International Nuclear Information System (INIS)
Ackermann, M.; Bechtol, K.; Berenji, B.; Blandford, R. D.; Bloom, E. D.; Borgland, A. W.; Bouvier, A.; Asano, K.; Atwood, W. B.; Axelsson, M.; Baldini, L.; Bellazzini, R.; Bregeon, J.; Ballet, J.; Barbiellini, G.; Baring, M. G.; Bastieri, D.; Bhat, P. N.; Bissaldi, E.; Bonamente, E.
2010-01-01
We present detailed observations of the bright short-hard gamma-ray burst GRB 090510 made with the Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) on board the Fermi observatory. GRB 090510 is the first burst detected by the LAT that shows strong evidence for a deviation from a Band spectral fitting function during the prompt emission phase. The time-integrated spectrum is fit by the sum of a Band function with E peak = 3.9 ± 0.3 MeV, which is the highest yet measured, and a hard power-law component with photon index -1.62 ± 0.03 that dominates the emission below ∼20 keV and above ∼100 MeV. The onset of the high-energy spectral component appears to be delayed by ∼0.1 s with respect to the onset of a component well fit with a single Band function. A faint GBM pulse and a LAT photon are detected 0.5 s before the main pulse. During the prompt phase, the LAT detected a photon with energy 30.5 +5.8 -2.6 GeV, the highest ever measured from a short GRB. Observation of this photon sets a minimum bulk outflow Lorentz factor, Γ∼> 1200, using simple γγ opacity arguments for this GRB at redshift z = 0.903 and a variability timescale on the order of tens of ms for the ∼100 keV-few MeV flux. Stricter high confidence estimates imply Γ ∼> 1000 and still require that the outflows powering short GRBs are at least as highly relativistic as those of long-duration GRBs. Implications of the temporal behavior and power-law shape of the additional component on synchrotron/synchrotron self-Compton, external-shock synchrotron, and hadronic models are considered.
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin
2014-10-10
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 σ ≡ B(2)/(4πnm(e)c(2))>1 and when the system size is sufficiently large. In the limit σ ≫ 1, the spectral index approaches p = 1 and most of the available energy is converted into nonthermal 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.
A Hard X-Ray Power-Law Spectral Cutoff in Centaurus X-4
DEFF Research Database (Denmark)
Chakrabarty, Deepto; Tomsick, John A.; Grefenstette, Brian W.
2015-01-01
The low-mass X-ray binary Cen X-4 is the brightest and closest (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...
A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4
Energy Technology Data Exchange (ETDEWEB)
Chakrabarty, Deepto; Nowak, Michael A. [MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Tomsick, John A.; Boggs, Steven E.; Craig, William W. [Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States); Grefenstette, Brian W.; Fürst, Felix; Harrison, Fiona A.; Rana, Vikram [Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States); Psaltis, Dimitrios [Department of Astronomy, University of Arizona, Tucson, AZ 85721 (United States); Bachetti, Matteo; Barret, Didier [Observatoire Midi-Pyrénées, Université de Toulouse III - Paul Sabatier, F-31400 Toulouse (France); Christensen, Finn E. [Division of Astrophysics, National Space Institute, Technical University of Denmark, DK-2800 Lyngby (Denmark); Hailey, Charles J. [Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027 (United States); Kaspi, Victoria M. [Department of Physics, McGill University, Montreal, PQ H3A 2T8 (Canada); Miller, Jon M. [Department of Astronomy, University of Michigan, Ann Arbor, MI 48109 (United States); Stern, Daniel [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 (United States); Wik, Daniel R.; Zhang, William W. [Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Wilms, Jörn, E-mail: deepto@mit.edu [Dr. Karl-Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Universität Erlangen-Nürnberg, D-96049 Bamberg (Germany)
2014-12-20
The low-mass X-ray binary (LMXB) Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1×10{sup 33} D{sub kpc}{sup 2} erg s{sup –1}, with ≅60% in the thermal component. We clearly detect a cutoff of the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. We show that thermal Comptonization and synchrotron shock origins for the hard X-ray emission are ruled out on physical grounds. However, the hard X-ray spectrum is well fit by a thermal bremsstrahlung model with kT{sub e} = 18 keV, which can be understood as arising either in a hot layer above the neutron star atmosphere or in a radiatively inefficient accretion flow. The power-law cutoff energy may be set by the degree of Compton cooling of the bremsstrahlung electrons by thermal seed photons from the neutron star surface. Lower thermal luminosities should lead to higher (possibly undetectable) cutoff energies. We compare Cen X-4's behavior with PSR J1023+0038, IGR J18245–2452, and XSS J12270–4859, which have shown transitions between LMXB and radio pulsar modes at a similar X-ray luminosity.
Evidence for two hard X-ray components in double power-law fits to the 1980 June 7 flare
Smith, Dean F.; Orwig, Larry E.
1988-01-01
The June 7, 1980 flare at 0312 UT was analyzed with double power-law fits on the basis of SMM hard X-ray burst spectrometer data. The flare is found to consist of seven peaks of characteristic time scale of about 8 sec followed by seven valleys which may contain significant peak components because of overlap. It is suggested that the possibility of thermal spectra for the peaks is unlikely. An investigation of the double power-law parameters through the third and fourth peaks revealed a hysteresis effect in the fourth peak. The present results have been interpreted in terms of a trap plus precipitation model.
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.
Zhang, Q.; Xiong, S. L.; Song, L. M.
2018-04-01
Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of p. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with p > 2, there are still a few GRBs suggestive of a hard (p power-law hard electron energy (DPLH) spectrum with 1 2 and an “injection break” assumed as γ b ∝ γ q in the highly relativistic regime, where γ is the bulk Lorentz factor of the jet. In this paper, we show that GRB 060614 and GRB 060908 provide further evidence for such a DPLH spectrum. We interpret the multiband afterglow of GRB 060614 with the DPLH model in a homogeneous interstellar medium by taking into account a continuous energy injection process, while, for GRB 060908, a wind-like circumburst density profile is used. The two bursts, along with GRB 091127, suggest a similar behavior in the evolution of the injection break, with q ∼ 0.5. Whether this represents a universal law of the injection break remains uncertain and more afterglow observations such as these are needed to test this conjecture.
Thomas, Hoben
1981-01-01
Psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions are examined. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates given for several common estimation situations.…
International Nuclear Information System (INIS)
Lucchin, F.; Matarrese, S.
1985-01-01
The outstanding cosmological problems (horizon, flatness, . . .) which may be solved by the usual inflationary models may also find a solution in the frame of a ''generalized'' inflationary cosmology which is characterized by a suitable phase of accelerated expansion. The usual exponential growth of the scale factor S is just a particular case of such a general idea. Following this line of thought, we study in some detail a simple inflationary model characterized by a scale factor which grows like Sapprox.t/sup p/, with p a constant greater than one, which we call power-law inflation (PLI). Some properties of PLI have been analyzed, in different contexts, also by other authors. We consider the constraints on this model coming from the requirement of solving the horizon, flatness, ''good'' reheating, and ''convenient'' perturbation-spectrum problems. In order to obtain the perturbation spectrum when re-entering the horizon during the Friedmann phase, we extend to PLI the gauge-invariant approach developed by Bardeen et al. for the usual inflationary models. We find that the above constraints can be suitably satisfied. Finally, we outline possible connections between PLI and particular inflationary models which have recently been proposed
Power laws in Ising nanostripes
International Nuclear Information System (INIS)
Drzewinski, A.; Sznajd, J.; Szota, K.
2005-01-01
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)
Power laws for nuclear observables
Peterson, R. J.
2018-01-01
Often mass-dependent nuclear observables are summarized by fits to a power law in the nuclear mass A , as proportional to Aα. In this work a simple justification of this usage is presented, also providing a simple expression for the exponent α , with one known parameter being the beam-nucleon total cross section and another parameter being a nuclear size r0A1 /3 . Measured power-law exponents α for total and reaction cross sections are near this simple formulation using r0=1.6 fm , whereas quasifree observables are near the simple expression using r0=1.2 fm .
Waves in plasmas with power-law distributions
International Nuclear Information System (INIS)
Hellberg, M.A.
2000-01-01
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
Power Laws in Firm Productivity
Mizuno, T.; Ishikawa, A.; Fujimoto, S.; Watanabe, T.
We estimate firm productivity for about 3.2 million firms from30 countries. We find that the distribution of firm productivity in each country, which is measured by total factor productivity (TFP), has a power law upper tail. However, the power law exponent of a TFP distribution in a country tends to be greater than that of a sales distribution in that country, indicating that the upper tail of a TFP distribution is less heavy compared to that of a sales distribution. We also find that the power law exponent of a TFP distribution tends to be greater than the power law exponents associated with the number of workers or tangible fixed assets. Given the idea that the sales of a firm is determined by the amount of various inputs employed by the firm (i.e., ``production function'' in the terminology of economics), these results suggest that the heavy tail of a sales distribution in a country comes not from the tail of a TFP distribution, but from the tail of the distribution of the number of workers or tangible fixed assets.
Quantum dissipation from power-law memory
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2012-01-01
A new quantum dissipation model based on memory mechanism is suggested. Dynamics of open and closed quantum systems with power-law memory is considered. The processes with power-law memory are described by using integration and differentiation of non-integer orders, by methods of fractional calculus. An example of quantum oscillator with linear friction and power-law memory is considered. - Highlights: ► A new quantum dissipation model based on memory mechanism is suggested. ► The generalization of Lindblad equation is considered. ► An exact solution of generalized Lindblad equation for quantum oscillator with linear friction and power-law memory is derived.
Automated image enhancement using power law transformations
Indian Academy of Sciences (India)
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 ...
Automated image enhancement using power law transformations
Indian Academy of Sciences (India)
Abstract. 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 ...
Power-Law Indices of Time Properties on Energy Zhao-Yang Peng
Indian Academy of Sciences (India)
of Gamma-Ray Burst (GRB) prompt emission. In earlier statistical analysis, GRB pulse width on energy was found to be a power-law function (e.g., Fenimore et al. 1995, Norris et al. 1996, Peng et al. 2006). Zhang & Qin (2008) found that this power-law relationship can be extended to X-ray bands. In addition, Zhang et al.
Power laws from linear neuronal cable theory
DEFF Research Database (Denmark)
Pettersen, Klas H; Lindén, Henrik Anders; Tetzlaff, Tom
2014-01-01
suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general...... expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements...... to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency [Formula: see text] power laws with power-law exponents analytically identified as [Formula: see text] for the soma...
