractions for the mixtures of symmetric non-additive hard disks. An interesting feature of the model is the fact that the internal energy is zero and the phase transitions are entropically driven. A cluster algorithm for Monte Carlo simulations in a semigrand ensemble was used. The finite size scaling analysis was employed to compute the critical packing fractions for infinite systems with high accuracy for a range of non-additivity parameters wider than in the previous studies.
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.
Prevention of damage and 'residual risk' in nuclear power laws
The concept of prevention of damage within the framework of nuclear power laws includes averting danger for the protection of third parties and preventing risks for the partial protection of third parties with the proviso that still a desire to use the concept 'residual risk' in addition, it should be limited, on the grounds of what can be reasonably expected, to those risks which cannot be reduced any further by the government, i.e. to risks which the public in general and third parties ('actually') must accept. In the future, questions regarding safety systems should be taken into account exclusively withing the context of 'what is necessary for protection against damage in keeping with the latest developments in science and technology' and not at the discretion of the law in denying permission according to Article 7 Paragraph 2 Atomic Energy Law. (orig.)
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.
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.
Resurrecting power law inflation in the light of Planck results
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
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 ...
Power-law defect energy in a single-crystal gradient plasticity framework: a computational study
Bayerschen, E.; Böhlke, T.
2016-03-01
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.
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.
Evidence for power-law Griffiths singularities in a layered Heisenberg magnet
We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.
Evidence for power-law Griffiths singularities in a layered Heisenberg magnet
Hrahsheh, Fawaz; Barghathi, Hatem; Vojta, Thomas [Department of Physics, Missouri University of Science and Technology, Rolla MO 65409 (United States); Mohan, Priyanka; Narayanan, Rajesh, E-mail: vojtat@mst.edu [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India)
2011-01-01
We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.
Pascal (Yang Hui) triangles and power laws in the logistic map
Velarde, Carlos; Robledo, Alberto
2015-04-01
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic-band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.
Magnetic characterization of HSLA steel by power-law decay exponents of Barkhausen emission signal
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.
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...
Power-law distribution of family names in Japanese societies
Miyazima, Sasuke; Lee, Youngki; Nagamine, Tomomasa; Miyajima, Hiroaki
2000-04-01
We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total number of different family names in a society scales as a power law of the population, (ii) the total number of family names of the same size decreases as the size increases with a power law and (iii) the relation between size and rank of a family name also shows a power law. These scaling properties are found to be consistent for five different regional communities in Japan.
Helmholtz solitons in power-law optical materials
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
Power Laws and the Cosmic Ray Energy Spectrum
Hague, J. D.; Becker, B. R.; Gold, M.S.; Matthews, J. A. J.
2006-01-01
Two separate statistical tests are applied to the AGASA and preliminary Auger Cosmic Ray Energy spectra in an attempt to find deviation from a pure power-law. The first test is constructed from the probability distribution for the maximum event of a sample drawn from a power-law. The second employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. The AGASA data show no significant deviation ...
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
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.
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.
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.
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.
The power-law reaction rate coefficient for barrierless reactions
We study the power-law reaction rate coefficient for barrierless reactions, when the reactions take place in systems with power-law distributions, and derive a generalized rate formula for the barrierless reactions in the Gorin model. We show that, unlike those for bimolecular and unimolcular reactions, due to the lack of barriers, the power-law rate coefficient for barrierless reactions does not have a power-law function, and thus is not very strongly dependent on the ν-parameter. Four barrierless reactions are taken as application examples to calculate the new rate coefficients, which with larger fitting ν-parameters can be exactly in agreement with measurements in the experimental studies. (paper)
Power-law graphs robustness and forest fires
Leri, M. M.; Pavlov, Yu. L.
2013-01-01
We study the robustness of power-law random graphs to “random break- downs” and to “targeted attacks” by computer simulation. We also consider one of the aspects connected with forest fire 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...
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.
Testing power-law cross-correlations: Rescaled covariance test
Krištoufek, Ladislav
2013-01-01
Roč. 86, č. 10 (2013), 418-1-418-15. ISSN 1434-6028 R&D Projects: GA ČR GA402/09/0965 Institutional support: RVO:67985556 Keywords : power-law cross-correlations * testing * long-term memory Subject RIV: AH - Economics Impact factor: 1.463, year: 2013 http://library.utia.cas.cz/separaty/2013/E/kristoufek-testing power-law cross-correlations rescaled covariance test.pdf
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 ...
Thresholded Power law Size Distributions of Instabilities in Astrophysics
Aschwanden, Markus J.
2015-11-01
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 x0; (3) contamination by an event-unrelated background xb; and (4) truncation effects at the largest events due to a finite system size. These effects can be modeled in the 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 x0 > 0 is positive for a threshold effect, while x0 critical threshold x0. We apply the thresholded power law distribution function to terrestrial, solar (HXRBS, BATSE, RHESSI), and stellar flare (Kepler) data sets. We find that the thresholded power law model provides an adequate fit to most of the observed data. Major advantages of this model are the automated choice of the power law fitting range, diagnostics of background contamination, physical instability thresholds, instrumental detection thresholds, and finite system size limits. When testing self-organized criticality models that predict ideal power laws, we suggest including these natural truncation effects.
Demixing and confinement of non-additive hard-sphere mixtures in slit pores.
Almarza, N G; Martín, C; Lomba, E; Bores, C
2015-01-01
Using Monte Carlo simulation, we study the influence of geometric confinement on demixing for a series of symmetric non-additive hard spheres mixtures confined in slit pores. We consider both a wide range of positive non-additivities and a series of pore widths, ranging from the pure two dimensional limit to a large pore width where results are close to the bulk three dimensional case. Critical parameters are extracted by means of finite size analysis. As a general trend, we find that for this particular case in which demixing is induced by volume effects, the critical demixing densities (and pressures) increase due to confinement between neutral walls, following the expected behavior for phase equilibria of systems confined by pure repulsive walls: i.e., confinement generally enhances miscibility. However, a non-monotonous dependence of the critical pressure and density with pore size is found for small non-additivities. In this latter case, it turns out that an otherwise stable bulk mixture can be unexpectedly forced to demix by simple geometric confinement when the pore width decreases down to approximately one and a half molecular diameters. PMID:25573573
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
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
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.
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-diverging geometries are used as examples to illustrate the application of this method.
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 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 .
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.
Relaxation Dynamics of Non-Power-Law Fluids
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong
2013-12-01
The relaxation of non-Newtonian liquids with non-power-law rheology on partially wetted surfaces is rarely investigated. This study assesses the relaxation behavior of 14 partial wetting systems with non-power-law fluids by sessile drop method. These systems are two carboxymethylcellulose sodium solutions on two kinds of slides, cover glass, and silicon wafer surfaces; three polyethylene glycol (PEG400) + silica nanoparticle suspensions on polymethyl methacrylate and polystyrene surfaces. The dynamic contact angle and moving velocity of contact line relationship data for relaxation drops of the 14 tested systems demonstrate a power-law fluid-like behavior, and the equivalent power exponent for a certain fluid on different solid substrates are uniform. By analyzing the relationship between the equivalent power exponent and shear rate, it is proposed that a fluid regime with shear rates of a few tens of s controls relaxation dynamics.
The power laws of nanoscale forces in ambient conditions
Chiesa, Matteo; Santos, Sergio; Lai, Chia-Yun
Power laws are ubiquitous in the physical sciences and indispensable to qualitatively and quantitatively describe physical phenomena. A nanoscale force law that accurately describes the phenomena observed in ambient conditions at several nm or fractions of a nm above a surface however is still lacking. Here we report a power law derived from experimental data and describing the interaction between an atomic force microscope AFM tip modelled as a sphere and a surface in ambient conditions. By employing a graphite surface as a model system the resulting effective power is found to be a function of the tip radius and the distance. The data suggest a nano to mesoscale transition in the power law that results in relative agreement with the distance-dependencies predicted by the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only
Power-law 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
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.
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 ...
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.
Human learning: Power laws or multiple characteristic time scales?
Gottfried Mayer-Kress
2006-09-01
Full Text Available The central proposal of A. Newell and Rosenbloom (1981 was that the power law is the ubiquitous law of learning. This proposition is discussed in the context of the key factors that led to the acceptance of the power law as the function of learning. We then outline the principles of an epigenetic landscape framework for considering the role of the characteristic time scales of learning and an approach to system identification of the processes of performance dynamics. In this view, the change of performance over time is the product of a superposition of characteristic exponential time scales that reflect the influence of different processes. This theoretical approach can reproduce the traditional power law of practice within the experimental resolution of performance data sets - but we hypothesize that this function may prove to be a special and perhaps idealized case of learning.
Exponential and power laws in public procurement markets
Krištoufek, Ladislav; Skuhrovec, J.
2012-01-01
Roč. 99, č. 2 (2012), 28005-1-28005-6. ISSN 0295-5075 R&D Projects: GA ČR GA402/09/0965 Grant ostatní: GA UK(CZ) 118310; SVV(CZ) 265 504; GA TA ČR(CZ) TD010133 Institutional support: RVO:67985556 Keywords : Public procurement * Scaling * Power law Subject RIV: AH - Economics Impact factor: 2.260, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kristoufek-exponential and power laws in public procurement markets.pdf
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...
Resurrecting power law inflation in the light of Planck results
Unnikrishnan, Sanil; Sahni, Varun
2013-01-01
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 $f_{_{\\mathbf{NL}}}^{\\mathrm{equil}}$ are in excellent agreement with Planck results. Inflation, in this model,...
Dehydrogenation of Methylcyclohexane: Parametric Sensitivity of the Power Law Kinetics
Arthur A. Garforth; David L. Cresswell; Usman, Muhammad R.
2013-01-01
For heterogeneous catalytic reactions, the empirical power law model is a valuable tool that explains variation in the kinetic behavior with changes in operating conditions, and therefore aids in the development of an appropriate and robust kinetic model. In the present work, experiments are performed on 1.0 wt% Pt/Al2O3 catalyst over a wide range of experimental conditions and parametric sensitivity of the power law model to the kinetics of the dehydrogenation of methylcyclohexane is studied...
Power-law creep from discrete dislocation dynamics.
Keralavarma, Shyam M; Cagin, T; Arsenlis, A; Benzerga, A Amine
2012-12-28
We report two-dimensional discrete dislocation dynamics simulations of combined dislocation glide and climb leading to "power-law" creep in a model aluminum crystal. The approach fully accounts for matter transport due to vacancy diffusion and its coupling with dislocation motion. The existence of quasiequilibrium or jammed states under the applied creep stresses enables observations of diffusion and climb over time scales relevant to power-law creep. The predictions for the creep rates and stress exponents fall within experimental ranges, indicating that the underlying physics is well captured. PMID:23368581
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
Cota, Wesley; Ferreira, Silvio C.; Ódor, Géza
2016-03-01
We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space λ1Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at λ2. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at λc=0 . Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.
The collision theory reaction rate coefficient for power-law distributions
Yin, Cangtao; Du, Jiulin
2014-01-01
The collision theory for power-law distributions and a generalized collision theory rate coefficient is studied when the reactions take place in nonequilibrium systems with power-law distributions. We obtain the power-law rate coefficient and by numerical analyses we show a very strong dependence of the rate coefficient on the power-law parameter. We find that the power-law collision theory can successfully overcome the two difficulties of Lindemann-Christiansen mechanism. We take three react...
Power Laws and Gaussians for Stock Market Fluctuations
Caglar Tuncay; Dietrich Stauffer
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.
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 ...
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.
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
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
Relation between dark matter density and temperature with power law
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.
Back-reaction effect in power-law inflation
Bellini, Mauricio
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 $p$.
Lee, S.R.; Irvine, T.F. Jr. [State Univ. of New York, Stony Brook, NY (United States). Dept. of Mechanical Engineering; Greene, G.A. [Brookhaven National Lab., Upton, NY (United States). Dept. of Advanced Technology
1998-04-01
An implicit finite difference method was applied to analyze laminar natural convection in a vertical channel with a modified power law fluid. This fluid model was chosen because it describes the viscous properties of a pseudoplastic fluid over the entire shear rate range likely to be found in natural convection flows since it covers the shear rate range from Newtonian through transition to simple power law behavior. In addition, a dimensionless similarity parameter is identified which specifies in which of the three regions a particular system is operating. The results for the average channel velocity and average Nusselt number in the asymptotic Newtonian and power law regions are compared with numerical data in the literature. Also, graphical results are presented for the velocity and temperature fields and entrance lengths. The results of average channel velocity and Nusselt number are given in the three regions including developing and fully developed flows. As an example, a pseudoplastic fluid (carboxymethyl cellulose) was chosen to compare the different results of average channel velocity and Nusselt number between a modified power law fluid and the conventional power law model. The results show, depending upon the operating conditions, that if the correct model is not used, gross errors can result.
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.
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...
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
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.
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.
Value at Risk in the Presence of the Power Laws
The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of several long positions in risky assets. We consider the case when the tail parts of distributions of logarithmic returns of these assets follow the power law of the same degree and the lower tail of associated copula C follows the power law of degree 1. We provide the asymptotic formula for Value at Risk and determine the optimal portfolio. We show that the part of the capital invested in the i-th asset should be equal to the conditional probability that the drop of the value of the i-th asset will be smaller than the others under the condition that the value of the all assets will be smaller than c times their initial value (c <<1). (author)
Power-law cosmology, SN Ia, and BAO
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
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 photoluminescence decay in indirect gap quantum dots
Menšík, Miroslav; Král, Karel
2013-01-01
Roč. 111, November (2013), s. 170-174. ISSN 0167-9317 R&D Projects: GA MŠk(CZ) OC10007; GA MŠk LH12186; GA MŠk LH12236; GA ČR(CZ) GAP205/10/2280 Institutional support: RVO:61389013 ; RVO:68378271 Keywords : quantum dots * indirect gap transition * power -law photoluminescence decay Subject RIV: BM - Solid Matter Physics ; Magnetism; BE - Theoretical Physics (FZU-D) Impact factor: 1.338, year: 2013
Characterizing and predicting the robustness of power-law networks
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
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
Econophysical anchoring of unimodal power-law distributions
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. (paper)
Analysis of Indentation-Derived Power-Law Creep Response
Martinez, Nicholas J.; Shen, Yu-Lin
2016-03-01
The use of instrumented indentation to characterize power-law creep is studied by computational modeling. Systematic finite element analyses were conducted to examine how indentation creep tests can be employed to retrieve the steady-state creep parameters pertaining to regular uniaxial loading. The constant indentation load hold and constant indentation-strain-rate methods were considered, first using tin (Sn)-based materials as a model system. The simulated indentation-strain rate-creep stress relations were compared against the uniaxial counterparts serving as model input. It was found that the constant indentation-strain-rate method can help establish steady-state creep, and leads to a more uniform behavior than the constant-load hold method. An expanded parametric analysis was then performed using the constant indentation-strain-rate method, taking into account a wide range of possible power-law creep parameters. The indentation technique was found to give rise to accurate stress exponents, and a certain trend for the ratio between indentation strain rate and uniaxial strain rate was identified. A contour-map representation of the findings serves as practical guidance for determining the uniaxial power-law creep response based on the indentation technique.
Low alloyed steel bars were co-extruded with pre-sintered tool steel powders with the addition of tungsten carbides (W2C/WC) as hard particles. During the hot extrusion process of these massive and powdery materials, an extrudate is formed consisting of a completely densified wear resistant coating layer and a bulk steel bar as the tough substrate core. This work combines experimental measurements (EPMA) and diffusion calculations (DICTRATM) to investigate the effect of hard particle addition and its dissolution, as well as the formation of M6C carbides on the properties of two different PM tool steel coatings hot extruded with a 1.2714 steel bar. A carburization effect resulting from the W2C hard particles is responsible for an increase of the 1.2344 steel matrix hardness. The mechanical properties of the interface region between coating matrix and substrate are influenced by chemical interdiffusion of carbon and other alloying elements occurring during heat treatment.
Silva, P.A. [Max-Planck-Institut fuer Eisenforschung GmbH, MPIE, Max-Planck-Strasse 1, D-40237 Duesseldorf (Germany); Weber, S., E-mail: weber@wtech.rub.de [Institut fuer Werkstoffe, Ruhr-Universitaet Bochum, Universitaetsstrasse, D-44780 Bochum (Germany); Helmholtz-Zentrum Berlin, Glienicker Strasse 100, D-14109 Berlin (Germany); Inden, G. [Max-Planck-Institut fuer Eisenforschung GmbH, MPIE, Max-Planck-Strasse 1, D-40237 Duesseldorf (Germany); Pyzalla, A.R. [Helmholtz-Zentrum Berlin, Glienicker Strasse 100, D-14109 Berlin (Germany)
2009-08-15
Low alloyed steel bars were co-extruded with pre-sintered tool steel powders with the addition of tungsten carbides (W{sub 2}C/WC) as hard particles. During the hot extrusion process of these massive and powdery materials, an extrudate is formed consisting of a completely densified wear resistant coating layer and a bulk steel bar as the tough substrate core. This work combines experimental measurements (EPMA) and diffusion calculations (DICTRA{sup TM}) to investigate the effect of hard particle addition and its dissolution, as well as the formation of M{sub 6}C carbides on the properties of two different PM tool steel coatings hot extruded with a 1.2714 steel bar. A carburization effect resulting from the W{sub 2}C hard particles is responsible for an increase of the 1.2344 steel matrix hardness. The mechanical properties of the interface region between coating matrix and substrate are influenced by chemical interdiffusion of carbon and other alloying elements occurring during heat treatment.
Stewart, Michael; Morgenstern, Uwe
2013-04-01
Understanding runoff generation is important for management of freshwater systems. Determining transit time distributions of streamwaters and how they change with discharge gives information on the flowpaths and recharge sources of streams - vital information for determining the responses of streams to stressors such as pollution, landuse change, or climate change. This work takes a first look at unique information on how transit time distributions change with discharge in some New Zealand catchments. Transit time distributions of streamwaters have been determined from tritium measurements on single samples in this work. This allows changes with stream discharge to be observed, in contrast to previous isotope studies which have given averaged transit time distributions based on series of samples. In addition, tritium reveals the wide spectrum of ages present in streams whereas oxygen-18 or chloride variations only show the younger ages (Stewart et al., 2010). It was found that the mean transit time (MTT) data could be reasonably represented by straight lines in log-log plots, indicating power law relationships between MTT and discharge. Similar power law behaviour has been observed for the rock forming elements such as silica in streamwaters (Godsey et al., 2009). Case studies are presented for two New Zealand catchments, both with volcanic ash substrates. Toenepi is a dairy catchment near Hamilton, which shows well-constrained power law relationships between MTT and discharge, and between silica concentration and discharge (Morgenstern et al., 2010). Baseflow MTTs vary from 2.5 to 157 years. Tutaeuaua is a pastoral farming catchment near Taupo. Results for nested catchments along the stream also show power law relationships for both MTT and silica with discharge. Streamwater MTTs vary from 1 to 11 years. The results indicate that (1) relatively old waters dominate many streams, (2) streamwater ages vary with discharge, and (3) age, like silica, varies according to
Scaling, dimensional analysis, and hardness measurements
Cheng, Yang-Tse; Cheng, Che-Min; Li, Zhiyong
2000-03-01
Hardness is one of the frequently used concepts in tribology. For nearly one hundred years, indentation experiments have been performed to obtain the hardness of materials. Recent years have seen significant improvements in indentation equipment and a growing need to measure the mechanical properties of materials on small scales. However, questions remain, including what properties can be measured using instrumented indention techniques and what is hardness? We discuss these basic questions using dimensional analysis together with finite element calculations. We derive scaling relationships for loading and unloading curve, initial unloading slope, contact depth, and hardness. Hardness is shown to depend on elastic, as well as plastic properties of materials. The conditions for "piling-up" and "sinking-in" of surface profiles in indentation are obtained. The methods for estimating contact area are examined. The work done during indentation is also studied. A relationship between hardness, elastic modulus, and the work of indentation is revealed. This relationship offers a new method for obtaining hardness and elastic modulus. In addition, we demonstrate that stress-strain relationships may not be uniquely determined from loading/unloading curves alone using a conical or pyramidal indenter. The dependence of hardness on indenter geometry is also studied. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and "indentation size effect" is established.
The power-law reaction rate coefficient for an elementary bimolecular reaction
Yin, Cangtao; Du, Jiulin
2013-01-01
The power-law TST reaction rate coefficient for an elementary bimolecular reaction is studied when the reaction takes place in a nonequilibrium system with power-law distributions. We derive a generalized TST rate coefficient, which not only depends on a power-law parameter but also on the reaction coordinate frequency of transition state. The numerical analyses show a very strong dependence of TST rate coefficient on the power-law parameter, and clearly indicate that a tiny deviation from un...
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
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.
Langevin equation for a free particle driven by power law type of noises
We study a generalized Langevin equation for a free particle driven by N internal noises. The mean square displacement and velocity autocorrelation function are derived in case of a mixture of Dirac delta, power law and Mittag-Leffler noises. Additionally, a frictional memory kernel of distributed order is considered. The long time limit and short time limit are analyzed, and the dominant contributions of noises on particle dynamics is discussed. Various different diffusive behaviors (subdiffusion, superdiffusion, normal diffusion, ultraslow diffusion) are obtained. The considered problem may be used in the theory of anomalous diffusion in complex environment.
Properties of hard alloys on the basis of WC-Co with the additives of nanodisperse TiN
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)
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
Failure analysis on China power grid based on power law
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.
Shannon Information and Power Law Analysis of the Chromosome Code
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.
Power-Law Persistence in the Atmosphere: Analysis and Applications
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 g...
Comment on "Observational constraints on power-law cosmologies"
Meetu, S; Daksh, L; Meetu, Sethi; Annu, Batra; Daksh, Lohiya
1999-01-01
"Power Law Cosmologies" are defined by their growth of the cosmological scale factor as $ t^\\alpha$ regardless of the matter content or cosmological epoch. Constraints from the current age of the Universe and from the high redshift supernovae data require ``large'' $\\alpha$ ($\\approx 1$). We reinforce this by latest available observations. Such a large $\\alpha$ is also consistent with the right amount of helium and the lowest observed metallicity in the universe for a model with the baryon entropy ratio $\\approx 8.1\\times 10^{-9}$.
Power-Law Tail in the Chinese Wealth Distribution
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.
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.
Approximability of the Vertex Cover Problem in Power Law Graphs
Gast, Mikael
2012-01-01
In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2-f(beta) for random Power Law Graphs (PLG) in the (alpha,beta)-model of Aiello et. al., where f(beta) is a strictly positive function of the parameter beta. We obtain this result by combining the Nemhauser and Trotter approach for Min-VC with a new deterministic rounding procedure which achieves an approximation ratio of 3/2 on a subset of low degree vertices for which the expected contribution to the cost of the associated linear program is sufficiently large.
Effects of Sorghum Flour Addition on Chemical and Rheological Properties of Hard White Winter Wheat
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
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...
Power Law Distributions of Patents as Indicators of Innovation
O'Neale, Dion; Hendy, Shaun
2013-03-01
The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Such figures however give an overly simplistic measure of innovation within a country. Here we present evidence that the distribution of patents amongst applicants within many countries is well-fitted to a power law distribution with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.
Power law distributions of patents as indicators of innovation.
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.
An inverse method for rheometry of power-law fluids
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
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.
Effect of yttrium additions on the tensile properties and hardness of an iron-nickel-chromium alloy
Results of the research work show that the addition of 0.1% yttrium does not significantly change the mechanical properties of the AL1 alloy with temperature (even though the yttrium-doped samples did show a slight increase in yield stress and hardness for tests above 7000C); the room temperature strength of the undoped AL1 alloy increases upon annealing at temperatures above 6000C; and the room temperature uniform and fracture strains of the undoped AL1 alloy decrease upon annealing at temperatures above 6000C
Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant
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.
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.
Bubble coalescence in a power-law fluid
Kamat, Pritish; Thete, Sumeet; Basaran, Osman
2015-11-01
As two spherical gas bubbles in a liquid are slowly brought together, the liquid film or sheet between them drains and ultimately ruptures, forming a circular hole that connects them. The high curvature near the edge of the liquid sheet drives flow radially outward, causing the film to retract and the radius of the hole to increase with time. Recent experimental and theoretical work in this area has uncovered self-similarity and universal scaling regimes when two bubbles coalesce in a Newtonian fluid. Motivated by applications such as polymer and composites processing, food and drug manufacture, and aeration/deaeration systems where the liquids often exhibit deformation-rate thinning rheology, we extend the recent Newtonian studies to bubble coalescence in power-law fluids. In our work, we use a combination of thin-film theory and full 3D, axisymmetric computations to probe the dynamics in the aftermath of the singularity.