Power-law Statistics of Driven Reconnection in the Magnetically Closed Corona
Knizhnik, K. J.; Uritsky, V. M.; Klimchuk, J. A.; DeVore, C. R.
2018-01-01
Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere.
Deformation of a Capsule in a Power-Law Shear Flow.
Tian, Fang-Bao
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
Corner Flow of Power Law Fluids
DEFF Research Database (Denmark)
Henriksen, P.; Hassager, Ole
1989-01-01
A local analysis of the flow of power law fluids near corners is performed. The equation for the stream function is shown to allow separated solutions in plane polar coordinates. The radial behavior is shown to be algebraic and results are given for the exponent for different values of corner angle...
Instabilities in power law gradient hardening materials
DEFF Research Database (Denmark)
Niordson, Christian Frithiof; Tvergaard, Viggo
2005-01-01
Tension and compression instabilities are investigated for specimens with dimensions in the micron range. A finite strain generalization of a higher order strain gradient plasticity theory is implemented in a finite element scheme capable of modeling power law hardening materials. Effects...
Power Laws, Scale-Free Networks and Genome Biology
Koonin, Eugene V; Karev, Georgy P
2006-01-01
Power Laws, Scale-free Networks and Genome Biology deals with crucial aspects of the theoretical foundations of systems biology, namely power law distributions and scale-free networks which have emerged as the hallmarks of biological organization in the post-genomic era. The chapters in the book not only describe the interesting mathematical properties of biological networks but moves beyond phenomenology, toward models of evolution capable of explaining the emergence of these features. The collection of chapters, contributed by both physicists and biologists, strives to address the problems in this field in a rigorous but not excessively mathematical manner and to represent different viewpoints, which is crucial in this emerging discipline. Each chapter includes, in addition to technical descriptions of properties of biological networks and evolutionary models, a more general and accessible introduction to the respective problems. Most chapters emphasize the potential of theoretical systems biology for disco...
Power law analysis of the human microbiome.
Ma, Zhanshan Sam
2015-11-01
Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs. © 2015 John Wiley & Sons Ltd.
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.
Zipf's law, power laws and maximum entropy
International Nuclear Information System (INIS)
Visser, Matt
2013-01-01
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 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)
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.
Instabilities in power law gradient hardening materials
DEFF Research Database (Denmark)
Niordson, Christian Frithiof; Tvergaard, Viggo
2005-01-01
Tension and compression instabilities are investigated for specimens with dimensions in the micron range. A finite strain generalization of a higher order strain gradient plasticity theory is implemented in a finite element scheme capable of modeling power law hardening materials. Effects...... of 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....
Gibbsian theory of power-law distributions.
Treumann, R A; Jaroschek, C H
2008-04-18
It is shown that power-law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium, which are expected to occur in collisionless plasmas containing fully developed quasistationary turbulence. Gibbsian theory is extended on the fundamental level to statistically dependent subsystems introducing an "ordering parameter" kappa. Particular forms for the entropy and partition functions are derived with superadditive (nonextensive) entropy, and a redefinition of temperature in such systems is given.
Beyond the power law: Uncovering stylized facts in interbank networks
Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen
2015-06-01
We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.
Power Law Analysis of Financial Index Dynamics
Directory of Open Access Journals (Sweden)
J. Tenreiro Machado
2012-01-01
Full Text Available Power law (PL and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices (DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.
Existence Theory for Stochastic Power Law Fluids
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Random sequential addition of hard spheres in high Euclidean dimensions
Torquato, S.; Uche, O. U.; Stillinger, F. H.
2006-12-01
Sphere packings in high dimensions have been the subject of recent theoretical interest. Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in d -dimensional Euclidean space Rd in the infinite-time or saturation limit for the first six space dimensions (1≤d≤6) . Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each of these dimensions. We find that for 2≤d≤6 , the saturation density ϕs scales with dimension as ϕs=c1/2d+c2d/2d , where c1=0.202048 and c2=0.973872 . We also show analytically that the same density scaling is expected to persist in the high-dimensional limit, albeit with different coefficients. A byproduct of this high-dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by ϕs≥(d+2)(1-S0)/2d+1 , where S0ɛ[0,1] is the structure factor at k=0 (i.e., infinite-wavelength number variance) in the high-dimensional limit. We demonstrate that a Palàsti-type conjecture (the saturation density in Rd is equal to that of the one-dimensional problem raised to the d th power) cannot be true for RSA hyperspheres. We show that the structure factor S(k) must be analytic at k=0 and that RSA packings for 1≤d≤6 are nearly “hyperuniform.” Consistent with the recent “decorrelation principle,” we find that pair correlations markedly diminish as the space dimension increases up to six. We also obtain kissing (contact) number statistics for saturated RSA configurations on the surface of a d -dimensional sphere for dimensions 2≤d≤5 and compare to the maximal kissing numbers in these dimensions. We determine the structure factor exactly for the related “ghost” RSA packing in Rd and demonstrate that its distance from “hyperuniformity” increases as the space dimension increases, approaching a constant asymptotic value
Deformation of a Capsule in a Power-Law Shear Flow
Directory of Open Access Journals (Sweden)
Fang-Bao Tian
2016-01-01
Full Text Available An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid. In this method, the flexible structure (e.g., capsule dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Poissonian renormalizations, exponentials, and power laws
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Anisotropic power-law k-inflation
Ohashi, Junko; Soda, Jiro; Tsujikawa, Shinji
2013-11-01
It is known that power-law k-inflation can be realized for the Lagrangian P=Xg(Y), where X=-(∂ϕ)2/2 is the kinetic energy of a scalar field ϕ and g is an arbitrary function in terms of Y=Xeλϕ/Mpl (λ is a constant and Mpl is the reduced Planck mass). In the presence of a vector field coupled to the inflaton with an exponential coupling f(ϕ)∝eμϕ/Mpl, we show that the models with the Lagrangian P=Xg(Y) generally give rise to anisotropic inflationary solutions with Σ/H=constant, where Σ is an anisotropic shear and H is an isotropic expansion rate. Provided these anisotropic solutions exist in the regime where the ratio Σ/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 and the Dirac-Born-Infeld model and we numerically show that the solutions with different initial conditions converge to the anisotropic power-law inflationary attractors. Even in the de Sitter limit (λ→0) such solutions can exist, but in this case the null energy condition is generally violated. The latter property is consistent with the Wald’s cosmic conjecture stating that the anisotropic hair does not survive on the de Sitter background in the presence of matter respecting the dominant/strong energy conditions.
Power law creep of polycarbonate by Berkovich nanoindentation
Gao, Chenghui; Liu, Ming
2017-10-01
Power-law creep of polycarbonate was investigated by Berkovich indentation under three different conditions at room temperature, namely: constant displacement rate condition, constant displacement loading condition, and constant ratio of loading rate over load condition. Only the data during the loading process were analysed, and the experiments under different loading conditions gave consistent results that accorded well with theoretical prediction by dimensional analysis of indentation of power-law creep material. Material constants were characterized by curve fitting of the experimental results with theoretical equations, and the power law exponent for the power-law creep relation was found to be about 0.138 for the notably soft polycarbonate.
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.
Power law scaling in synchronization of brain signals depends on cognitive load
Directory of Open Access Journals (Sweden)
Jose Luis ePerez Velazquez
2014-05-01
Full Text Available As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task. There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa, which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviours.
A mechanism producing power law etc. distributions
Li, Heling; Shen, Hongjun; Yang, Bin
2017-07-01
Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.
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.
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning.
Enhanced discriminability for nonbiological motion violating the two-thirds power law.
Salomon, Roy; Goldstein, Ariel; Vuillaume, Laurène; Faivre, Nathan; Hassin, Ran R; Blanke, Olaf
2016-06-01
The two-thirds power law describes the relationship between velocity and curvature in human motor movements. Interestingly, this motor law also affects visual motion perception, in which stimuli moving according to the two-thirds power law are perceived to have a constant velocity compared to stimuli actually moving at constant velocity. Thus, visual motion adhering to biological motion principles causes a kinematic illusion of smooth and velocity-invariant motion. However, it is yet unclear how this motion law affects the discrimination of visual stimuli and if its encoding requires attention. Here we tested the perceptual discrimination of stimuli following biological (two-thirds power law) or nonbiological movement under conditions in which the stimuli were degraded or masked through continuous flash suppression. Additionally, we tested subjective perception of naturalness and velocity consistency. Our results show that the discriminability of a visual target is inversely related to the perceived "naturalness" of its movement. Discrimination of stimuli following the two-thirds power law required more time than the same stimuli moving at constant velocity or nonecological variants of the two-thirds power law and was present for both masked and degraded stimuli.
Constraints on the tensor-to-scalar ratio for non-power-law models
International Nuclear Information System (INIS)
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M.P.
2013-01-01
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r LD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys
Power series like relation of power law and coupled creep ...
African Journals Online (AJOL)
When a solid deforms at high temperature its microstructure may in some sense be altered- holes and cracks may nucleate and grow inside the solid by various mechanism controlled by diffusion and by power law creep or by a combination of these mechanisms. Considering a coupled diffusion power law creep mechanism ...
determination of the power law exponent for southern highlands
African Journals Online (AJOL)
Mgina
ABSTRACT. The 1/7th power law is among the methods that have been used to extrapolate wind speed to the hub heights of wind turbines from the measuring levels. However, it tends to underestimate the actual long-term average wind speeds. In this paper, the power law exponent for Makambako, a site located in the ...
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.
Prevention of damage and 'residual risk' in nuclear power laws
International Nuclear Information System (INIS)
Greipl, C.
1992-01-01
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.) [de
Power-law confusion: You say incremental, I say differential
Colwell, Joshua E.
1993-01-01
Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.
Fractional power-law spatial dispersion in electrodynamics
International Nuclear Information System (INIS)
Tarasov, Vasily E.; Trujillo, Juan J.
2013-01-01
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media
Visiting Power Laws in Cyber-Physical Networking Systems
Directory of Open Access Journals (Sweden)
Ming Li
2012-01-01
Full Text Available Cyber-physical networking systems (CPNSs are made up of various physical systems that are heterogeneous in nature. Therefore, exploring universalities in CPNSs for either data or systems is desired in its fundamental theory. This paper is in the aspect of data, aiming at addressing that power laws may yet be a universality of data in CPNSs. The contributions of this paper are in triple folds. First, we provide a short tutorial about power laws. Then, we address the power laws related to some physical systems. Finally, we discuss that power-law-type data may be governed by stochastically differential equations of fractional order. As a side product, we present the point of view that the upper bound of data flow at large-time scaling and the small one also follows power laws.