Power laws and extreme values in antibody repertoires
Boyer, Sebastien; Biswas, Dipanwita; Scaramozzino, Natale; Kumar, Ananda Soshee; Nizak, Clément; Rivoire, Olivier
2015-03-01
Evolution by natural selection involves the succession of three steps: mutations, selection and proliferation. We are interested in describing and characterizing the result of selection over a population of many variants. After selection, this population will be dominated by the few best variants, with highest propensity to be selected, or highest ``selectivity.'' We ask the following question: how is the selectivity of the best variants distributed in the population? Extreme value theory, which characterizes the extreme tail of probability distributions in terms of a few universality class, has been proposed to describe it. To test this proposition and identify the relevant universality class, we performed quantitative in vitro experimental selections of libraries of >105 antibodies using the technique of phage display. Data obtained by high-throughput sequencing allows us to fit the selectivity distribution over more than two decades. In most experiments, the results show a striking power law for the selectivity distribution of the top antibodies, consistent with extreme value theory.
Bose-Einstein condensation in dark power-law laser traps
Jaouadi, A.; Gaaloul, N.; Viaris de Lesegno, B.; Telmini, M.; Pruvost, L.; Charron, E.
2010-08-01
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.
Bose-Einstein condensation in dark power-law laser traps
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.
Fractal Analysis of Power-Law Fluid in a Single Capillary
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.
Non-equilibrium thermodynamics of dark energy on the power-law entropy corrected apparent horizon
Farooq, M. Umar; Jamil, Mubasher(School of Natural Sciences (SNS), National University of Science and Technology (NUST), H-12, Islamabad, Pakistan)
2011-01-01
We investigate the Friedmann-Robertson-Walker (FRW) universe (containing dark energy) as a non-equilibrium (irreversible) thermodynamical system by considering the power-law correction to the horizon entropy. By taking power-law entropy area law which appear in dealing with the entanglement of quantum fields in and out the horizon, we determine the power-law entropy corrected apparent horizon of the FRW universe.
Furusawa, Chikara; Kaneko, Kunihiko
2005-01-01
The evolutionary origin of universal statistics in biochemical reaction network is studied, to explain the power-law distribution of reaction links and the power-law distributions of chemical abundances. Using cell models with catalytic reaction network, we find evidence that the power-law distribution in abundances of chemicals emerges by the selection of cells with higher growth speeds. Through the further evolution, this inhomogeneity in chemical abundances is shown to be embedded in the d...
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
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...
A mechanism to derive multi-power law functions: an application in the econophysics framework
Scarfone, A M
2006-01-01
It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a two-power law distribution starting from a single power law function recently obtained, in the frameworks of the generalized statistical mechanics based on the Sharma-Taneja-Mittal information measure. In order to test the method, we fit the cumulative distribution of personal income and gross domestic production of several countries, obtaining a good agreement for a wide range of data.
Universal Power Law for Relationship between Rainfall Kinetic Energy and Rainfall Intensity
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.
Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source
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.
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.
Rubinstein, Robert
2015-11-01
It is well known that collision models based on an assumed intermolecular potential (IPL, LJ, ...) can be successfully replaced by simplified surrogates (VHS, VSS, VS, ...) in DSMC calculations. But these surrogates only reproduce certain gross properties of the molecular model, for example, the temperature dependence of the viscosity; they do not approximate, and even mis-state, the details of the particle interactions. The success of the simplified models in problems at finite Knudsen number, where the Navier-Stokes approximation is not valid, may therefore seem surprising. To understand this success in a very special case, we showed that the first seven relaxation rates of the linearized Boltzmann equation for Maxwellian molecules are well approximated by the corresponding relaxation rates of its VHS surrogate. We will show that this analysis can be extended in somewhat less generality to IPL interactions, and to some extent to more realistic models including LJ. We believe that this analysis can help address the more general problem of identifying the properties of the collision model that dominate the predictions of the Boltzmann equation.
Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra
Brown, J. C.; Kašparová, Jana; Massone, A.M.; Piana, M.
2008-01-01
Roč. 486, č. 3 (2008), s. 1023-1029. ISSN 0004-6361 R&D Projects: GA ČR GP205/06/P135 Institutional research plan: CEZ:AV0Z10030501 Keywords : sun flares * X-rays * gamma rays Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 4.153, year: 2008
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.
Consistency relation in power law G-inflation
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
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 models of totally anisotropic scattering
Tuntsov, Artem V; Walker, Mark A; 10.1093/mnras/sts527
2012-01-01
The interstellar scattering responsible for pulsar parabolic arcs, and for intra-day variability of compact radio quasars, is highly anisotropic in some cases. We numerically simulate these observed phenomena using totally anisotropic, power-law models for the electron density fluctuations which cause the scattering. By comparing our results to the scattered image of PSR B0834+06 and, independently, to dual-frequency light curves of the quasar PKS1257-326, we constrain the nature of the scattering media on these lines of sight. We find that models with spectral indices slightly below \\beta=3, including the one-dimensional Kolmogorov model, are broadly consistent with both data sets. We confirm that a single physical model suffices for both sources, with the scattering medium simply being more distant in the case of B0834+06. This reinforces the idea that intra-day variability and parabolic arcs have a common cause in a type of interstellar structure which, though obscure, is commonplace. However, the implied ...
Folding of a finite length power law layer
Schmid, Daniel W.; Podladchikov, Yuri Y.; Marques, Fernando O.
2004-03-01
Folding of an isolated finite length power law layer embedded in a Newtonian viscous matrix is investigated and compared to conventional folding experiments where the layer is of infinite length or in direct contact with lateral boundaries. The approach employed is a combination of the complex potential method for the basic state and the thin plate approximation for the linear stability analysis and is verified by finite element models. The resulting theory reveals that the aspect ratio of a layer has a first-order influence on the development of folds. The aspect ratio competes with the effective viscosity contrast for dominant influence on the folding process. If the aspect ratio is substantially larger than the effective viscosity contrast, the conventional theories are applicable. In other situations, where the aspect ratio is smaller than the effective viscosity contrast, substantial corrections must be taken into account, which lead to a new folding mode that is mainly characterized by decreasing growth rates with increasing effective viscosity contrast (relative to the far-field shortening rate). This new folding mode helps explain the absence of large wavelength to thickness ratio folds in nature, which may be due to the limitations of aspect ratios rather than large effective viscosity contrasts.
Power-law forgetting in synapses with metaplasticity
The idea of using metaplastic synapses to incorporate the separate storage of long- and short-term memories via an array of hidden states was put forward in the cascade model of Fusi et al. In this paper, we devise and investigate two models of a metaplastic synapse based on these general principles. The main difference between the two models lies in their available mechanisms of decay, when a contrarian event occurs after the build-up of a long-term memory. In one case, this leads to the conversion of the long-term memory to a short-term memory of the opposite kind, while in the other, a long-term memory of the opposite kind may be generated as a result. Appropriately enough, the response of both models to short-term events is not affected by this difference in architecture. On the contrary, the transient response of both models, after long-term memories have been created by the passage of sustained signals, is rather different. The asymptotic behaviour of both models is, however, characterised by power-law forgetting with the same universal exponent
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
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...
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
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.
Modified bosonic gas trapped in a generic 3-dim power law potential
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.
Chakraborty, B.; Kodagali, V.N.
is operable at 15.5 kHz, is used in this study Estimated power law parameters using H-K and composite roughness models are compared from the same areas. Interestingly, multibeam backscatter study result establishes a relationship between the power law...
Uniformity measure for power-law mass spectrum in nuclear fragmentation
Description is given in terms of the Renyi entropy and the uniformity for the canonical ensemble, the grand canonical ensemble and the power-law probability measures. The study is presented of the power-law spectra of cluster masses observed in nuclear interactions in the vicinity of the liquid-gas transition point. 6 figs., 1 tab., 15 refs. (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
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 are...
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
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.
POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING
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.
AEGIS: A MULTIWAVELENGTH STUDY OF SPITZER POWER-LAW GALAXIES
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.
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
Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid
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.
Roziamarni Che Abdul Aziz
2012-01-01
Full Text Available The objective of this study is to investigate the effect of silica hybrid nanoparticles on the hardness of the dental nanocomposites. The silica hybrid nanoparticles were synthesized by sol-gel method. The powders were modified with 3-methacryloxy-propyltrimethoxy silane (γ-MPS either by co-condensation method or one-pot method. The silanized silica were then mixed with a mixture of bisglycidyl methacrylate (BisGMA, triethylene glycol methacrylate (TEGDMA, camphorquinone (CQ and dimethylaminoethyl methacrylate (DMAEMA to form dental nanocomposites. The hardness of the nanocomposites were determined using vickers hardness. The results shown that hardness of the dental composites using silica hybrid nanoparticles synthesized via one-pot method was higher compared to the synthesized via co-condensation method. Transmission Electron Microscope (TEM, and Fourier Transform Infrared Spectroscopy (FTIR were used for characterization.
Energy consumption reduction in existing HVAC-R systems via a power law controlling kit
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
Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media
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.
The origin of power-law distributions in self-organized criticality
Yang, C. B.
2004-01-01
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. 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. This shows that power-law distributions in self-organized critica...
Two universal physical principles shape the power-law statistics of real-world networks
Lorimer, Tom; Stoop, Ruedi
2015-01-01
The study of complex networks has pursued an understanding of macroscopic behavior by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex networks generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations.
Two universal physical principles shape the power-law statistics of real-world networks
Lorimer, Tom; Gomez, Florian; Stoop, Ruedi
2015-07-01
The study of complex networks has pursued an understanding of macroscopic behaviour by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex network generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations.
Isomorphs in the phase diagram of a model liquid without inverse power law repulsion
Veldhorst, Arnold Adriaan; Bøhling, Lasse; Dyre, J. C.; Schrøder, Thomas
2012-01-01
scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence the...... dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does not...... depend critically on the mathematical form of the repulsion being an inverse power law....
Fitting inverse power-law quintessence models using the SNAP satellite
Eriksson, Martin; Amanullah, Rahman
2002-01-01
We investigate the possibility of using the proposed SNAP satellite in combination with low-z supernova searches to distinguish between different inverse power-law quintessence models. If the true model is that of a cosmological constant, we determine the prospects of ruling out the inverse power-law potential. We show that SNAP combined with e.g. the SNfactory and an independent measurement of the mass energy density to 17% accuracy can distinguish between an inverse power-law potential and ...
The power-law TST reaction rate coefficient with tunneling correction
Yin, Cangtao; Zhou, Yanjun; Du, Jiulin
2014-01-01
We study the TST reaction rate for the systems with power-law distributions. We derive the expressions of the reaction rate coefficient with tunneling correction, which strongly depends on the power-law parameter. The numerical results show that a small deviation from one in the parameter can result in a significant change in the rate coefficient, but only cause a small change in the tunneling correction. Thus the tunneling correction is not sensitive to the power-law distributions. As an app...
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.
Focusing effect of radially power-law channel on an intense laser beam
Tang, Rong-An; Hong, Xue-Ren; Gao, Ji-Ming; Xue, Ju-Kui
2016-03-01
To study the focusing effect of the power-law channel, the evolution equation of the laser spot size is derived for the laser propagation in a radially power-law channel by using variational method. It is found that there exists a small critical region of the ratio of the initial laser spot size to the channel radius. Below the critical region, the laser power for constant spot size varies dramatically with the increase of the power-law exponent of the channel and so do other focusing behaviors. Quite opposite behaviors are observed above the critical region.
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.
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 8000C in 1000C steps at strain rates of 2.2 x 10-3 and 2.2 x 10-4 sec-1. Hardness tests were performed from room temperature to 8500C in 500C 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 6000C and 300 to 6000C for the lower and higher strain rate, respectively
The origin of power-law distributions in self-organized criticality
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. 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. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime. (letter to the editor)
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time
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.
A penalty method for approximations of the stationary power-law Stokes problem
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.
A NEW MODEL FOR FLOW AND HEAT OF A POWER LAW FLUID IN A PIPE
Botong Li
2011-01-01
Full Text Available In this paper, a new model is proposed for flow and heat transfer of a power law fluid in a pipe. The flow is hydro-dynamically fully-developed and laminar while the characteristic of the fluid viscosity changes with the entrance distance considered. We assume that the power-law index is no longer a constant but a function of the entrance distance. Also, in terms of analogy between the viscous boundary layer and the thermal one, the thermal diffusion coefficient is considered as a power-law function of temperature gradient as Zheng's model. A control volume technique based on the finite difference model coupled with the LU decomposition method is adopted and the least squares polynomial is used to approximate the non-linear item. The results show that the heat transfer behavior strongly depend on the value of the power law index.
Power-law Relationship in Describing Temporal and Spatial Precipitation Pattern in Turkey
Kadiğlu, M.; Şen, Z.
Wet and dry spell properties of monthly rainfall series at five meteorology stations in Turkey are examined by plotting successive wet and dry month duration versus their number of occurrences on the double-logarithmic paper. Straight line relationships on such graphs show that power-laws govern the pattern of successive persistent wet and dry monthly spells. Functional power law relationships between the number of dry and wet spells for a given monthly period are derived from the available monthly precipitation data. The probability statements for wet and dry period spells are obtained from the power law expressions. Comparison of power-law behaviours at five distinct sites in Turkey provides useful interpretation about the temporal and spatial rainfall pattern. As in temperate areas such as Turkey the rainfall amounts change mostly due to one-month-long dry or wet spells.
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...
Mauro, B.; Fava, F.; Frattini, P.; Camia, A.; Colombo, R.; Migliavacca, M.
2015-01-01
Monthly wildfire burned area frequency is here modeled with a power law distribution and scaling exponent across different European biomes are estimated. Data sets, spanning from 2000 to 2009, comprehend the inventory of monthly burned areas from the European Forest Fire Information System (EFFIS) and simulated monthly burned areas from a recent parameterization of a Land Surface Model (LSM), that is the Community Land Model (CLM). Power law exponents are estimated with a Ma...
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...
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.
Garanina, O. S.; Romanovsky, M. Yu.
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 c...
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...
Finite sample properties of power-law cross-correlations estimators
Ladislav Kristoufek
2014-01-01
We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presented broad Monte Carlo simulation study focuses on different time series lengths, specific methods' parameter setting, and memory strength. We find that each method is best suite...
Power-law expansion and Higgs-type potential in a scalar-tensor model
Granda, L. N.
2014-01-01
In the scalar-tensor model with Gauss-Bonnet and kinetic couplings, the power-law dark energy solution may be described by Higgs-type potential. It was found that in the solution describing early time epoch of matter dominance, the potential presents symmetry breaking phase, and the power law solution leading to accelerated expansion corresponds to Higgs-type potential in its symmetric shape.
Transition state theory: a generalization to nonequilibrium systems with power-law distributions
Du, Jiulin
2011-01-01
Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the Langevin equations and corresponding Fokker-Planck equations. It is assumed that the system far away from equilibrium has not to relax to a thermal equilibrium state with Boltzmann-Gibbs distribution, but asymptotically approaches to a nonequilibrium stationary-...
Important Property of GRB Pulse: Power-Law Indices of Time Properties on Energy
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 behaviour evaluation from foreign exchange market data using a wavelet transform method
Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.
Spitzer Power-law AGN Candidates in the Chandra Deep Field-North
Donley, J L; Pérez-González, P G; Rigby, J R; Alonso-Herrero, A
2007-01-01
We define a sample of 62 galaxies in the Chandra Deep Field-North whose Spitzer IRAC SEDs exhibit the characteristic power-law emission expected of luminous AGN. We study the multiwavelength properties of this sample, and compare the AGN selected in this way to those selected via other Spitzer color-color criteria. Only 55% of the power-law galaxies are detected in the X-ray catalog at exposures of >0.5 Ms, although a search for faint emission results in the detection of 85% of the power-law galaxies at the > 2.5 sigma detection level. Most of the remaining galaxies are likely to host AGN that are heavily obscured in the X-ray. Because the power-law selection requires the AGN to be energetically dominant in the near- and mid-infrared, the power-law galaxies comprise a significant fraction of the Spitzer-detected AGN population at high luminosities and redshifts. The high 24 micron detection fraction also points to a luminous population. The power-law galaxies comprise a subset of color-selected AGN candidates...
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
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
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.
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.
This study has been carried out to investigate the effect of Cu addition (0.1–3 wt%) on the microstructure, hardness and tensile properties of Al–15%Mg2Si–0.15%Li in-situ metal matrix composite before and after solutionizing heat treatment. It was found that the presence of Cu at higher concentrations (>1 wt%) results in the formation of hard Cu-rich intermetallics segregated in cell boundaries which intensifies ultimate tensile strength (UTS) values, but reduces elongation percentage (El%). Further results revealed that solution heat treatment partially dissolves different types of intermetallics which leads to proper distribution of such hard particles and ductility enhancement. The study of the fracture surfaces of the heat treated specimens via scanning electron microscopy (SEM) revealed fine dimples which are the main characteristic of ductile fracture mode
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 ...
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.
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 ...
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
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.
Inglis, A. R.; Ireland, J.; Dominique, M.
2015-01-01
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.
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.
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
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...
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
Double Power Laws in the Event-integrated Solar Energetic Particle Spectrum
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K.
2016-04-01
A double power law or a power law with exponential rollover at a few to tens of MeV nucleon-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-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.
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 ...
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 Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment
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 f1, 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.
Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts
Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.
The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.
Yunes, N; Yunes, Nicolas; Visser, Matt
2003-01-01
We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. This Frobenius-like series can be viewed as a variant of Liapunov's expansion theorem. As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and demonstrate (both numerically and analytically) that the solution exhibits oscillatory power-law behaviour as the star approaches the p...
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...
Origin of power laws for reactions at metal surfaces mediated by hot electrons
Olsen, Thomas
2009-01-01
A wide range of experiments have established that certain chemical reactions at metal surfaces can be driven by multiple hot electron mediated excitations of adsorbates. A high transient density of hot electrons is obtained by means of femtosecond laser pulses and a characteristic feature of such experiments is the emergence of a power law dependence of the reaction yield on the laser fluence $Y\\sim F^n$. We propose a model of multiple inelastic scattering by hot electrons, which reproduces this power law and the experimentally found exponents of a large class of experiments, including desorption induced by single or multiple electronic transitions; diffusion and reactions induced by Scanning Tunneling Microscope tips; and chemistry induced by hot electrons generated in a Metal-Insulator-Metal device. All parameters of the model are calculated within Density Functional Theory and the Delta Self-Consistent Field method. With a simplified assumption, that mimics the numerical results, the power law becomes exac...
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
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
Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction
Hayat, Tasawar; Rashid, Madiha; Imtiaz, Maria; Alsaedi, Ahmed
2015-11-01
This paper deals with the boundary layer flow of nanofluid over power-law stretched surface. Analysis has been carried out in the presence of applied magnetic field and chemical reaction. Heat and mass transfer characteristics are studied using heat and mass convective conditions. The governing partial differential equations are transferred to the nonlinear ordinary differential equations. Convergent series solutions are obtained for fluid velocity, temperature and concentrations fields. Influences of pertinent parameters including Hartman number, thermal and concentration Biot numbers and chemical reaction parameters are discussed on the velocity, temperature and concentration profiles. Graphical result are presented and discussed. Computations for local Nusselt and Sherwood numbers are carried out. It is observed that the heat transfer rate is enhanced by increasing power-law index, thermal Biot number and chemical reaction parameter while mass transfer rate increases for power-law index and chemical reaction parameter.
Origin of Power Laws for Reactions at Metal Surfaces Mediated by Hot Electrons
Olsen, Thomas; Schiøtz, Jakob
2009-01-01
experiments is the emergence of a power law dependence of the reaction yield on the laser fluence Y similar to F-n. We propose a model of multiple inelastic scattering by hot electrons which reproduces this power law and the observed exponents of several experiments. All parameters are calculated within...... density functional theory and the delta self-consistent field method. With a simplifying assumption, the power law becomes exact and we obtain a simple physical interpretation of the exponent n, which represents the number of adsorbate vibrational states participating in the reaction.......A wide range of experiments have established that certain chemical reactions at metal surfaces can be driven by multiple hot-electron-mediated excitations of adsorbates. A high transient density of hot electrons is obtained by means of femtosecond laser pulses and a characteristic feature of such...
POWER LAW DISTRIBUTION AND SELF-ORGANIZED CRITICALITY OF DISPERSED PARTICLES
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.
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...
Similarity solutions for non-Newtonian power-law fluid flow
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.
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.
Power-law singularities in string theory and M-theory
Papadopoulos, G
2004-01-01
We extend the definition of the Szekeres-Iyer power-law singularities to supergravity, string and M-theory backgrounds, and find that are characterized by Kasner type exponents. The near singularity geometries of brane and some intersecting brane backgrounds are investigated and the exponents are computed. The Penrose limits of some of these power-law singularities have profiles $A\\sim {\\rm u}^{-\\gamma}$ for $\\gamma\\geq 2$. We find the range of the exponents for which $\\gamma=2$ and the frequ...
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.
Ruling out the power-law form of the scalar primordial spectrum
Hazra, Dhiraj Kumar; Shafieloo, Arman; Smoot, George F.; Starobinsky, Alexei A.
2014-01-01
Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than $3\\sigma$ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the fo...
One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase
We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|β, with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a 'Luttinger staircase'. Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.
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 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.
Reed, William J.; Hughes, Barry D.
2002-12-01
We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes of incomes, cities, internet files, biological taxa, and in gene family and protein family frequencies.
Using the formulation of Nickerson and Smiley, the variation of the wind profile power-law exponent in terms of surface roughness and atmospheric stability,has been obtained for specifying the vertical variation of the horizontal wind. A good comparison between the notional estimates of the power-law exponent and power- law exponent data from various sources has been obtained.These calculations have been performed seasonally adopting meteorological data for Inshas site - Egypt
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, Fe92Ni8 alloys with Zr and nano-Y2O3 additions were produced by ball milling and then annealed at high temperatures. Emphasis was placed on understanding the effects of dispersed nano-Y2O3 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 Y2O3 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 Y2O3 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 Y2O3 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.
Power-law cosmic expansion in f(R) gravity models
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for Rn gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
Extended Power Law and Hall Anomaly of High-Temperature Superconductors
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)
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.
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 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.
Degree-degree distribution in a power law random intersection graph with clustering
Bloznelis, Mindaugas
2014-01-01
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree distribution of a sparse inhomogeneous random intersection graph and discuss its relation to the clustering and power law properties of the graph.
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.
Quantum dots with indirect band gap: power-law photoluminescence decay
Král, Karel; Menšík, Miroslav
2014-01-01
Roč. 11, č. 5 (2014), s. 507-512. ISSN 1708-5284 R&D Projects: GA MŠk LH12236; GA MŠk LH12186 Institutional support: RVO:68378271 ; RVO:61389013 Keywords : photoluminescence * quantum dots * electron-phonon interaction * inter-valley deformation potential interaction * power- law decay Subject RIV: BM - Solid Matter Physics ; Magnetism
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...
Peristaltic Motion of Power-Law Fluid with Heat and Mass Transfer
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.
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...
Power-law entropic corrections to Newton's law and Friedmann equations
A possible source of black hole entropy could be the entanglement of quantum fields inside and outside the horizon. The entanglement entropy of the ground state obeys the area law. However, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. Inspired by the power-law corrections to entropy and adopting the viewpoint that gravity emerges as an entropic force, we derive modified Newton's law of gravitation as well as the corrections to Friedmann equations. In a different approach, we obtained power-law-corrected Friedmann equation by starting from the first law of thermodynamics at the apparent horizon of a Friedmann-Robertson-Walker universe, and assuming that the associated entropy with apparent horizon has a power-law-corrected relation. Our study shows a consistency between the obtained results of these two approaches. We also examine the time evolution of the total entropy including the power-law-corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon and show that the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.
Point Processes Modeling of Time Series Exhibiting Power-Law Statistics
Kaulakys, B; Gontis, V
2010-01-01
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.
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.
Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise, and multifractality.