Fractional power-law spatial dispersion in electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation); Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain); Trujillo, Juan J., E-mail: jtrujill@ullmat.es [Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain)
2013-07-15
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media.
Power laws in citation distributions: evidence from Scopus.
Brzezinski, Michal
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in "Physics and Astronomy". Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.
Analysis of electroosmotic flow of power-law fluids in a slit microchannel.
Zhao, Cunlu; Zholkovskij, Emilijk; Masliyah, Jacob H; Yang, Chun
2008-10-15
Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.
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.
Modified power law equations for vertical wind profiles. [in investigation of windpower plant siting
Spera, D. A.; Richards, T. R.
1979-01-01
In an investigation of windpower plant siting, equations are presented and evaluated for a wind profile model which incorporates both roughness and wind speed effects, while retaining the basic simplicity of the Hellman power law. These equations recognize the statistical nature of wind profiles and are compatible with existing analytical models and recent wind profile data. Predictions of energy output based on the proposed profile equations are 10% to 20% higher than those made with the 1/7 power law. In addition, correlation between calculated and observed blade loads is significantly better at higher wind speeds when the proposed wind profile model is used than when a constant power model is used.
Why does the power law for stock price hold?
International Nuclear Information System (INIS)
Kaizoji, Taisei; Miyano, Michiko
2016-01-01
The aim of this paper is to explain why the power law for stock price holds. We first show that the complementary cumulative distributions of stock prices follow a power law using a large database assembled from the balance sheets and stock prices of a number of worldwide companies for the period 2004 through 2013. Secondly, we estimate company fundamentals from a simple cross-sectional regression model using three financial indicators-dividends per share, cash flow per share, and book value per share—as explanatory variables for stock price. Thirdly, we demonstrate that the complementary cumulative distributions of fundamentals follow a power law. We find that the power laws for stock prices and for fundamentals hold for the 10-year period of our study, and that the estimated values of the power law exponents are close to unity. Furthermore, we illustrate that the tail distribution of fundamentals closely matches the tail distribution of stock prices. On these grounds, we conclude that the power law for stock price is caused by the power law behavior of the fundamentals.
Helmholtz solitons in power-law optical materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-01-01
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
Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes
Walicka, A.
2018-02-01
In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.
Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources
Fiorito, Ralph; Titarchuk, Lev
2004-01-01
Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.
Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes
Directory of Open Access Journals (Sweden)
Walicka A.
2018-02-01
Full Text Available In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.
Hard Fats As Additives In Palm Oil And Its Relationships To Crystallization Process And Polymorphism
de Oliveira; Glazieli Marangoni; Ribeiro; Ana Paula Badan; dos Santos; Adenilson Oliveira; Cardoso; Lisandro Pavie; Kieckbusch; Theo Guenter
2016-01-01
The application of palm oil in fat-based product can be inappropriate due to its low crystallization rates and formation of crystalline clusters in post-processing stages. The adjustment of these properties can be achieved with the addition of hard fats, which are low-cost industrial products resulting from the process of total catalytic hydrogenation of liquid oils. During the crystallization of palm oil, these components can act as preferential nuclei in a crystalline ordering process, and ...
Synergetic effect of additives on the hardness and adhesion of thin electrodeposited copper films
Directory of Open Access Journals (Sweden)
Mladenović Ivana
2017-01-01
Full Text Available Thin copper films were electrodeposited on a polycrystalline coldrolled copper substrate. The composition of the laboratory-made copper sulphate electrolyte was changed by the addition of various additives. The influence of chloride ion (Cl-, polyethylene glycol (PEG and 3-mercapto-1-propane sulfonic acid (MPSA on mechanical and adhesion properties of the electrodeposited copper films was investigated using Vickers microindentation technique. Calculations of the film hardness and adhesion were carried out using composite hardness models of Korsunsky and Chen-Gao. The hardness of the composite system is influenced by the adhesion of the copper film to the substrate. Increasing adhesion corresponds to increasing values of the calculated adhesion parameter b, named the critical reduced depth. When additives are added to a plating solution, the copper deposition mechanism is changed and fine-grained microstructure without the formation of microscopic nodules is obtained. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR 32008, Grant no. TR 34011 and Grant no. III 45019
Preinflationary dynamics in loop quantum cosmology: Power-law potentials
Shahalam, M.; Sharma, Manabendra; Wu, Qiang; Wang, Anzhong
2017-12-01
In this paper, we study the preinflationary dynamics for the power-law potential [V (ϕ )∝ϕn] with n consideration and compare our results with the ones obtained previously for different potentials.
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.
Testing power-law cross-correlations: Rescaled covariance test
Czech Academy of Sciences Publication Activity Database
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
Singularity problems of the power law for modeling creep compliance
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
Stevens' power law and the problem of meaningfulness.
Augustin, Thomas
2008-05-01
Frequently, it is postulated that the results of a ratio production (resp., ratio estimation) experiment can be summarized by Stevens' power law psi=alphaphi(beta). In the present article, it is argued that the power law parameters depend, among other things, on the standard stimulus presented as a reference point, and the physical stimulus scale by which the physical intensities are measured. To formalize this idea, a new formulation of Stevens' power law is presented. We show that the exponent in Stevens' power law can only be interpreted in a meaningful way if the stimulus scale is a ratio scale. Furthermore, we present empirically testable axioms (termed invertibility and weak multiplicativity) which are both necessary and sufficient for the power law exponent to be invariant under changes of the standard stimulus. Finally, invertibility and weak multiplicativity are evaluated in a ratio production experiment. Ten participants were required to adjust the area of variable circles to prescribed ratio production factors. Both axioms are violated for all participants. The results cast doubts on the well-established practice of comparing power law exponents across different modalities.
Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology
Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang
2018-03-01
In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.
A theory of power-law distributions in financial market fluctuations.
Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, H Eugene
2003-05-15
Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financial system, huge databases now exist that facilitate the analysis of large fluctuations and the characterization of their statistical behaviour. Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations in stock price, trading volume and the number of trades. Surprisingly, the exponents that characterize these power laws are similar for different types and sizes of markets, for different market trends and even for different countries--suggesting that a generic theoretical basis may underlie these phenomena. Here we propose a model, based on a plausible set of assumptions, which provides an explanation for these empirical power laws. Our model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants. Starting from an empirical characterization of the size distribution of those large market participants (mutual funds), we show that the power laws observed in financial data arise when the trading behaviour is performed in an optimal way. Our model additionally explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades.
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.
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.
The speed-curvature power law of movements: a reappraisal.
Zago, Myrka; Matic, Adam; Flash, Tamar; Gomez-Marin, Alex; Lacquaniti, Francesco
2018-01-01
Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.
A generalization of the power law distribution with nonlinear exponent
Prieto, Faustino; Sarabia, José María
2017-01-01
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
Energy Technology Data Exchange (ETDEWEB)
Guerra L, F.V. [Instituto de Inv. En Metalurgia y Materiales UMSNH, México (Mexico); Bedolla-Jacuinde, A., E-mail: abedollj@icloud.com [Instituto de Inv. En Metalurgia y Materiales UMSNH, México (Mexico); Mejía, I. [Instituto de Inv. En Metalurgia y Materiales UMSNH, México (Mexico); Facultad de Ingeniería Mecánica UAEH, México (Mexico); Zuno, J. [Facultad de Ingeniería Mecánica UAEH, México (Mexico); Maldonado, C. [Instituto de Inv. En Metalurgia y Materiales UMSNH, México (Mexico)
2015-11-11
The present work analyzes the effect of boron addition to an Austempered Ductile Iron, in amounts from zero to 120 ppm. It has been found that boron has a strong effect on the equivalent carbon content, resulting in an increase on the precipitated graphite volume and a decrease in the dissolved carbon content in the matrix. This in turn, increases the ferrite volume fraction in the as-cast conditions from 0.24 in the base alloy to 0.78 for the iron with 120 ppm of boron. Furthermore, a decrease in the nodularity from 100% in the base alloy to 83% with 120 ppm of boron has been observed. During austempering, the transformation to ausferrite was faster and lower volumes of martensite and unstable austenite were detected when boron increased; this promoted lower hardness values, 239 HV for the base iron and 189 HV for the 120 ppm boron alloy. The increase in hardness and strength, typical for the start of bainite formation, were not observed in the boron added irons, but just in the base alloy. Under this basis, it is assumed that at least the addition of 60 ppm of boron extended the optimal processing window. The higher values of strength and ductility were obtained for the alloy with 60 ppm of boron; these results are discussed in terms of the graphitizing effect of boron in these irons and the reduced amount of carbon dissolved in austenite.
Bounds of memory strength for power-law series
Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao
2017-05-01
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α . By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α , which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1 3 , the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
Human learning: Power laws or multiple characteristic time scales?
Directory of Open Access Journals (Sweden)
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.
A COSMIC COINCIDENCE: THE POWER-LAW GALAXY CORRELATION FUNCTION
International Nuclear Information System (INIS)
Watson, Douglas F.; Berlind, Andreas A.; Zentner, Andrew R.
2011-01-01
We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of ξ(r), the galaxy two-point correlation function. While ξ(r) at large scales is set by primordial fluctuations, departures from a power law are governed by galaxy pair counts at small scales, subject to nonlinear dynamics. We assume that galaxies reside within dark matter halos and subhalos. Therefore, the shape of the correlation function at small scales depends on the amount of halo substructure. We use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal mass loss and, to a lesser extent, dynamical friction dramatically deplete the number of subhalos within larger host halos over time, resulting in a ∼90% reduction by z = 0 compared to the number of distinct mergers that occur during the assembly of a host halo. We show that these nonlinear processes resulting in this depletion are essential for achieving a power law ξ(r). We investigate how the shape of ξ(r) depends on subhalo mass (or luminosity) and redshift. We find that ξ(r) breaks from a power law at high masses, implying that only galaxies of luminosities ∼ * should exhibit power-law clustering. Moreover, we demonstrate that ξ(r) evolves from being far from a power law at high redshift, toward a near power-law shape at z = 0. We argue that ξ(r) will once again evolve away from a power law in the future. This is in large part caused by the evolving competition between the accretion and destruction rates of subhalos over time, which happen to strike just the right balance at z ∼ 0. We then investigate the conditions required for ξ(r) to be a power law in a general context. We use the halo model, along with simple parameterizations of the halo occupation distribution, to probe galaxy occupation at various masses and redshifts. We show that the key ingredients determining the shape of ξ(r) are the fraction of galaxies that
Bounds of memory strength for power-law series.
Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao
2017-05-01
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α. By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α, which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 13, the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
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. Copyright © 2013 John Wiley & Sons, Ltd.
Exponential and power laws in public procurement markets
Czech Academy of Sciences Publication Activity Database
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 - others: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
Flow of power-law fluids in simplex atomizers
Energy Technology Data Exchange (ETDEWEB)
Mandal, A. [Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072 (United States); Jog, M.A. [Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072 (United States)], E-mail: Milind.Jog@uc.edu; Xue, J.; Ibrahim, A.A. [Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072 (United States)
2008-10-15
This paper presents a computational analysis of flow of time-independent, purely-viscous, power-law fluids in simplex atomizers using the volume-of-fluid (VOF) method. Flow of shear-thinning (0.4 < n < 1), Newtonian (n = 1) and shear thickening fluids (1 < n < 1.2) has been considered. The effect of power-law index and atomizer geometry on the flow and atomizer performance has been investigated. Three geometry parameters have been considered, viz., the atomizer constant which is the ratio of inlet area to the product of swirl chamber diameter and the exit diameter, the ratio of swirl chamber diameter to exit orifice diameter, and the length-to-diameter ratio of the exit orifice. The dimensionless film thickness at exit, spray cone angle, and the discharge coefficient for different values power-law index as well as those with varying atomizer geometry are reported. The pressure drop across the atomizer has been kept constant in all simulations. A change in the power-law index significantly alters the flow field in the in the swirl chamber of the atomizer. The velocity magnitudes and liquid film thickness at the orifice exit change with the power-law index. With fixed atomizer geometry, the pseudoplastic fluids tend to produce thinner liquid sheet, larger spray cone angle, and have lower discharge coefficient compared to dilatant fluids. Changes in the atomizer geometry have a significant impact on the flow for all values of power-law index. The spray cone angle decreases and the discharge coefficient and the film thickness increase with increasing atomizer constant. With increasing D{sub s}/d{sub o}, the dimensionless film thickness at exit increases whereas the dimensional film thickness decreases monotonically. The discharge coefficient increases and the spray cone angle decreases with increasingD{sub s}/d{sub o}. The discharge coefficient, the spray cone angle, and the film thickness decrease with increasing l{sub o}/d{sub o}. A significant finding is that the
Power-law relaxation in human violent conflicts
Picoli, Sergio; Antonio, Fernando J.; Itami, Andreia S.; Mendes, Renio S.
2017-08-01
We study relaxation patterns of violent conflicts after bursts of activity. Data were obtained from available catalogs on the conflicts in Iraq, Afghanistan and Northern Ireland. We find several examples in each catalog for which the observed relaxation curves can be well described by an asymptotic power-law decay (the analog of the Omori's law in geophysics). The power-law exponents are robust, nearly independent of the conflict. We also discuss the exogenous or endogenous nature of the shocks. Our results suggest that violent conflicts share with earthquakes and other natural and social phenomena a common feature in the dynamics of aftershocks.
a modified power law for determinig flow characteristics of fluid
African Journals Online (AJOL)
user
1986-09-01
Sep 1, 1986 ... CHARACTERISTICS OF FLUID. BY. G. SODAH AYERNOR. Department of Food Science and Technology. University of Nigeria Nsukka. ABSTRACT. A modified power law derived with “angle of deviation flow was used to determine the, rheological properties of corn syrup (CS), honey (H), emulsion salad ...
Avalanches and power-law behaviour in lung inflation
Suki, Béla; Barabási, Albert-László; Hantos, Zoltán; Peták, Ferenc; Stanley, H. Eugene
1994-04-01
WHEN lungs are emptied during exhalation, peripheral airways close up1. For people with lung disease, they may not reopen for a significant portion of inhalation, impairing gas exchange2,3. A knowledge of the mechanisms that govern reinflation of collapsed regions of lungs is therefore central to the development of ventilation strategies for combating respiratory problems. Here we report measurements of the terminal airway resistance, Rt , during the opening of isolated dog lungs. When inflated by a constant flow, Rt decreases in discrete jumps. We find that the probability distribution of the sizes of the jumps and of the time intervals between them exhibit power-law behaviour over two decades. We develop a model of the inflation process in which 'avalanches' of airway openings are seen-with power-law distributions of both the size of avalanches and the time intervals between them-which agree quantitatively with those seen experimentally, and are reminiscent of the power-law behaviour observed for self-organized critical systems4. Thus power-law distributions, arising from avalanches associated with threshold phenomena propagating down a branching tree structure, appear to govern the recruitment of terminal airspaces.
Financial power laws: Empirical evidence, models, and mechanisms
International Nuclear Information System (INIS)
Lux, Thomas; Alfarano, Simone
2016-01-01
Financial markets (share markets, foreign exchange markets and others) are all characterized by a number of universal power laws. The most prominent example is the ubiquitous finding of a robust, approximately cubic power law characterizing the distribution of large returns. A similarly robust feature is long-range dependence in volatility (i.e., hyperbolic decline of its autocorrelation function). The recent literature adds temporal scaling of trading volume and multi-scaling of higher moments of returns. Increasing awareness of these properties has recently spurred attempts at theoretical explanations of the emergence of these key characteristics form the market process. In principle, different types of dynamic processes could be responsible for these power-laws. Examples to be found in the economics literature include multiplicative stochastic processes as well as dynamic processes with multiple equilibria. Though both types of dynamics are characterized by intermittent behavior which occasionally generates large bursts of activity, they can be based on fundamentally different perceptions of the trading process. The present paper reviews both the analytical background of the power laws emerging from the above data generating mechanisms as well as pertinent models proposed in the economics literature.
Meson Spectra: Power Law Potential Model in the Dirac Equation ...
African Journals Online (AJOL)
A single mass-spectra potential model has been used to predict the spectra of both light and heavy mesons (including leptonic decay-widths) in the Dirac equation. In fact a power law potential has been proposed with effective power where is the mass of the constituent quarks (in GeV) of the mesons considered.
A Modified Power Law for Determining Flow Characteristics of Fluid ...
African Journals Online (AJOL)
A modified power law derived with “angle of deviation flow was used to determine the, rheological properties of corn syrup (CS), honey (H), emulsion salad dressing cream (SC) and mixture of SC and H: CS. The model proved useful in calculating the flow behaviour index (n) and estimating the, critical shear rate ( ). Results ...
Constraints on cosmological parameters in power-law cosmology
International Nuclear Information System (INIS)
Rani, Sarita; Singh, J.K.; Altaibayeva, A.; Myrzakulov, R.; Shahalam, M.
2015-01-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H 0 (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H 0 average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → −1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details
Medical practices display power law behaviors similar to spoken languages.
Paladino, Jonathan D; Crooke, Philip S; Brackney, Christopher R; Kaynar, A Murat; Hotchkiss, John R
2013-09-04
Medical care commonly involves the apprehension of complex patterns of patient derangements to which the practitioner responds with patterns of interventions, as opposed to single therapeutic maneuvers. This complexity renders the objective assessment of practice patterns using conventional statistical approaches difficult. Combinatorial approaches drawn from symbolic dynamics are used to encode the observed patterns of patient derangement and associated practitioner response patterns as sequences of symbols. Concatenating each patient derangement symbol with the contemporaneous practitioner response symbol creates "words" encoding the simultaneous patient derangement and provider response patterns and yields an observed vocabulary with quantifiable statistical characteristics. A fundamental observation in many natural languages is the existence of a power law relationship between the rank order of word usage and the absolute frequency with which particular words are uttered. We show that population level patterns of patient derangement: practitioner intervention word usage in two entirely unrelated domains of medical care display power law relationships similar to those of natural languages, and that-in one of these domains-power law behavior at the population level reflects power law behavior at the level of individual practitioners. Our results suggest that patterns of medical care can be approached using quantitative linguistic techniques, a finding that has implications for the assessment of expertise, machine learning identification of optimal practices, and construction of bedside decision support tools.
On the universality of power laws for tokamak plasma predictions
Garcia, J.; Cambon, D.; Contributors, JET
2018-02-01
Significant deviations from well established power laws for the thermal energy confinement time, obtained from extensive databases analysis as the IPB98(y,2), have been recently reported in dedicated power scans. In order to illuminate the adequacy, validity and universality of power laws as tools for predicting plasma performance, a simplified analysis has been carried out in the framework of a minimal modeling for heat transport which is, however, able to account for the interplay between turbulence and collinear effects with the input power known to play a role in experiments with significant deviations from such power laws. Whereas at low powers, the usual scaling laws are recovered with little influence of other plasma parameters, resulting in a robust power low exponent, at high power it is shown how the exponents obtained are extremely sensitive to the heating deposition, the q-profile or even the sampling or the number of points considered due to highly non-linear behavior of the heat transport. In particular circumstances, even a minimum of the thermal energy confinement time with the input power can be obtained, which means that the approach of the energy confinement time as a power law might be intrinsically invalid. Therefore plasma predictions with a power law approximation with a constant exponent obtained from a regression of a broad range of powers and other plasma parameters which can non-linearly affect and suppress heat transport, can lead to misleading results suggesting that this approach should be taken cautiously and its results continuously compared with modeling which can properly capture the underline physics, as gyrokinetic simulations.
Power-law phenomena in adhesive de-bonding
Kendall, Gay
Acoustic emission (AE) was recorded during the peeling of pressure-sensitive adhesive (PSA) tapes from their surfaces. The viscous and non-linear behavior of PSA tapes produces significant energy dissipation in the form of adhesive fibril formation, elongation and final failure within the peel zone. AE generated during the peeling process corresponds to the final de-bonding event, in which elastic energy is rapidly released to the substrate. The recording and analyzing of AE generated during peeling is used here in a novel application for characterizing microscopic de-bonding events. Present results indicate that the distribution of AE event magnitudes have the form of power-laws and the power spectral densities have the form of flicker noise. Both power-law dependencies and flicker noise are recognized as consequences of SOC in homogeneous systems. A significant feature of power-law dependencies is the absence of any characteristic length or time scales. The present results, however, indicate that the interface is not homogeneous and that pre-existing surface conditions cause non-uniform adhesive bonding. This is heavily supported by the literature regarding the nature of engineering surfaces. Consequentially, Mandelbrot's fractal concepts were applied to characterize the heterogeneous adhesive interface, and to investigate the relation of interfacial structure with the power-law features of the PSA de-bonding process. It is concluded that fractally distributed variations in adhesive bond strengths at the PSA-glass interface produce the observed hyperbolic distributions in AE events. All the formalism of SOC: applies under this alternative explanation of PSA de-bonding phenomena because of the observed hyperbolic distributions of the AE data. It may be that the explanation based on an underlying fractal structure may be a more general explanation to power law and flicker noise phenomena than the SOC model for heterogeneous systems.