Kendal, Wayne S; Jørgensen, Bent
2011-12-01
Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality. PMID:22304168
Maximal planar networks with large clustering coefficient and power-law degree distribution
In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called random Apollonian networks (RANs) as they can be considered as a variation of Apollonian networks. We obtain the analytic results of power-law exponent γ=3 and clustering coefficient C=(46/3)-36 ln (3/2)≅0.74, which agree with the simulation results very well. We prove that the increasing tendency of average distance of RANs is a little slower than the logarithm of the number of nodes in RANs. Since most real-life networks are both scale-free and small-world networks, RANs may perform well in mimicking the reality. The RANs possess hierarchical structure as C(k)∼k-1 that are in accord with the observations of many real-life networks. In addition, we prove that RANs are maximal planar networks, which are of particular practicability for layout of printed circuits and so on. The percolation and epidemic spreading process are also studied and the comparisons between RANs and Barabasi-Albert (BA) as well as Newman-Watts (NW) networks are shown. We find that, when the network order N (the total number of nodes) is relatively small (as N∼104), the performance of RANs under intentional attack is not sensitive to N, while that of BA networks is much affected by N. And the diseases spread slower in RANs than BA networks in the early stage of the suseptible-infected process, indicating that the large clustering coefficient may slow the spreading velocity, especially in the outbreaks
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...
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.
Koyama, Hiroko; KONISHI, Tetsuro
2000-01-01
Long-time behavior of spatial power-law correlation in one-dimensional self-gravitating system is numerically investigated. It is found that the power-law structure persists even after the system is virialized. The structure gradually disappears owing to energy exchange among particles. Energy distribution is quasi-stationary after the system is virialized.
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.
Kristoufek, Ladislav
2015-06-01
We study power-law correlations properties of the Google search queries for Dow Jones Industrial Average (DJIA) component stocks. Examining the daily data of the searched terms with a combination of the rescaled range and rescaled variance tests together with the detrended fluctuation analysis, we show that the searches are in fact power-law correlated with Hurst exponents between 0.8 and 1.1. The general interest in the DJIA stocks is thus strongly persistent. We further reinvestigate the cross-correlation structure between the searches, traded volume and volatility of the component stocks using the detrended cross-correlation and detrending moving-average cross-correlation coefficients. Contrary to the universal power-law correlations structure of the related Google searches, the results suggest that there is no universal relationship between the online search queries and the analyzed financial measures. Even though we confirm positive correlation for a majority of pairs, there are several pairs with insignificant or even negative correlations. In addition, the correlations vary quite strongly across scales.
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
Deposition from evaporating drops: Power laws and new morphologies in coffee stains
Freed-Brown, Julian E.
We investigate the structure of stains formed through evaporative deposition in sessile drops. Commonly, the deposited stain has a high surface density near the three phase contact line of the drying drop and much less solute in the bulk of the drop. This is known as the ``coffee ring effect'' and primarily arises due to contact line pinning. While many features of the stain depend on subtle physical phenomena within the drop, the coffee ring effect stands out as a robust feature that persists in many varied experimental realizations. In 2009, Witten predicted another robust feature of deposited stains: an asymptotic regime where a robust power law governs the fadeout profile of the stain into the interior of the drop. This power law is only controlled by geometric properties at a single point and the power does not vary along the contact line. We investigate the approach to this power law using numerical methods. For many evaporation profiles (including common experimental ones) the numerics show good agreement with the power law prediction. However, we demonstrate an intuitive scheme to construct evaporation profiles that subvert the power law prediction. We find that, in general, the approach to the power law cannot be known without full knowledge of the evaporation and height profile. We also extend this work in another way. We apply the basic arguments of the coffee ring effect to the case where the drop has a receding contact line. Here, we develop a new theoretical framework for deposition that has not previously been studied. In this context, the surface density profile can be directly calculated. Unlike a pinned contact line, receding contact lines push fluid into the interior of the drop. This effect can be overcome by strong evaporation near the contact line, but in general the intuition from contact line pinning is reversed. Following Witten's example, we find that the surface density of the stain near the center of the drop goes as eta ∝ rnu, where
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...
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...
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
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 [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.
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.
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...
Power laws reveal phase transitions in landscape controls of fire regimes.
McKenzie, Donald; Kennedy, Maureen C
2012-01-01
Understanding the environmental controls on historical wildfires, and how they changed across spatial scales, is difficult because there are no surviving explicit records of either weather or vegetation (fuels). Here we show how power laws associated with fire-event time series arise in limited domains of parameters that represent critical transitions in the controls on landscape fire. Comparison to a self-organized criticality model shows that the latter mimics historical fire only in a limited domain of criticality, and is not an adequate mechanism to explain landscape fire dynamics, which are shaped by both endogenous and exogenous controls. Our results identify a continuous phase transition in landscape controls, marked by power laws, and provide an ecological analogue to critical behaviour in physical and chemical systems. This explicitly cross-scale analysis provides a paradigm for identifying critical thresholds in landscape dynamics that may be crossed in a rapidly changing climate. PMID:22395617
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.
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.
Forced convection heat transfer to power-law non-Newtonian fluids inside triangular ducts
Chaves, Cleber; Quaresma, Joao; Macedo, Emanuel [Universidade Federal do Para, Campus Universitario do Guama, Chemical and Food Engineering Dept., Belem, PA (Brazil); Pereira, Luiz [Universidade do Vale do Paraiba, Research and Development Inst., S.J. Campos, SP (Brazil); Lima, Joao [Universidade Federal do Rio Grande do Norte, Mechanical Engineering Dept., Natal, RN (Brazil)
2004-07-01
A hybrid analytical-numerical approach based on the Generalized Integral Transform Technique is employed to simulate the laminar forced convection (hydrodynamically fully developed and thermally developing laminar flow) of power-law non-Newtonian fluids inside ducts with arbitrary shaped cross-sections. The analysis is illustrated through consideration of both right angularly and isosceles triangular ducts subjected to constant wall temperature as thermal boundary condition. Reference results for quantities of practical interest such as dimensionless average temperature and Nusselt numbers within the thermal entry region were produced for different values of power-law index and apex angles. Finally, critical comparisons are performed with results available in the literature for direct numerical and approximate approaches. (Author)
Hypersonic aerodynamic characteristics of a family of power-law, wing body configurations
Townsend, J. C.
1973-01-01
The configurations analyzed are half-axisymmetric, power-law bodies surmounted by thin, flat wings. The wing planform matches the body shock-wave shape. Analytic solutions of the hypersonic small disturbance equations form a basis for calculating the longitudinal aerodynamic characteristics. Boundary-layer displacement effects on the body and the wing upper surface are approximated. Skin friction is estimated by using compressible, laminar boundary-layer solutions. Good agreement was obtained with available experimental data for which the basic theoretical assumptions were satisfied. The method is used to estimate the effects of power-law, fineness ratio, and Mach number variations at full-scale conditions. The computer program is included.
Theoretical model to deduce a PDF with a power law tail using Extreme Physical Information
Bonilla, Ricardo; Valdivia, Juan Alejandro
2011-01-01
The theory of Extreme Physical Information (EPI) is used to deduce a probability density function (PDF) of a system that exhibits a power law tail. The computed PDF is useful to study and fit several observed distributions in complex systems. This new approach permits to describe extreme and rare events in the tail, and also the frequent events in the distribution head. Using EPI an information functional is constructed, and minimized using Euler-Lagrange equations. As a solution a second order differential equation is derived. By solving this equation a family of functions is calculated. These functions allow describing the system in terms of a eigenstates. A dissipative term is introduced into the model, as a relevant term to study open systems. One of the main results is a mathematical relation between the scaling parameter of the power law observed in the tail and the shape of the head.
The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function
Basu, Shantanu; Auddy, Sayantan
2015-01-01
This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modeling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like...
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).
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...
Generalized second law of thermodynamics for FRW cosmology with power-law entropy correction
In this work, we have considered the power-law correction of entropy on the horizon. If the flat FRW Universe is filled with the n components fluid with interactions, the GSL of thermodynamics for apparent and event horizons have been investigated for equilibrium and non-equilibrium cases. If we consider a small perturbation around the de Sitter spacetime, the general conditions of the validity of GSL have been found. Also if a phantom dominated Universe has a pole-like type scale factor, the validity of GSL has also been analyzed. Further we have obtained constraints on the power-law parameter α in the phantom and quintessence dominated regimes. Finally we obtain conditions under which GSL breaks down in a cosmological background. (orig.)
Shear Force Distribution and Heat Transfer in Laminar Boundary Layer Flows for Power Law Fluid
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).
On the origin of power-law distributions in systems with constrained phase space
E.V. Vakarin
2013-01-01
Full Text Available Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.
Statefinder Parameters for Coupled Quintessence Scenario in a Power Law Case
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.
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.
Underestimating extreme events in power-law behavior due to machine-dependent cutoffs
Radicchi, Filippo
2014-01-01
Power law distributions are typical macroscopic features occurring in almost all complex systems observable in nature, so that researchers have often the necessity, in quantitative analyses, to generate random synthetic variates obeying power law distributions. This task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subjected to severe machine-dependent limitations. As results, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, that are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretatio...
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...
Symmetry Reductions of a Flow with Power Law Fluid and Contaminant-Modified Viscosity
Moitsheki, R.; Abelman, S.; T. Hayat
2010-01-01
In this study symmetry analysis is carried out for a system dealing with nonreactive pollutant transport along a single channel. Constitutive equations obeying a power law fluid are used in the description of the mathematical problem. We obtain forms of the source term for which the governing system admits extra point symmetries. Invariant solutions which satisfy physical boundary conditions are constructed. In some cases we resort to numerical methods to obtain approximate solutions.
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...
Finite sample properties of power-law cross-correlations estimators
Krištoufek, Ladislav
2015-01-01
Roč. 419, č. 1 (2015), s. 513-525. ISSN 0378-4371 R&D Projects: GA ČR(CZ) GP14-11402P Keywords : power-law cross-correlations * long-term memory * econophysics Subject RIV: AH - Economics Impact factor: 1.732, year: 2014 http://library.utia.cas.cz/separaty/2014/E/kristoufek-0433530.pdf
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.
Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling
Cohen, Joel E.; Xu, Meng
2015-01-01
One of the most widely confirmed empirical patterns in ecology is Taylor’s law (TL): The variance of population density is approximately a power-law function of the mean population density. We showed analytically that, when observations are randomly sampled in blocks from a single frequency distribution, the sample variance will be related to the sample mean by TL, and the parameters of TL can be predicted from the first four moments of the frequency distribution. The estimate of the exponent...
Power law of engagement:Transferring disengaged householders into retrofitting energy savers
Weeks, Christopher; Delalonde, Charles; Preist, Chris
2014-01-01
How can we take householders from being disengaged passive energy consumers towards being highly motivated retrofitting energy saving masters? In this paper the “Power law of engagement model for energy saving” is introduced, which breaks down the process of engaging householders into 8 defined stages. The model is based on the householder’s level of engagement and commitment, but applies Fogg’s behaviour model at key stages to help evaluate the decision process of the householder. The focus ...
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...
Kai Zhao; Mirco Musolesi; Pan Hui; Weixiong Rao; Sasu Tarkoma
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/B...
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...
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.
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...
NEW METHOD TO ESTIMATE SCALING OF POWER-LAW DEGREE DISTRIBUTION AND HIERARCHICAL NETWORKS
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.
Poiseuille flow of power-law fluids in concentric annuli - limiting cases
Filip, Petr; David, Jiří
Pretoria : HEFAT, 2008, FP1. ISBN 978-1-86854-691-6. [Annual Heat Transfer , Fluid Mechanics and Thermodynamics Conference /6./. Pretoria (ZA), 30.06.2008-02.07.2008] R&D Projects: GA ČR GA103/06/1033 Institutional research plan: CEZ:AV0Z20600510 Keywords : Poiseuille flow * power-law fluids * concentric annuli Subject RIV: BK - Fluid Dynamics
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.
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.
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.
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...
Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction
Tasawar Hayat; Madiha Rashid; Maria Imtiaz; Ahmed Alsaedi
2015-01-01
This paper deals with the boundary layer flow of nanofluid over power-law stretched surface. Analysis has been carried out in the presence of applied magnetic field and chemical reaction. Heat and mass transfer characteristics are studied using heat and mass convective conditions. The governing partial differential equations are transferred to the nonlinear ordinary differential equations. Convergent series solutions are obtained for fluid velocity, temperature and concentrations fields. Infl...
Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-01-01
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 thi...
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.
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...
Dark optical solitons in power law media with time-dependent coefficients
This Letter talks about the dynamics of dark optical solitons that are governed by the nonlinear Schroedinger's equation with power law nonlinearity. The solitons are considered in presence of linear attenuation, third order dispersion and self-steepening terms, all with time-dependent coefficients. The solitary wave ansatz is used to carry out the integration and an exact soliton solution is obtained. It is only necessary that these time-dependent coefficients are Riemann integrable.