Ionic pairing in binary liquids of charged hard spheres with non-additive diameters
International Nuclear Information System (INIS)
Pastore, G.; Giaquinta, P.V.; Thakur, J.S.; Tosi, M.P.
1985-07-01
We examine types of short range order that arise in binary liquids from a combination of Coulombic interactions and non-additivity of excluded volumes, the initial motivation being observations of complex formation by hydrated ions in concentrated aqueous solutions. The model is a fluid of charged hard spheres with contact distances σsub(+-)not=1/2(σsub(++)+σsub(--)), its structural functions being evaluated in the mean spherical approximation and in the hypernetted chain approximation. Cation-anion pairing is clearly seen in the calculated structural functions for negative deviations from additivity (σsub(+-) σsub(++)=σsub(--)) favour long-wavelength concentration fluctuations and demixing in a neutral mixture: these are suppressed by Coulombic interactions in favour of microscopic intermixing of the two species in the local liquid structure, up to like-ion pairing. Contact is made with diffraction from concentrated aqueous solutions of cadmium sulphate and other instances of possible applicability of the model are pointed out. (author)
Effect of phosphorus additions on hot pressing temperature and some properties of WC-Co hard alloys
International Nuclear Information System (INIS)
Dotsenko, V.M.; Simkina, Eh.S.; Tsypin, N.V.
1977-01-01
Results of studies on the effect of phosphorus additions on hot pressing temperature and some properties of VK6 and VK15 hard alloys are given. It is shown that alloying of hard alloys with 3-6 wt % phosphorus gives opportunity to lower substantially (for 200-300 deg) their hot pressing temperature. Hardness and density of alloys with phosphorus do not practically change. Some decrease of strength and wear-resistance characteristics is observed which is obviously connected with irregular distribution of phosphorus in the alloy
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws
Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.
2011-01-01
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.
Anika Prastyowati; Lorensia Maria Ekawati Purwijantiningsih; Fransiskus Sinung Pranata
2015-01-01
Cattle diseases caused by bacterial infection and unqualified feed can decrease production of beef which people consume more in Indonesia. This research objective is to know quality of hard candy as cattle feed additive including chemistry and microbiology characteristics. Research steps consist of material preparation test, making sirih leaf extract, making hard candy, chemistry tests (The levels of water, ashes, reduction sugar, sacarose and atsiri oil, respectively) and microbiology test (...
Power-law distribution in Japanese racetrack betting
Ichinomiya, Takashi
2006-08-01
Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)∝1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.
On heat transfer of weakly compressible power-law flows
Directory of Open Access Journals (Sweden)
Li Botong
2017-01-01
Full Text Available This paper completes a numerical research on steady momentum and heat transfer in power-law fluids in a channel. Weakly compressible laminar fluids are studied with no slip at the walls and uniform wall temperatures. The full governing equations are solved by continuous finite element method. Three thermal conductivity models are adopted in this paper, that is, constant thermal conductivity model, thermal conductivity varying as a function of temperature gradient, and a modified temperature-gradient-dependent thermal conductivity model. The results are compared with each other and the physical characteristics for values of parameters are also discussed in details. It is shown that the velocity curve from the solution becomes straight at higher power-law index. The effects of Reynolds numbers on the dilatant fluid and the pseudo-plastic look similar to each other and their trends can be easily predicted. Furthermore, for different models, the temperature curves also present pseudo-plastic and dilatant properties.
Ising Models on Power-Law Random Graphs
Dommers, Sander; Giardinà, Cristian; van der Hofstad, Remco
2010-11-01
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent τ>2), for which the random graph has a tree-like structure. For this, we closely follow the analysis by Dembo and Montanari (Ann. Appl. Probab. 20(2):565-592, 2010) which assumes finite variance degrees ( τ>3), adapting it when necessary and also simplifying it when possible. Our results also apply in cases where the degree distribution does not obey a power law. We further identify the thermodynamic limits of various physical quantities, such as the magnetization and the internal energy.
COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS
International Nuclear Information System (INIS)
Mota, David F.; Winther, Hans A.
2011-01-01
In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to ΛCDM, but can in some special cases enhance the growth of the linear perturbations at low redshifts. For the models we consider, it is found that this region of the parameter space is ruled out by local gravity constraints. Imposing a coupling to dark matter only, the local constraints are avoided, and it is possible to have observable signatures on the linear matter perturbations.
Wind Velocity Vertical Extrapolation by Extended Power Law
Directory of Open Access Journals (Sweden)
Zekai Şen
2012-01-01
Full Text Available Wind energy gains more attention day by day as one of the clean renewable energy resources. We predicted wind speed vertical extrapolation by using extended power law. In this study, an extended vertical wind velocity extrapolation formulation is derived on the basis of perturbation theory by considering power law and Weibull wind speed probability distribution function. In the proposed methodology not only the mean values of the wind speeds at different elevations but also their standard deviations and the cross-correlation coefficient between different elevations are taken into consideration. The application of the presented methodology is performed for wind speed measurements at Karaburun/Istanbul, Turkey. At this location, hourly wind speed measurements are available for three different heights above the earth surface.
Dynamic intersectoral models with power-law memory
Tarasova, Valentina V.; Tarasov, Vasily E.
2018-01-01
Intersectoral dynamic models with power-law memory are proposed. The equations of open and closed intersectoral models, in which the memory effects are described by the Caputo derivatives of non-integer orders, are derived. We suggest solutions of these equations, which have the form of linear combinations of the Mittag-Leffler functions and which are characterized by different effective growth rates. Examples of intersectoral dynamics with power-law memory are suggested for two sectoral cases. We formulate two principles of intersectoral dynamics with memory: the principle of changing of technological growth rates and the principle of domination change. It has been shown that in the input-output economic dynamics the effects of fading memory can change the economic growth rate and dominant behavior of economic sectors.
Power law and multiscaling properties of the Chinese stock market
Bai, Man-Ying; Zhu, Hai-Bo
2010-05-01
We investigate the cumulative probability density function (PDF) and the multiscaling properties of the returns in the Chinese stock market. By using returns data adjusted for thin trading, we find that the distribution has power-law tails at shorter microscopic timescales or lags. However, the distribution follows an exponential law for longer timescales. Furthermore, we investigate the long-range correlation and multifractality of the returns in the Chinese stock market by the DFA and MFDFA methods. We find that all the scaling exponents are between 0.5 and 1 by DFA method, which exhibits the long-range power-law correlations in the Chinese stock market. Moreover, we find, by MFDFA method, that the generalized Hurst exponents h(q) are not constants, which shows the multifractality in the Chinese stock market. We also find that the correlation of Shenzhen stock market is stronger than that of Shanghai stock market.
Power law relationships for rain attenuation and reflectivity
Devasirvatham, D. M. J.; Hodge, D. B.
1978-01-01
The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.
Power-law cross-correlations estimation under heavy tails
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2016-01-01
Roč. 40, č. 1 (2016), s. 163-172 ISSN 1007-5704 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : Power-law cross-correlations * Heavy tails * Monte Carlo study Subject RIV: AH - Economics Impact factor: 2.784, year: 2016 http://library.utia.cas.cz/separaty/2016/E/kristoufek-0472030.pdf
DEFF Research Database (Denmark)
Baloković, M.; Paneque, D.; Madejski, G.
2016-01-01
. NuSTAR yielded previously unattainable sensitivity in the 3-79 keV range, revealing that the spectrum softens when the source is dimmer until the X-ray spectral shape saturates into a steep τ≈3 power law, with no evidence for an exponential cutoff or additional hard components up to ∼80 ke...
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.
Characterizing and predicting the robustness of power-law networks
International Nuclear Information System (INIS)
LaRocca, Sarah; Guikema, Seth D.
2015-01-01
Power-law networks such as the Internet, terrorist cells, species relationships, and cellular metabolic interactions are susceptible to node failures, yet maintaining network connectivity is essential for network functionality. Disconnection of the network leads to fragmentation and, in some cases, collapse of the underlying system. However, the influences of the topology of networks on their ability to withstand node failures are poorly understood. Based on a study of the response of 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
Power-law citation distributions are not scale-free.
Golosovsky, Michael
2017-09-01
We analyze time evolution of statistical distributions of citations to scientific papers published in the same year. While these distributions seem to follow the power-law dependence we find that they are nonstationary and the exponent of the power-law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of the low-cited and highly cited papers. By measuring citation trajectories of papers we found that citation careers of the low-cited papers come to saturation after 10-15 years while those of the highly cited papers continue to increase indefinitely: The papers that exceed some citation threshold become runaways. Thus, we show that although citation distribution can look as a power-law dependence, it is not scale free and there is a hidden dynamic scale associated with the onset of runaways. We compare our measurements to our recently developed model of citation dynamics based on copying-redirection-triadic closure and find explanations to our empirical observations.
Generalized fluctuation relation for power-law distributions.
Budini, Adrián A
2012-07-01
Strong violations of existing fluctuation theorems may arise in nonequilibrium steady states characterized by distributions with power-law tails. The ratio of the probabilities of positive and negative fluctuations of equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and E. G. D. Cohen, Phys. Rev. E 76, 020101(R) (2007)]. Here, we propose an alternative definition of fluctuation relation (FR) symmetry that, in the power-law regime, is characterized by a monotonic linear behavior. The proposal is consistent with a large deviationlike principle. As an example, we study the fluctuations of the work done on a dragged particle immersed in a complex environment able to induce power-law tails. When the environment is characterized by spatiotemporal temperature fluctuations, distributions arising in nonextensive statistical mechanics define the work statistics. In that situation, we find that the FR symmetry is solely defined by the average bath temperature. The case of a dragged particle subjected to a Lévy noise is also analyzed in detail.
Power law deformation of Wishart–Laguerre ensembles of random matrices
International Nuclear Information System (INIS)
Akemann, Gernot; Vivo, Pierpaolo
2008-01-01
We introduce a one-parameter deformation of the Wishart–Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of β, in terms of the orthogonal polynomials of the standard Wishart–Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Marčenko–Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on β and the difference M−N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart–Laguerre ensembles. To illustrate these findings, the generalized Marčenko–Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices
van Mierlo, Trevor; Hyatt, Douglas; Ching, Andrew T
2015-06-25
Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, Ppower distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that
Do we have an acceptable model of power-law creep?
CSIR Research Space (South Africa)
Nabarro, FRN
2004-12-15
Full Text Available probable power law of 5. However, the observations of Andrade and Hanson, which may apply to the regime of power-law breakdown rather than power-law creep strongly, indicate that deformation is localized at the grain boundaries. If this is the case...
Power laws from individual differences in learning and forgetting: mathematical analyses
Murre, J.M.J.; Chessa, A.G.
2011-01-01
It has frequently been claimed that learning performance improves with practice according to the so-called "Power Law of Learning." Similarly, forgetting may follow a power law. It has been shown on the basis of extensive simulations that such power laws may emerge through averaging functions with
Energy Technology Data Exchange (ETDEWEB)
Qu, Jun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Zhou, Yan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Leonard, Donovan N [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Meyer, III, Harry M [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Luo, Huimin [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-03-01
The objectives for this considerations described here are to; investigate the compatibility of engine lubricant antiwear (AW) additives, specifically conventional zinc dialkyldithiophosphate (ZDDP) and newly developed ionic liquids (ILs), with selected commercial hard coatings, and provide fundamental understanding to guide future development of engine lubricants.
Power laws, discontinuities and regional city size distributions
Garmestani, A.S.; Allen, Craig R.; Gallagher, C.M.
2008-01-01
Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classes in the city size distributions are snapshots of stable states within urban systems in flux.
Elastohydrodynamic analysis using a power law pressure-viscosity relation
Loewenthal, S. H.; Zaretsky, E. V.
1973-01-01
An isothermal elastohydrodynamic (EHD) inlet analysis of the Grubin type which considers a power law pressure-viscosity relation and a finite pressure at the inlet edge of the Hertzian contact zone was performed. Comparisons made with published X-ray EHD film thickness data for a synthetic paraffinic oil and when conventional EHD theory showed that the present theory exhibits a slightly stronger film thickness load dependence than do previous isothermal EHD theories but far less than that exhibited by the measured data.
Power-law photoluminescence decay in indirect gap quantum dots
Czech Academy of Sciences Publication Activity Database
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
Urban, Vanessa M; Lima, Thiago F; Bueno, Mirian G; Giannini, Marcelo; Arioli Filho, João N; de Almeida, Ana Lúcia P F; Neppelenbroek, Karin H
2015-04-01
While the incorporation of antimicrobial agents into soft denture liners has been suggested as a reliable alternative treatment for denture stomatitis, it may affect the liner's properties. The effect of addition of antimicrobial agents for the treatment of denture stomatitis on the surface roughness and Shore A hardness of soft lining materials was evaluated. The test groups comprised specimens (36 × 7 × 6 mm(3) ) of soft materials (Softone and Trusoft) without (control) or with incorporation of drugs (nystatin, miconazole, ketoconazole, chlorhexidine diacetate, and itraconazole). Hardness (Shore A) and roughness (Ra) were evaluated after immersion of specimens (n = 10) in distilled water at 37°C for 24 hours, 7 and 14 days. Data were analyzed by 3-way ANOVA/Tukey's test (α = 0.05). After 14 days, an increase (p hardness of soft materials with time for the modified specimens, except for itraconazole. Addition of drugs increased the Softone roughness only for the addition of miconazole and chlorhexidine (p hardness and roughness with time in the modified groups compared to controls were observed for itraconazole groups for both materials. © 2014 by the American College of Prosthodontists.
Indian English Evolution and Focusing Visible Through Power Laws
Directory of Open Access Journals (Sweden)
Vineeta Chand
2017-11-01
Full Text Available New dialect emergence and focusing in language contact settings is difficult to capture and date in terms of global structural dialect stabilization. This paper explores whether diachronic power law frequency distributions can provide evidence of dialect evolution and new dialect focusing, by considering the quantitative frequency characteristics of three diachronic Indian English (IE corpora (1970s–2008. The results demonstrate that IE consistently follows power law frequency distributions and the corpora are each best fit by Mandelbrot’s Law. Diachronic changes in the constants are interpreted as evidence of lexical and syntactic collocational focusing within the process of new dialect formation. Evidence of new dialect focusing is also visible through apparent time comparison of spoken and written data. Age and gender-separated sub-corpora of the most recent corpus show minimal deviation, providing apparent time evidence for emerging IE dialect stability. From these findings, we extend the interpretation of diachronic changes in the β coefficient—as indicative of changes in the degree of synthetic/analytic structure—so that β is also sensitive to grammaticalization and changes in collocational patterns.
The power law as behavioral illusion: reappraising the reappraisals.
Marken, Richard S; Shaffer, Dennis M
2018-03-08
Marken and Shaffer (Exp Brain Res 235:1835-1842, 2017) have argued that the power law of movement, which is generally thought to reflect the mechanisms that produce movement, is actually an example of what Powers (Psychol Rev 85:417-435, 1978) dubbed a behavioral illusion, where an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not. Zago et al. (Exp Brain Res. https://doi.org/10.1007/s0022-017-5108-z , 2017) and Taylor (Exp Brain Res, https://doi.org/10.1007/s00221-018-5192-8 , 2018) have "reappraised" this argument, claiming that it is based on logical, mathematical, statistical and theoretical errors. In the present paper we answer these claims and show that the power law of movement is, indeed, an example of a behavioral illusion. However, we also explain how this apparently negative finding can point the study of movement in a new and more productive direction, with research aimed at understanding movement in terms of its purposes rather than its causes.
Power law distributions of patents as indicators of innovation.
Directory of Open Access Journals (Sweden)
Dion R J O'Neale
Full Text Available The total number of patents produced by a country (or the number of patents produced per capita is often used as an indicator for innovation. Here we present evidence that the distribution of patents amongst applicants within many countries is well-described by power laws with exponents that vary between 1.66 (Japan and 2.37 (Poland. We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.
Power law distributions of patents as indicators of innovation.
O'Neale, Dion R J; Hendy, Shaun C
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 countries is well-described by power laws with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.
Power-law 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.
Optimal numerical flux of power-law fluids in some partially full pipes
Lefton, Lew; Wei, Dongming; Liu, Yu
2014-07-01
Consider the steady state pressure driven flow of a power-law fluid in a partially filled straight pipe. It is known that an increase in flux can be achieved for a fixed pressure by partially filling the pipe and having the remaining volume either void or filled with a less viscous, lubricating fluid. If the pipe has circular cross section, the fluid level which maximizes flux is the level which avoids contact with exactly 25% of the boundary. This result can be proved analytically for Newtonian fluids and has been verified numerically for certain non-Newtonian models. This paper provides a generalization of this work numerically to pipes with non-circular cross sections which are partially full with a power-law fluid. A simple and physically plausible geometric condition is presented which can be used to approximate the fluid level that maximizes flux in a wide range of pipe geometries. Additional increases in flux for a given pressure can be obtained by changing the shape of the pipe but leaving the perimeter fixed. This computational analysis of flux as a function of both fluid level and pipe geometry has not been considered to our knowledge. Fluxes are computed using a special discretization scheme, designed to uncover general properties which are only dependent on fluid level and/or pipe cross-sectional geometry. Computations use finite elements and take advantage of the variational structure inherent in the power-law model. A minimization technique for approximating the critical points of the associated non-linear energy functional is used. In particular, the numerical scheme for the non-linear partial differential equation has been proved to be convergent with known error estimates. The numerical results obtained in this work can be useful for designing pipes and canals for transportation of non-Newtonian fluids, such as those in chemical engineering and food processing engineering.
International Nuclear Information System (INIS)
Silva, P.A.; Weber, S.; Inden, G.; Pyzalla, A.R.
2009-01-01
Low alloyed steel bars were co-extruded with pre-sintered tool steel powders with the addition of tungsten carbides (W 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 TM ) to investigate the effect of hard particle addition and its dissolution, as well as the formation of M 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 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.
Ojiambo, Peter S; Gent, David H; Mehra, Lucky K; Christie, David; Magarey, Roger
2017-01-01
Empirical and mechanistic modeling indicate that pathogens transmitted via aerially dispersed inoculum follow a power law, resulting in dispersive epidemic waves. The spread parameter ( b ) of the power law model, which is an indicator of the distance of the epidemic wave front from an initial focus per unit time, has been found to be approximately 2 for several animal and plant diseases over a wide range of spatial scales under conditions favorable for disease spread. Although disease spread and epidemic expansion can be influenced by several factors, the stability of the parameter b over multiple epidemic years has not been determined. Additionally, the size of the initial epidemic area is expected to be strongly related to the final epidemic extent for epidemics, but the stability of this relationship is also not well established. Here, empirical data of cucurbit downy mildew epidemics collected from 2008 to 2014 were analyzed using a spatio-temporal model of disease spread that incorporates logistic growth in time with a power law function for dispersal. Final epidemic extent ranged from 4.16 ×10 8 km 2 in 2012 to 6.44 ×10 8 km 2 in 2009. Current epidemic extent became significantly associated ( P power law model. These results suggest that the spread parameter b may not be stable over multiple epidemic years. However, b ≈ 2 may be considered the lower limit of the distance traveled by epidemic wave-fronts for aerially transmitted pathogens that follow a power law dispersal function.
Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements.
Schaal, S; Sternad, D
2001-01-01
The 2/3 power law, the nonlinear relationship between tangential velocity and radius of curvature of the end-effector trajectory, is thought to be a fundamental constraint of the central nervous system in the formation of rhythmic endpoint trajectories. However, studies on the 2/3 power law have been confined largely to planar drawing patterns of relatively small size. With the hypothesis that this strategy overlooks nonlinear effects that are constitutive in movement generation, the present experiments tested the validity of the power law in elliptical patterns that were not confined to a planar surface and which were performed by the unconstrained 7-degrees of freedom (DOF) arm, with significant variations in pattern size and workspace orientation. Data were recorded from five human subjects where the seven joint angles and the endpoint trajectories were analyzed. Additionally, an anthropomorphic 7-DOF robot arm served as a "control subject" whose endpoint trajectories were generated on the basis of the human joint angle data, modeled as simple harmonic oscillations. Analyses of the endpoint trajectories demonstrate that the power law is systematically violated with increasing pattern size, in both exponent and the goodness of fit. The origins of these violations can be explained analytically based on smooth, rhythmic trajectory formation and the kinematic structure of the human arm. We conclude that, in unconstrained rhythmic movements, the power law seems to be a by-product of a movement system that favors smooth trajectories, and that it is unlikely to serve as a primary movement-generating principle. Our data rather suggest that subjects employed smooth oscillatory pattern generators in joint space to realize the required movement patterns.