Applicability of the limiting cases for axial annular flow of power-law fluids
Filip, Petr; David, Jiří
Fukuoka: WSEAS Press, 2013 - ( Fujita , H.; Tuba, M.; Sasaki, J.), s. 45-48 ISBN 978-1-61804-177-7. ISSN 1790-5117. [Recent advances in automatic control, modelling and simulation. Morioka City (JP), 23.04.2013-25.04.2013] R&D Projects: GA ČR GA103/09/2066 Institutional support: RVO:67985874 Keywords : annular flow * power-law fluids * poiseuille flow * flow rate * pressure drop Subject RIV: BK - Fluid Dynamics
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...
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
The quest for obscured AGN at cosmological distances: Infrared Power-Law Galaxies
Alonso-Herrero, A; Rieke, G H; Rigby, J R; Pérez-González, P G; Alonso-Herrero, Almudena; Donley, Jennifer L.; Rieke, George H.; Rigby, Jane R.; Perez-Gonzalez, Pablo G.
2006-01-01
We summarize multiwavelength properties of a sample of galaxies in the CDF-N and CDF-S whose Spectral Energy Distributions (SEDs) exhibit the characteristic power-law behavior expected for AGN in the Spitzer/IRAC 3.6-8micron bands. AGN selected this way tend to comprise the majority of high X-ray luminosity AGN, whereas AGN selected via other IRAC color-color criteria might contain more star-formation dominated galaxies. Approximately half of these IR power-law galaxies in the CDF-S are detected in deep (1Ms) Chandra X-ray imaging, although in the CDF-N (2Ms) about 77% are detected at the 3sigma level. The SEDs and X-ray upper limits of the sources not detected in X-rays are consistent with those of obscured AGN, and are significantly different from those of massive star-forming galaxies. About 40% of IR power-law galaxies detected in X-rays have SEDs resembling that of an optical QSO and morphologies dominated by bright point source emission. The remaining 60% have SEDs whose UV and optical continuum are muc...
AC losses in superconductors with a power-law constitutive relation
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 B0m, m = 3–4 and I3 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
Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.
Zhao, Cunlu; Yang, Chun
2013-03-01
EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field. PMID:23229874
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
Cyclotron Maser Emission from Power-law Electrons with Strong Pitch-angle Anisotropy
Zhao, G. Q.; Feng, H. Q.; Wu, D. J.; Chen, L.; Tang, J. F.; Liu, Q.
2016-05-01
Energetic electrons with power-law spectra are 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 the X2 mode rapidly decreases with respect to the electron pitch-angle cosine μ 0 at which the electron distribution peaks, while the growth rates for other modes (X1, O1, O2) initially increase before decreasing as μ 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 the type of electron pitch-angle distribution. This result presents a significant extension of the recent researches on ECME driven by the lower energy cutoff of power-law electrons, in which the X mode is generally the fastest growth mode.
Multiplicative processes and power laws in human reaction times derived from hyperbolic functions
In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéron's law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipf's law are analyzed. -- Highlights: ► I have examined human reaction time variability by random multiplicative processes. ► A transition from power law to log-normal distributions is described. ► The transition depends on the transfer of information in neurons. ► Zipf's law in reaction time distributions depends on the exponent of Piéron's law.
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.
AC losses in superconductors with a power-law constitutive relation
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.
Distributed power-law seismicity changes and crustal deformation in the SW Hellenic ARC
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...
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.
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
The mean first passage time in an energy-diffusion controlled regime with power-law distributions
Zhou, Yanjun; Du, Jiulin
2013-01-01
Based on the mean first passage time (MFPT) theory, we derive the expression of the MFPT in the energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. thermal energy is not small with respect to the potential barrier) and compare it with the Kramers infinite barrier result both in the power-law distribution and in a Maxwell-Boltzmann distribution. It is shown that the MFPT with the power-law distribution extends the Kramers' low damping re...
The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author)
Hard electronics; Hard electronics
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.
Liu, Hsing; Chen, Ying-Hsing; Lih, Jiann-Shing
2015-05-01
Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution.
Dralle, David; Karst, Nathaniel; Thompson, Sally E.
2015-11-01
The falling limb of the hydrograph—the streamflow recession—is frequently well approximated by power law functions, in the form dq/dt = -aqb, so that recessions are often characterized in terms of their power law parameters (a, b). The empirical determination and interpretation of the parameter a is typically biased by the presence of a ubiquitous mathematical artifact resulting from the scale-free properties of the power law function. This reduces the information available from recession parameter analysis and creates several heretofore unaddressed methodological "pitfalls." This letter outlines the artifact, demonstrates its genesis, and presents an empirical rescaling method to remove artifact effects from fitted recession parameters. The rescaling process reveals underlying climatic patterns obscured in the original data and, we suggest, could maximize the information content of fitted power laws.
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker–Planck equation, we can obtain a condition under which these power-law distributions are accurately created in a system away from equilibrium. This condition is an energy-dependent relation between the diffusion coefficient and the friction coefficient and thus it provides a fluctuation-dissipation relation for nonequilibrium systems with power-law distributions. Further, we study the specific forms of the Fokker–Planck equation that correctly lead to such power-law distributions, and then present a possible generalization of the Klein–Kramers equation and the Smoluchowski equation to a complex system, whose stationary-state solutions are exactly a Tsallis distribution
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
On the interplay between short and long term memory in the power-law cross-correlations setting
Ladislav Kristoufek
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 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...
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...
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.
Protein family and fold occurrence in genomes: power-law behaviour and evolutionary model.
Qian, J; Luscombe, N M; Gerstein, M
2001-11-01
Global surveys of genomes measure the usage of essential molecular parts, defined here as protein families, superfamilies or folds, in different organisms. Based on surveys of the first 20 completely sequenced genomes, we observe that the occurrence of these parts follows a power-law distribution. That is, the number of distinct parts (F) with a given genomic occurrence (V) decays as F=aV(-b), with a few parts occurring many times and most occurring infrequently. For a given organism, the distributions of families, superfamilies and folds are nearly identical, and this is reflected in the size of the decay exponent b. Moreover, the exponent varies between different organisms, with those of smaller genomes displaying a steeper decay (i.e. larger b). Clearly, the power law indicates a preference to duplicate genes that encode for molecular parts which are already common. Here, we present a minimal, but biologically meaningful model that accurately describes the observed power law. Although the model performs equally well for all three protein classes, we focus on the occurrence of folds in preference to families and superfamilies. This is because folds are comparatively insensitive to the effects of point mutations that can cause a family member to diverge beyond detectable similarity. In the model, genomes evolve through two basic operations: (i) duplication of existing genes; (ii) net flow of new genes. The flow term is closely related to the exponent b and can accommodate considerable gene loss; however, we demonstrate that the observed data is reproduced best with a net inflow, i.e. with more gene gain than loss. Moreover, we show that prokaryotes have much higher rates of gene acquisition than eukaryotes, probably reflecting lateral transfer. A further natural outcome from our model is an estimation of the fold composition of the initial genome, which potentially relates to the common ancestor for modern organisms. Supplementary material pertaining to this work
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).
Chae, K H
2002-01-01
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two power-law ellipsoidal mass distributions are presented. The cusped two power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or, transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and $\\eta$ models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two power-law mass distributions are relatively simple, and allow a very fast calculation even for a chosen small fractional calculational error (e.g. $10^{-5}$). These results will be particularly useful for studying lensed systems which provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single power-law mass model are made publi...
Chae, Kyu-Hyun
2002-04-01
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two-power-law ellipsoidal mass distributions are presented. The cusped two-power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and η models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two-power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e.g., 10-5). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two-power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single-power-law mass model are made publicly available.
Wang, Q.; Yang, M.; Song, X. L.; Jia, J.; Xiang, Z. D.
2016-05-01
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).
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 ...
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.
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.
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...
Void growth in copper during high-temperature power-law creep
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.
Relaxation of the distribution function tails for gases with power-law interaction potentials
The relaxation of rarefied gases of particles with the power-law interaction potentials U=α/rs, where 1≤s<4, is considered. The formation and evolution of the distribution function tails are investigated on the basis of the one-dimensional kinetic Landau endash Fokker-Planck equation. For long times, the constructed asymptotic solutions have a propagating-wave appearance in the high velocity region. The analytical solutions are expressed explicitly in terms of the error function. The analytical consideration is accomplished by numerical calculations. The obtained analytical results are in a good agreement with the numerical simulation results. copyright 1997 The American Physical Society
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.
Model-based fit procedure for power-law-like spectra
Milotti, E
2005-01-01
$1/f^\\alpha$ noises are ubiquitous and affect many measurements. These noises are both a nuisance and a peculiarity of several physical systems; in dielectrics, glasses and networked liquids it is very common to study this noise to gather useful information. Sometimes it happens that the noise has a power-law shape only in a certain frequency range, and contains other important features, that are however difficult to study because simple fits often fail. Here I propose a model-based fit procedure that performs well on spectra obtained in a molecular dynamics simulation.
Model-based fit procedure for power-law-like spectra
Milotti, Edoardo
2005-01-01
$1/f^\\alpha$ noises are ubiquitous and affect many measurements. These noises are both a nuisance and a peculiarity of several physical systems; in dielectrics, glasses and networked liquids it is very common to study this noise to gather useful information. Sometimes it happens that the noise has a power-law shape only in a certain frequency range, and contains other important features, that are however difficult to study because simple fits often fail. Here I propose a model-based fit proce...
Light Fragment Production and Power Law Behavior in Au + Au Collisions
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
Hysteresis and creep: Comparison between a power-law model and Kuhnen's model
Oliveri, Alberto; Stellino, Flavio; Parodi, Mauro; Storace, Marco
2016-04-01
In this paper we analyze some properties of a recently proposed model of hysteresis and creep (related to a circuit model, whose only nonlinear element is based on a power law) and compare it with the well-known Kuhnen's model. A first qualitative comparison relies on the analysis of the behavior of the elementary cell of each model. Their responses to step inputs (which allow to better evidence the creep effect) are analyzed and compared. Then, a quantitative comparison is proposed, based on the fitting performances of the two models on experimental data measured from a commercial piezoelectric actuator.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
Bakalis, Evangelos, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it [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 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 ...
Power-Law Entropic Corrections to Newton's Law and Friedmann Equations
Sheykhi, Ahmad; Hendi, Seyed Hossein
2010-01-01
A possible source of black hole entropy could be the entanglement of quantum fields in and out the horizon. The entanglement entropy of the ground state obeys the area law. However, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. Inspired by the power-law corrections to entropy and adopting the viewpoint that gravity emerges as an entropic force, we derive modified Newton's law of gravitation as well as th...
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.
Laboratory constraints on chameleon dark energy and power-law fields
Steffen, Jason H.; /Fermilab; Upadhye, Amol; /KICP, Chicago; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; /Fermilab; Weltman, Amanda; /Cape Town U.; Wester, William; /Fermilab
2010-10-01
We report results from the GammeV Chameleon Afterglow Search - a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
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
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
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.
Void growth in copper during high-temperature power-law creep
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.
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...
Magnetohydrodynamic Boundary Layer Slip Flow and Heat Transfer of Power Law Fluid over a Flat Plate
Jacob Hirschhorn
2016-01-01
Full Text Available In this paper, we consider the magnetohydrodynamic (MHD boundary layer flow and heat transfer of power law fluid over a flat plate with slip boundary conditions. We use a similarity transformation to convert the governing nonlinear partial differential equations into a system of ordinary differential equations and solve the resulting system numerically using MATLAB’s boundary value solver, bvp4c, and the shooting method. We present velocity and temperature profiles within the boundary layer and demonstrate the effect of changing the magnetic parameter, Prandtl number, and slip parameters.
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.
Fractional-order formulation of power-law and exponential distributions
We present a novel approach to data analysis using fractional order calculus. In principle the approach can be applied to any distribution and shows remarkable improvement even if the parameters of a particular distribution have been optimised to achieve the best fit to data. The method is demonstrated for two important distributions that are used in data analysis, namely, power-law and exponential distributions. We show that the approach can allow composite distributions to be constructed for improved accuracy and robustness in the characterisation of data sets
Chaotic inflation with a fractional power-law potential in strongly coupled gauge theories
Models of chaotic inflation with a fractional power-law potential are not only viable but also testable in the foreseeable future. We show that such models can be realized in simple strongly coupled supersymmetric gauge theories. In these models, the energy scale during inflation is dynamically generated by the dimensional transmutation due to the strong gauge dynamics. Therefore, such models not only explain the origin of the fractional power in the inflationary potential but also provide a reason why the energy scale of inflation is much smaller than the Planck scale
Hard electronics; Hard electronics
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.