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.
Manuel Castell’s general power law, 1976-2009
Directory of Open Access Journals (Sweden)
Esteban Torres
2013-09-01
Full Text Available According to Manuel Castells the first law of society is a power law: if there is domination there is resistance to domination. In this article, we analyze that postulate, which is displayed between 1976 and 2009, taking into account three aspects: its concrete application in our author’s social research, those arguments belonging to Castells himself which tend to refute it, and finally a limited dialoque with the fifth proposition about power that makes Michel Foucault in The History of Sexuality . This process will allow us to identify the main theoretical operations and conceptual change movements our author displays in relation to the mentioned general law, as well as to try a general critique of his position.
Nanoadhesion of a Power-Law Graded Elastic Material
International Nuclear Information System (INIS)
Shao-Hua, Chen; Pei-Jian, Chen
2010-01-01
The Dugdale—Barenblatt model is used to analyze the adhesion of graded elastic materials at the nanoscale with Young's modulus E varying with depth z according to a power law E = E 0 (z/c 0 ) (0 0 is a referenced Young's modulus, k is the gradient exponent and c 0 is a characteristic length describing the variation rate of Young's modulus. We show that, when the size of a rigid punch becomes smaller than a critical length, the adhesive interface between the punch and the graded material detaches due to rupture with uniform stresses, rather than by crack propagation with stress concentration. The critical length can be reduced to the one for isotropic elastic materials only if the gradient exponent k vanishes
Nanoadhesion of a Power-Law Graded Elastic Material
Chen, Shao-Hua; Chen, Pei-Jian
2010-10-01
The Dugdale—Barenblatt model is used to analyze the adhesion of graded elastic materials at the nanoscale with Young's modulus E varying with depth z according to a power law E = E0(z/c0) (0 < k < 1) while Poisson's ratio v remains a constant, where E0 is a referenced Young's modulus, k is the gradient exponent and c0 is a characteristic length describing the variation rate of Young's modulus. We show that, when the size of a rigid punch becomes smaller than a critical length, the adhesive interface between the punch and the graded material detaches due to rupture with uniform stresses, rather than by crack propagation with stress concentration. The critical length can be reduced to the one for isotropic elastic materials only if the gradient exponent k vanishes.
The Discrepancy between Einstein Mass and Dynamical Mass for SIS and Power-law Mass Models
Li, Rui; Wang, Jiancheng; Shu, Yiping; Xu, Zhaoyi
2018-03-01
We investigate the discrepancy between the two-dimensional projected lensing mass and the dynamical mass for an ensemble of 97 strong gravitational lensing systems discovered by the Sloan Lens ACS Survey, the BOSS Emission-Line Lens Survey (BELLS), and the BELLS for GALaxy-Lyα EmitteR sYstems Survey. We fit the lensing data to obtain the Einstein mass and use the velocity dispersion of the lensing galaxies provided by the Sloan Digital Sky Survey to get the projected dynamical mass within the Einstein radius by assuming the power-law mass approximation. The discrepancy is found to be obvious and quantified by Bayesian analysis. For the singular isothermal sphere mass model, we obtain that the Einstein mass is 20.7% more than the dynamical mass, and the discrepancy increases with the redshift of the lensing galaxies. For the more general power-law mass model, the discrepancy still exists within a 1σ credible region. We suspect the main reason for this discrepancy is mass contamination, including all invisible masses along the line of sight. In addition, the measurement errors and the approximation of the mass models could also contribute to the discrepancy.
Power laws from individual differences in learning and forgetting: mathematical analyses
Murre, Jaap M. J.; Chessa, Antonio G.
2011-01-01
It has frequently been claimed that learning performance improves with practice according to the so-called “Power Law of Learning.” Similarly, forgetting may follow a power law. It has been shown on the basis of extensive simulations that such power laws may emerge through averaging functions with other, nonpower function shapes. In the present article, we supplement these simulations with a mathematical proof that power functions will indeed emerge as a result of averaging over exponential f...
Flux decay during thermonuclear X-ray bursts analysed with the dynamic power-law index method
Kuuttila, J.; Kajava, J. J. E.; Nättilä, J.; Motta, S. E.; Sánchez-Fernández, C.; Kuulkers, E.; Cumming, A.; Poutanen, J.
2017-08-01
The cooling of type-I X-ray bursts can be used to probe the nuclear burning conditions in neutron star envelopes. The flux decay of the bursts has been traditionally modelled with an exponential, even if theoretical considerations predict power-law-like decays. We have analysed a total of 540 type-I X-ray bursts from five low-mass X-ray binaries observed with the Rossi X-ray Timing Explorer. We grouped the bursts according to the source spectral state during which they were observed (hard or soft), flagging those bursts that showed signs of photospheric radius expansion (PRE). The decay phase of all the bursts were then fitted with a dynamic power-law index method. This method provides a new way of probing the chemical composition of the accreted material. Our results show that in the hydrogen-rich sources the power-law decay index is variable during the burst tails and that simple cooling models qualitatively describe the cooling of presumably helium-rich sources 4U 1728-34 and 3A 1820-303. The cooling in the hydrogen-rich sources 4U 1608-52, 4U 1636-536, and GS 1826-24, instead, is clearly different and depends on the spectral states and whether PRE occurred or not. Especially the hard state bursts behave differently than the models predict, exhibiting a peculiar rise in the cooling index at low burst fluxes, which suggests that the cooling in the tail is much faster than expected. Our results indicate that the drivers of the bursting behaviour are not only the accretion rate and chemical composition of the accreted material, but also the cooling that is somehow linked to the spectral states. The latter suggests that the properties of the burning layers deep in the neutron star envelope might be impacted differently depending on the spectral state.
Fitting inverse power-law quintessence models using the SNAP satellite
International Nuclear Information System (INIS)
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 a cosmological constant and put severe constraints on the power-law exponent
Chen, Hui; Cai, Li-Xun
2018-04-01
Based on the power-law stress-strain relation and equivalent energy principle, theoretical equations for converting between Brinell hardness (HB), Rockwell hardness (HR), and Vickers hardness (HV) were established. Combining the pre-existing relation between the tensile strength ( σ b ) and Hollomon parameters ( K, N), theoretical conversions between hardness (HB/HR/HV) and tensile strength ( σ b ) were obtained as well. In addition, to confirm the pre-existing σ b -( K, N) relation, a large number of uniaxial tensile tests were conducted in various ductile materials. Finally, to verify the theoretical conversions, plenty of statistical data listed in ASTM and ISO standards were adopted to test the robustness of the converting equations with various hardness and tensile strength. The results show that both hardness conversions and hardness-strength conversions calculated from the theoretical equations accord well with the standard data.
International Nuclear Information System (INIS)
Hopkins, Paul; Schmidt, Matthias
2010-01-01
Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, r→∞, decay of the partial pair correlation functions, g ij (r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g ij (r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.
Power-law forgetting in synapses with metaplasticity
International Nuclear Information System (INIS)
Mehta, A; Luck, J M
2011-01-01
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
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.
Power-law connections: From Zipf to Heaps and beyond
International Nuclear Information System (INIS)
Eliazar, Iddo I.; Cohen, Morrel H.
2013-01-01
In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf’s law, Pareto’s law, and Heaps’ law—three elemental empirical power-laws that are ubiquitously observed in the sciences. -- Highlights: ► The large-ensemble asymptotic statistics of rank distributions are explored. ► Lorenzian, oligarchic, and Heapsian asymptotic analyses are applied. ► Associated oligarchy sizes and induced innovation rates are analyzed. ► General elemental statistical connections are established. ► The underlying connections between Zipf’s, Pareto’s and Heaps’ laws are unveiled
Quantum healing of classical singularities in power-law spacetimes
Energy Technology Data Exchange (ETDEWEB)
Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)
2007-07-07
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.
Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs
van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.
2018-04-01
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299-2361, 2012). It was proved that when the degrees obey a power law with exponent τ \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.
Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra
Czech Academy of Sciences Publication Activity Database
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
Analytical Solution of Unsteady Gravity Flows of A Power-Law Fluid ...
African Journals Online (AJOL)
We investigate the power-law viscosity index, the Darcy parameter on the temperature profiles and the results were discussed. Keywords: Unsteady gravity flows; Porous media; Non – Newtonian power- law fluid. Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 223 – 228 ...
Important Property of GRB Pulse: Power-Law Indices of Time ...
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... 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 ...
Power-law tail probabilities of drainage areas in river basins
Veitzer, S.A.; Troutman, B.M.; Gupta, V.K.
2003-01-01
The significance of power-law tail probabilities of drainage areas in river basins was discussed. The convergence to a power law was not observed for all underlying distributions, but for a large class of statistical distributions with specific limiting properties. The article also discussed about the scaling properties of topologic and geometric network properties in river basins.
Asymptotic expansion of unsteady gravity flow of a power-law fluid ...
African Journals Online (AJOL)
We investigate the power-law viscosity exponent on the flow, the Darcy parameter on the temperature profiles and the results obtained are discussed. Keywords: Unsteady gravity flows; Porous media; Non – Newtonian power- law fluid and Asymptotic expansion. Journal of the Nigerian Association of Mathematical Physics, ...
Do wealth distributions follow power laws? Evidence from ‘rich lists’
Brzezinski, Michal
2014-07-01
We use data on the wealth of the richest persons taken from the 'rich lists' provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012, and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.
The power law of movement: an example of a behavioral illusion.
Marken, Richard S; Shaffer, Dennis M
2017-06-01
The curved movements produced by living organisms follow a power law where the velocity of movement is a power function of the degree of curvature through which the movement is made. The exponent of the power function is close to either 1/3 or 2/3 depending on how velocity and curvature are measured. This power law is thought to reflect biological and/or kinematic constraints on how organisms produce movements. The present paper shows that the power law is actually a statistical artifact that results from mistaking a correlational for a causal relationship between variables. The power law implies that curvature influences the velocity of movement. In fact, the power law is a mathematical consequence of the way that these variables are calculated. The appearance that curvature affects the velocity of movement is shown to be an example of a "behavioral illusion" that results from ignoring the purpose of behavior.