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.
Generation of potential/surface density pairs in flat disks Power law distributions
Hure, J -M; Pierens, A
2007-01-01
We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk, and a ``residual'' pair. This residual component is converted into an infinite series of integrals over the radial extent of the disk. For a certain class of surface density distributions (like power laws of the radius), this series is fully analytical. The extraction of the homogeneous pair is equivalent to a convergence acceleration technique, in a matematical sense. In the case of power law distributions, the convergence rate of the residual series is shown to be cubic inside the source. As a consequence, very accurate potential values are obtained by low order truncation of the series. At zero order, relative errors on potential values do not exceed a few percent typically, and scale with the order N of truncation as 1/N**3. This method is superior to the classical mul...
Ruling out the power-law form of the scalar primordial spectrum
Hazra, Dhiraj Kumar; Shafieloo, Arman [Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790-784 (Korea, Republic of); Smoot, George F. [Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Starobinsky, Alexei A., E-mail: dhiraj@apctp.org, E-mail: arman@apctp.org, E-mail: gfsmoot@lbl.gov, E-mail: alstar@landau.ac.ru [Landau Institute for Theoretical Physics RAS, Moscow, 119334 (Russian Federation)
2014-06-01
Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3σ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large r and at the same time provide suppression in scalar primordial spectrum at large scales.
Ruling out the power-law form of the scalar primordial spectrum
Hazra, Dhiraj Kumar; Smoot, George F; Starobinsky, Alexei A
2014-01-01
Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than $3\\sigma$ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4] can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5] can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Plan...
Ruling out the power-law form of the scalar primordial spectrum
Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3σ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large r and at the same time provide suppression in scalar primordial spectrum at large scales
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.
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...
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.
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.
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.
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...
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...
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.
Double power-law spectra of energetic electrons in the Earth magnetotail
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.
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 ...
The MLP distribution: a modified lognormal power-law model for the stellar initial mass function
Basu, Shantanu; Gil, M.; Auddy, Sayantan
2015-05-01
This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modelling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.
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.
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.
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...
Numerical simulation of flow in swirl injector for power-law fluid
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.
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.
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...
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.
The US business cycle: power law scaling for interacting units with complex internal structure
Ormerod, Paul
2002-11-01
In the social sciences, there is increasing evidence of the existence of power law distributions. The distribution of recessions in capitalist economies has recently been shown to follow such a distribution. The preferred explanation for this is self-organised criticality. Gene Stanley and colleagues propose an alternative, namely that power law scaling can arise from the interplay between random multiplicative growth and the complex structure of the units composing the system. This paper offers a parsimonious model of the US business cycle based on similar principles. The business cycle, along with long-term growth, is one of the two features which distinguishes capitalism from all previously existing societies. Yet, economics lacks a satisfactory theory of the cycle. The source of cycles is posited in economic theory to be a series of random shocks which are external to the system. In this model, the cycle is an internal feature of the system, arising from the level of industrial concentration of the agents and the interactions between them. The model-in contrast to existing economic theories of the cycle-accounts for the key features of output growth in the US business cycle in the 20th century.
Spectral function of the Tomonaga-Luttinger model revisited: Power laws and universality
Markhof, L.; Meden, V.
2016-02-01
We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum dependence of the two-particle interaction V (q ) . Usually, V (q ) is assumed to be a constant and integrals are regularized in the ultraviolet "by hand" employing an ad hoc procedure. As the momentum dependence of the interaction is irrelevant in the renormalization group sense, this does not affect the universal low-energy properties of the model, e.g., exponents of power laws, if all energy scales are sent to zero. If, however, the momentum k is fixed away from the Fermi momentum kF, with |k - kF| setting a nonvanishing energy scale, the details of V (q ) start to matter. We provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys power-law scaling of the momentum-resolved spectral function as a function of energy. Even for |k - kF| much smaller than the momentum-space range of the interaction the spectral line shape depends on the details of V (q ) . The significance of our results for universality in the Luttinger liquid sense, for experiments on quasi-one-dimensional metals, and for recent results on the spectral function of one-dimensional correlated systems taking effects of the curvature of the single-particle dispersion into account ("nonlinear LL phenomenology") is discussed.
Underestimating extreme events in power-law behavior due to machine-dependent cutoffs
Radicchi, Filippo
2014-11-01
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subject to severe machine-dependent limitations. As a result, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, which are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies, they also pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.
Birth and death of protein domains: A simple model of evolution explains power law behavior
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
Large scale molecular dynamics (MD) simulations are performed to study and to model the ejecta production from the dynamic fragmentation of shock-loaded metals under melt conditions. A generic 3D crystal in contact with vacuum containing about 108 atoms and with a sinusoidal free surface roughness is shock loaded so as to undergo a solid-liquid phase change on shock. The reflection of the shock wave at the interface metal/vacuum gives rise to the ejection of 2D jets/sheets of atoms (Richtmyer-Meshkov instabilities in the continuum limit), which develop and break up, forming ejecta (fragments) of different volumes (or mass). The fragmentation process is investigated by analyzing the evolution of the resulting volume distribution of the ejecta as a function of time. Two metals are studied (Cu and Sn) and the amplitude of the roughness is varied. The simulations show that the associated distributions exhibit a generic behavior with the sum of two distinct terms of varying weight, following the expansion rate of the jets: in the small size limit, the distribution obeys a power law dependence with an exponent equal to 1.15 ± 0.08; and in the large size limit, it obeys an exponential form. These two components are interpreted, with the help of additional simple simulations, as the signature of two different basic mechanisms of fragmentation. The power law dependence results from the fragmentation of a 2D network of ligaments arranged following a fractal (scale free) geometry and generated when the sheets of liquid metal expand and tear. The exponential distribution results from a 1D Poisson fragmentation process of the largest ligaments previously generated. Unlike the power law distribution, it is governed by a characteristic length scale, which may be provided by energy balance principle
Relaxation rates in the Maxwellian collision model and its variable hard sphere surrogate
Rubinstein, Robert
2015-08-01
The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in direct simulation Monte Carlo calculations. We attempt to provide theoretical support for this remarkable success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian collision model with those of its variable hard sphere surrogate. The comparison demonstrates that the linearized collision operator with variable hard sphere interactions can accurately approximate the linearized collision operator with Maxwellian inverse power law interactions under well-defined and broadly applicable conditions. Extensions of the analysis to the general inverse power law model and to more realistic intermolecular potentials are briefly discussed.
We have derived asymptotic forms for the degree of polarization of the optically thin synchrotron and for synchrotron self-absorption (SSA) spectra assuming a power-law particle distribution of the form N(γ) ∼ γ–p with γ1 2, especially for a finite high-energy limit, γ2, in the case of an arbitrary pitch angle. The new results inferred concern more especially the high-frequency range x >> η2 with parameter η = γ2/γ1. The calculated SSA spectra concern instantaneous photon emission where cooling effects are not considered. They have been obtained by also ignoring likely effects such as Comptonization, pair creation and annihilation, as well as magnetic photon splitting. To that aim, in addition to the two usual absorption frequencies, a third possible one has been derived and expressed in terms of the Lambert W function based on the analytical asymptotic form of the absorption coefficient, αν, for the high-frequency range ν >> ν2 (with ν2 the synchrotron frequency corresponding to γ2). We have shown that the latter frequency may not have realistic applications in astrophysics, except in the case of an adequate set of parameters allowing one to neglect Comptonization effects. More detailed calculations and discussions are presented.
Schmidt, Robert; Krasselt, Cornelius; Göhler, Clemens; von Borczyskowski, Christian
2014-04-22
The photoluminescence (PL) of single emitters like semiconductor quantum dots (QDs) shows PL intermittency, often called blinking. We explore the PL intensities of single CdSe/ZnS QDs in polystyrene (PS), on polyvenylalcohol (PVA), and on silicon oxide (SiOx) by the change-point analysis (CPA). By this, we relate results from the macrotime (sub-ms to 1000 s) and the microtime (0.1-100 ns) range to discrete PL intensities. We conclude that the intensity selected "on"-times in the ms range correspond to only a few (discrete) switching times, while the PL decays in the ns range are multiexponential even with respect to the same selected PL intensity. Both types of relaxation processes depend systematically on the PL intensity in course of a blinking time trace. The overall distribution of on-times does not follow a power law contrary to what has often been reported but can be compiled into 3-4 characteristic on-times. The results can be explained by the recently suggested multiple recombination centers model. Additionally, we can identify a well-defined QD state with a very low PL intensity above the noise level, which we assign to the strongly quenched exciton state. We describe our findings by a model of a hierarchical sequence of hole and electron trapping. Blinking events are the consequence of slow switching processes among these states and depend on the physicochemical properties of the heterogeneous nanointerface of the QDs. PMID:24580107
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
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
Power laws and self-organized criticality in theory and nature
Marković, Dimitrije, E-mail: markovic@cbs.mpg.de [Institute for Theoretical Physics, Goethe University Frankfurt (Germany); Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig (Germany); Biomagnetic Center, Hans Berger Clinic for Neurology, University Hospital Jena, Jena (Germany); Gros, Claudius, E-mail: gros@itp.uni-frankfurt.de [Institute for Theoretical Physics, Goethe University Frankfurt (Germany)
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
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.
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 ...
Scalar field probes of power-law space-time singularities
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 inverse square behaviour ∼ x-2 in the 'tortoise coordinate' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels obtained 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
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.
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.
Highly optimized tolerance and power laws in dense and sparse resource regimes
Manning, M; Doyle, J
2005-01-01
Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\\geq l)\\sim l^{-\\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\\alpha= 1+ 1/d $. In this paper we describe and analyze a third model, the cuts m...
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)
On energy boundary layer equations in power law non-Newtonian fluids
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.
Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential
We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spin-zero particles in any arbitrary spherically symmetric potential, the non-Coulombic effective power-law potential is used as a kernel to produce the spin-averaged bound states of the non-self-conjugate mesons. The analytical formulae are also applicable to the self-conjugate mesons in the equal-mass case. The flavor-independent case is investigated in this work. The calculations are carried out to the third-order correction of the energy series. Results are consistent with those obtained before. (author). 14 refs, 1 tab
A new model for the explanation of the universal dielectric response law is proposed. It differs significantly from all previous works on the subject. The presented model is based on the assumption that individual dipoles and their environment do not remain independent during the process of relaxation. Therefore, the time θi, needed for the regression to equilibrium of polarization fluctuations in a random variable which depends for each relaxing dipole on two other random variables: the waiting time ηi and the dissipation rate βi. As a consequence we derive a general relaxation equation which gives the universal dielectric response in the power law form (as a special case the stretched exponential form is obtained). (author). 47 refs, 2 figs
Exploring Parameter Constraints on Quintessential Dark Energy: the Inverse Power Law Model
Yashar, Mark; Abrahamse, Augusta; Albrecht, Andreas; Barnard, Michael
2008-01-01
We report on the results of a Markov Chain Monte Carlo (MCMC) analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data sets as a representation of future dark energy experiments. We generate simulated data sets for a Lambda-CDM background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model and present our results in the form of likelihood contours generated by these two background cosmologies. We find that the relative constraining power of the various DETF data sets on the IPL model parameters is broadly equivalent to the DETF results for the w_{0}-w_{a} parameterization of dark energy. Finally, we gauge the power of DETF "Stage 4" data by demonstrating a specific IPL model which, if realized in the universe, would allow Stage 4 data to exclude a cosmological constant at better than the 3-sigma level.
Exploring parameter constraints on quintessential dark energy: The inverse power law model
We report on the results of a Markov chain Monte Carlo analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data sets as a representation of future dark energy experiments. We generate simulated data sets for a ΛCDM background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model, and present our results in the form of likelihood contours generated by these two background cosmologies. We find that the relative constraining power of the various DETF data sets on the IPL model parameters is broadly equivalent to the DETF results for the w0-wa parametrization of dark energy. Finally, we gauge the power of DETF 'stage 4' data by demonstrating a specific IPL model which, if realized in the universe, would allow stage 4 data to exclude a cosmological constant at better than the 3σ level.
Exploring parameter constraints on quintessential dark energy: The inverse power law model
Yashar, Mark; Bozek, Brandon; Abrahamse, Augusta; Albrecht, Andreas; Barnard, Michael
2009-05-01
We report on the results of a Markov chain Monte Carlo analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data sets as a representation of future dark energy experiments. We generate simulated data sets for a ΛCDM background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model, and present our results in the form of likelihood contours generated by these two background cosmologies. We find that the relative constraining power of the various DETF data sets on the IPL model parameters is broadly equivalent to the DETF results for the w0-wa parametrization of dark energy. Finally, we gauge the power of DETF “stage 4” data by demonstrating a specific IPL model which, if realized in the universe, would allow stage 4 data to exclude a cosmological constant at better than the 3σ level.
Length of inflation and WMAP data in the case of power-law inflation
Hirai, S; Hirai, Shiro; Takami, Tomoyuki
2005-01-01
The effect of the length of inflation on the power spectra of scalar and tensor perturbations is estimated using the power-law inflation model with a scale factor of a(t) = t^q. Considering various pre-inflation models with radiation-dominated or matter-dominated periods before inflation in combination with two matching conditions, the power spectrum of curvature perturbations at large scales is calculated. Comparison of the derived angular power spectrum with the Wilkinson Microwave Anisotropy Probe (WMAP) data reveals a possibility that the WMAP can be explained by the finite length of inflation model if the length of inflation is near 60 e-folds and q>200.
Power-Law Behavior in Signal Scattering Process in Vertical Granular Chain with Light Impurities
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
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.
Mass transport in a thin layer of power-law fluid in an Eulerian coordinate system
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.
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.
Costa, U. M. S.; Lyra, M. L.; Plastino, A. R.; Tsallis, C.
1997-07-01
Power-law sensitivity to initial conditions, characterizing the behavior of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear one-dimensional logisticlike maps xt+1=1-a\\|xt\\|z (z>1 00[Δx(t)/Δx(0)]=[1+(1-q)λqt]1/(1-q) (equal to eλ1t for q=1, and proportional, for large t, to t1/(1-q) for q≠1 q∈R is the entropic index appearing in the recently introduced nonextensive generalized statistics). The relation between the parameter q and the fractal dimension df of the onset-to-chaos attractor is revealed: q appears to monotonically decrease from 1 (Boltzmann-Gibbs, extensive, limit) to -∞ when df varies from 1 (nonfractal, ergodiclike, limit) to zero.
Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions
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
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.
Onsager vortex formation in Bose-Einstein condensates in two-dimensional power-law traps
Groszek, Andrew J.; Simula, Tapio P.; Paganin, David M.; Helmerson, Kristian
2016-04-01
We study computationally dynamics of quantized vortices in two-dimensional superfluid Bose-Einstein condensates confined in highly oblate power-law traps. We have found that the formation of large-scale Onsager vortex clusters prevalent in steep-walled traps is suppressed in condensates confined by harmonic potentials. However, the shape of the trapping potential does not appear to adversely affect the evaporative heating efficiency of the vortex gas. Instead, the suppression of Onsager vortex formation in harmonic traps can be understood in terms of the energy of the vortex configurations. Furthermore, we find that the vortex-antivortex pair annihilation that underpins the vortex evaporative heating mechanism requires the interaction of at least three vortices. We conclude that experimental observation of Onsager vortices should be the most apparent in flat or inverted-bottom traps.
Quantum Probes of Timelike Naked Singularities in 2+1-Dimensional Power-Law Spacetimes
The formation of naked singularities in 2+1-dimensional power-law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field, respectively, are considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon and Dirac equations are used to probe the classical timelike naked singularities developed at r=0. We show that when the classically singular spacetimes probed with scalar waves, the considered spacetimes remain singular. However, the spinorial wave probe of the singularity in the metric of a self-interacting real scalar field remains quantum regular. The notable outcome in this study is that the quantum regularity/singularity cannot be associated with the energy conditions
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.
Real critical current density and material power law of YBa2Cu3O7-δ
The current-voltage characteristics have been measured on a YBa2Cu3O7-δ epitaxial thin film. Using a material power law, we determine the temperature and field dependencies of the characteristic pinning potential UJ and the real critical current density Jc at different fields and temperatures. It is shown that Jc is completely different from the conventional critical current density JE, which is determined by the electronic-field criterion. Thus, the time-honoured electronic-field criterion is no longer reasonable for high-Tc superconductors. By further investigation of the results of Jc and UJ, we are able to present a physical picture of the transformation of the pinning potential well with increasing temperature and hence determine the transition point from vortex-glass phase to vortex-liquid phase. Copyright (2000) CSIRO Australia
Elastic-plastic growth of plane stress mode II cracks in power law hardening solids
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
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.
OBTAINING THE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINNING FOR POWER LAW POLYMER FLUIDS
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.
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.
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.
Critical Scaling of Extended Power Law Ⅰ-Ⅴ Isotherms near Vortex Glass Transition
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.
Numerical extension of the power law Jc(B) to zero field in thin superconducting films
Numerical simulations of the current and field distribution in thin superconducting films are carried out for a given material law Jc(B) and as a function of the applied field H, taking the sample's self-field into account. The dependence of the critical current density on the applied field Jc(H) is computed for comparison with experiment, considering the geometry of transport measurements. We show that extrapolating the high-field power law Jc∝B-α to the lowest fields results in a finite critical current at zero applied field Jc(H=0), despite the singularity of Jc(B). Moreover, particular features of the experiment, such as a low field plateau in Jc(H), are reproduced and found to be determined by the self-field.
The Cost of Mitigating Power Law Delay in Random Access Networks
Bi, Suzhi
2012-01-01
Exponential backoff (EB) is a widely adopted collision resolution mechanism in many popular random-access networks including Ethernet and WLAN. The prominence of EB is primarily attributed to its asymptotic throughput stability, which ensures a non-zero throughput even when the number of users in the network goes to infinity. Recent studies, however, show that EB is fundamentally unsuitable for applications that are sensitive to large delay and delay jitters, as it induces divergent second- and higher-order moments of medium access delay. Essentially, the medium access delay follows a power law distribution, a subclass of heavy-tailed distribution. To understand and alleviate the issue, this paper systematically analyzes the tail delay distribution of general backoff functions, with EB being a special case. In particular, we establish a tradeoff between the tail decaying rate of medium access delay distribution and the stability of throughput. To be more specific, convergent delay moments are attainable only ...
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.
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.
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.
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...
Dipole–dipole interactions in optical lattices do not follow an inverse cube power law
We study the effective dipole–dipole interactions in ultracold quantum gases on optical lattices as a function of asymmetry in confinement along the principal axes of the lattice. In particular, we study the matrix elements of the dipole–dipole interaction in the basis of lowest band Wannier functions which serve as a set of low-energy states for many-body physics on the lattice. We demonstrate that, for shallow lattices in quasi-reduced dimensional scenarios, the effective interaction between dipoles in an optical lattice is non-algebraic in the inter-particle separation at short to medium distance on the lattice scale and has a long-range power-law tail, in contrast to the pure power-law behavior of the dipole–dipole interaction in free space. The modifications to the free-space interaction can be sizable; we identify differences of up to 36% from the free-space interaction at the nearest-neighbor distance in quasi-one-dimensional arrangements. The interaction difference depends essentially on asymmetry in confinement, due to the d-wave anisotropy of the dipole–dipole interaction. Our results do not depend on statistics, applying to both dipolar Bose–Einstein condensates and degenerate Fermi gases. Using matrix product state simulations, we demonstrate that use of the correct lattice dipolar interaction leads to significant deviations from many-body predictions using the free-space interaction. Our results are relevant to up and coming experiments with ultracold heteronuclear molecules, Rydberg atoms and strongly magnetic atoms in optical lattices. (paper)
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.
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.
Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-01-01
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. PMID:22355125
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
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
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...
Hughes, Timothy; Liberles, David A
2008-05-15
Genome sequencing has shown that the number of homologous gene families of a given size declines rapidly with family size. A power-law has been shown to provide the best mathematical description of this relationship. However, it remains unclear what evolutionary forces drive this observation. We use models of gene duplication, pseudogenisation and accumulation of replacement substitutions, which have been validated and parameterised using genomic data, to build a model of homologous gene evolution. We use this model to simulate the evolution of the distribution of gene family size and show that the power-law distribution is driven by the pseudogenisation rate's heterogeneity across gene families and its correlation within families. Moreover, we show that gene duplication and pseudogenisation are necessary and sufficient for the emergence of the power-law. PMID:18378100
Sensitivity of the power-law exponent in gene expression distribution to mRNA decay rate
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...
Shiner, J S
1999-01-01
The disorder and a simple convex measure of complexity are studied for rank ordered power law distributions, indicative of criticality, in the case where the total number of ranks is large. It is found that a power law distribution may produce a high level of complexity only for a restricted range of system size (as measured by the total number of ranks), with the range depending on the exponent of the distribution. Similar results are found for disorder. Self-organized criticality thus does ...
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.
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.
Discovery of Power-Law Growth in the Self-Renewal of Heterogeneous Glioma Stem Cell Populations.
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
Dayane Rosalyn Izidoro
2009-12-01
Full Text Available In this work, the rheological behaviour of emulsions (mayonnaises stabilized by green banana pulp using the response surface methodology was studied. In addition, the emulsions stability was investigated. Five formulations were developed, according to design for constrained surfaces and mixtures, with the proportion, respectively: water/soy oil/green banana pulp: F1 (0.10/0.20/0.70, F2 (0.20/0.20/0.60, F3 (0.10/0.25/0.65, F4 (0.20/0.25/0.55 and F5 (0.15/0.225/0.625 .Emulsions rheological properties were performed with a rotational Haake Rheostress 600 rheometer and a cone and plate geometry sensor (60-mm diameter, 2º cone angle, using a gap distance of 1mm. The emulsions showed pseudoplastic behaviour and were adequately described by the Power Law model. The rheological responses were influenced by the difference in green banana pulp proportions and also by the temperatures (10 and 25ºC. The formulations with high pulp content (F1 and F3 presented higher shear stress and apparent viscosity. Response surface methodology, described by the quadratic model,showed that the consistency coefficient (K increased with the interaction between green banana pulp and soy oil concentration and the water fraction contributed to the flow behaviour index increase for all emulsions samples. Analysis of variance showed that the second-order model had not significant lack-of-fit and a significant F-value, indicating that quadratic model fitted well into the experimental data. The emulsions that presented better stability were the formulations F4 (0.20/0.25/0.55 and F5 (0.15/0.225/0.625.No presente trabalho, foi estudado o comportamento reológico de emulsões adicionadas de polpa de banana verde utilizando a metodologia de superfície de resposta e também foram investigadas a estabilidade das emulsões. Foram desenvolvidas cinco formulações, de acordo com o delineamento para superfícies limitadas e misturas, com as proporções respectivamente: água/óleo de
Cusp-latitude Pc3 spectra: band-limited and power-law components
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
Hui, D.; Luo, Y.; Jackson, R. B.
2005-12-01
A power function, Y=Y0 Mbeta, can be used to describe the relationship of physiological variables with body size over a wide range of scales, typically many orders of magnitude. One of the key issues in the renewed power law debate is whether the allometric scaling exponent β equals 3/4 or 2/3. The analysis could be remarkably affected by sampling size, measurement error, and analysis methods, but these effects have not been explored systematically. We investigated the influences of these three factors based on a data set of 626 pairs of base metabolic rate and mass in mammals with the calculated β=0.711. Influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo approach. Results showed that estimated parameter b varied considerably from sample to sample. For example, when the sample size was n=63, b varied from 0.582 to 0.776. Even though the original data set did not support either β=3/4 or β=2/3, we found that 39.0% of the samples supported β=2/3, 35.4% of the samples supported β=3/4. Influence of measurement error on parameter estimations was also tested using Bayesian theory. Virtual data sets were created using the mass in the above-mentioned data set, with given parameters α and β (β=2/3 or β=3/4) and certain measurement error in base metabolic rate and/or mass. Results showed that as measurement error increased, more estimated bs were found to be significantly different from the parameter β. When measurement error (i.e., standard deviation) was 20% and 40% of the measured mass and base metabolic rate, 15.4% and 14.6% of the virtual data sets were found to be significant different from the parameter β=3/4 and β=2/3, respectively. Influence of different analysis methods on parameter estimations was also demonstrated using the original data set and the pros and cons of these methods were further discussed. We urged cautions in interpreting the power law analysis, especially from a small data sample, and