Zreihan, Noam; Faran, Eilon; Vives, Eduard; Planes, Antoni; Shilo, Doron
2018-01-01
It is generally claimed that physical processes which display scale-invariant power-law distributions are subjected to a dynamic criticality that prohibits a well-defined kinetic law. In this paper, we demonstrate the coexistence of these two apparently contradicting behaviors during the same physical process—the motion of type-II twin boundaries in martensite Ni-Mn-Ga. The process is investigated by combined measurements of the temporal twin-boundary velocity and the acoustic emitted energy. Velocity values are extracted from high-resolution force measurements taken during displacement-driven mechanical tests, as well as from force-driven magnetic tests, and cover an overall range of six orders of magnitude. Acoustic emission (AE) is measured during mechanical tests. Velocity values follow a normal distribution whose characteristic value is determined by the material's kinetic relation, and its width scales with the average velocity. In addition, it is observed that velocity distributions are characterized by a heavy tail at the right (i.e., faster) end that exhibits a power law over more than one and a half orders of magnitude. At the same time, the AE signals follow a scale-invariant power-law distribution, which is not sensitive to the average twin-boundary velocity. The coexistence of these two different statistical behaviors reflects the complex nature of twin-boundary motion and suggests the possibility that the transformation proceeds through physical subprocesses that are close to criticality alongside other processes that are not.
Use of ANTARES and IceCube Data to Constrain a Single Power-law Neutrino Flux
Chianese, Marco; Mele, Rosa; Miele, Gennaro; Migliozzi, Pasquale; Morisi, Stefano
2017-12-01
We perform the first statistical combined analysis of the diffuse neutrino flux observed by ANTARES (nine-year) and IceCube (six-year) by assuming a single astrophysical power-law flux. The combined analysis reduces by a few percent the best-fit values for the flux normalization and the spectral index. Both data samples show an excess in the same energy range (40-200 TeV), suggesting the presence of a second component. We perform a goodness-of-fit test to scrutinize the null assumption of a single power-law, scanning different values for the spectral index. The addition of the ANTARES data reduces the p-value by a factor 2\\div3. In particular, a single power-law component in the neutrino flux with the spectral index deduced by the six-year up-going muon neutrinos of IceCube is disfavored with a p-value smaller than 10-2.
Power law olivine crystal size distributions in lithospheric mantle xenoliths
Armienti, P.; Tarquini, S.
2002-12-01
Olivine crystal size distributions (CSDs) have been measured in three suites of spinel- and garnet-bearing harzburgites and lherzolites found as xenoliths in alkaline basalts from Canary Islands, Africa; Victoria Land, Antarctica; and Pali Aike, South America. The xenoliths derive from lithospheric mantle, from depths ranging from 80 to 20 km. Their textures vary from coarse to porphyroclastic and mosaic-porphyroclastic up to cataclastic. Data have been collected by processing digital images acquired optically from standard petrographic thin sections. The acquisition method is based on a high-resolution colour scanner that allows image capturing of a whole thin section. Image processing was performed using the VISILOG 5.2 package, resolving crystals larger than about 150 μm and applying stereological corrections based on the Schwartz-Saltykov algorithm. Taking account of truncation effects due to resolution limits and thin section size, all samples show scale invariance of crystal size distributions over almost three orders of magnitude (0.2-25 mm). Power law relations show fractal dimensions varying between 2.4 and 3.8, a range of values observed for distributions of fragment sizes in a variety of other geological contexts. A fragmentation model can reproduce the fractal dimensions around 2.6, which correspond to well-equilibrated granoblastic textures. Fractal dimensions >3 are typical of porphyroclastic and cataclastic samples. Slight bends in some linear arrays suggest selective tectonic crushing of crystals with size larger than 1 mm. The scale invariance shown by lithospheric mantle xenoliths in a variety of tectonic settings forms distant geographic regions, which indicate that this is a common characteristic of the upper mantle and should be taken into account in rheological models and evaluation of metasomatic models.
Directory of Open Access Journals (Sweden)
N Parvin
2014-12-01
Full Text Available In this research, infiltration behavior of W-Ag composite compacts with Nickel and Cobalt as additives has been investigated. Nickel and Cobalt were added to Tungsten powder by two distinct methods: mixing elementally and reduction of salt solution. The coated Tungsten powders were compacted under controlled pressures to make porous skeleton with 32-37 vol. % porosity. Infiltration process was carried out at 1100 ̊C under a reducing atmosphere for 1h. The effect of additives on infiltration of Ag and density were evaluated by SEM and Archimedes methods. Properties of the specimens were compared following two distinct processes namely: I sintering simultaneously with infiltration process and II sintering prior to infiltration (pre-sintering process. It was found that specimens which were pre-sintered and then infiltrated with molten silver represent higher hardness and finer microstructure than the specimens infiltrated simultaneously with sintering.
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
Directory of Open Access Journals (Sweden)
Anika Prastyowati
2015-06-01
results showed that hard candy made fulfill SNI (Indonesia National Standar considered of water level, ashes level, sacarose level, total count, and yeast fungi level. Atsiri oil level before sirih leaves are made into hard candy is 0,405% and it still exists in hard candy with increasing atsiri oil level, 0,1333%.
Energy consumption reduction in existing HVAC-R systems via a power law controlling kit
International Nuclear Information System (INIS)
Pinnola, C.F.; Vargas, J.V.C.; Buiar, C.L.; Ordonez, J.C.
2015-01-01
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
Directory of Open Access Journals (Sweden)
Peter S. Ojiambo
2017-06-01
Full Text Available Empirical and mechanistic modeling indicate that pathogens transmitted via aerially dispersed inoculum follow a power law, resulting in dispersive epidemic waves. The spread parameter (b of the power law model, which is an indicator of the distance of the epidemic wave front from an initial focus per unit time, has been found to be approximately 2 for several animal and plant diseases over a wide range of spatial scales under conditions favorable for disease spread. Although disease spread and epidemic expansion can be influenced by several factors, the stability of the parameter b over multiple epidemic years has not been determined. Additionally, the size of the initial epidemic area is expected to be strongly related to the final epidemic extent for epidemics, but the stability of this relationship is also not well established. Here, empirical data of cucurbit downy mildew epidemics collected from 2008 to 2014 were analyzed using a spatio-temporal model of disease spread that incorporates logistic growth in time with a power law function for dispersal. Final epidemic extent ranged from 4.16 ×108 km2 in 2012 to 6.44 ×108 km2 in 2009. Current epidemic extent became significantly associated (P < 0.0332; 0.56 < R2 < 0.99 with final epidemic area beginning near the end of April, with the association increasing monotonically to 1.0 by the end of the epidemic season in July. The position of the epidemic wave-front became exponentially more distant with time, and epidemic velocity increased linearly with distance. Slopes from the temporal and spatial regression models varied with about a 2.5-fold range across epidemic years. Estimates of b varied substantially ranging from 1.51 to 4.16 across epidemic years. We observed a significant b ×time (or distance interaction (P < 0.05 for epidemic years where data were well described by the power law model. These results suggest that the spread parameter b may not be stable over multiple epidemic
Absence of power-law mid-infrared conductivity in gravitational crystals
Energy Technology Data Exchange (ETDEWEB)
Langley, Brandon W.; Vanacore, Garrett; Phillips, Philip W. [Department of Physics and Institute for Condensed Matter Theory, University of Illinois, 1110 W. Green Street, Urbana, IL 61801 (United States)
2015-10-26
We compute conductivities of strongly-interacting and non-uniform charge densities dual to inhomogeneous anti-de Sitter-black hole spacetimes. Backreacting bulk scalars with periodic boundary profiles, we construct generalizations of Reissner-Nordström-AdS that interpolate between those used in two previous studies — one that reports power-law scaling for the boundary optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors.
Isomorphs in the phase diagram of a model liquid without inverse power law repulsion
DEFF Research Database (Denmark)
Veldhorst, Arnold Adriaan; Bøhling, Lasse; Dyre, J. C.
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....
Origin of Power Laws for Reactions at Metal Surfaces Mediated by Hot Electrons
DEFF Research Database (Denmark)
Olsen, Thomas; Schiøtz, Jakob
2009-01-01
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....... of such 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...
Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media
Directory of Open Access Journals (Sweden)
Meijuan Yun
2014-01-01
Full Text Available We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.
On the origin of power-law X-ray spectra of active galactic nuclei
Schlosman, I.; Shaham, J.; Shaviv, G.
1984-01-01
In the present analytical model for a power law X-ray continuum production in active galactic nuclei, the dissipation of turbulent energy flux above the accretion disk forms an optically thin transition layer with an inverted temperature gradient. The emitted thermal radiation has a power law spectrum in the 0.1-100 keV range, with a photon energy spectral index gamma of about 0.4-1.0. Thermal X-ray contribution from the layer is 5-10 percent of the total disk luminosity. The gamma value of 0.75 is suggested as a 'natural' power law index for Seyfert galaxies and QSOs.
Blinking in quantum dots: The origin of the grey state and power law statistics
Ye, Mao; Searson, Peter C.
2011-09-01
Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Gilson F. de, E-mail: gilson@otica.ufpb.br; Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos [Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB (Brazil); Souza Cavalcante, Hugo L. D. de [Departamento de Informática, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB (Brazil)
2014-03-15
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.
The power law for the perception of rotation by airline pilots.
Clark, B.; Stewart, J. D.
1972-01-01
The purpose of this study was to determine the power laws for the perception of rotation about the three major body axes. Eighteen airline pilots made magnitude estimates of 5-sec pulses of nine angular accelerations having a range of acceleration x time of 10-150 deg/sec. The results showed that (1) the power law with an exponent of 1.4 describes the subjective motion of these pilots for all three major body axes, (2) the power law also describes the perception of motion for individual pilots with a substantial range of exponents, (3) there were significant correlations among the exponents for the three body axes, and (4) the data suggest that the power law over the wide range used may be more complex than implied by a formula with a single exponent.
Increasing power-law range in avalanche amplitude and energy distributions
Navas-Portella, Víctor; Serra, Isabel; Corral, Álvaro; Vives, Eduard
2018-02-01
Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.
Stochastic model of Zipf's law and the universality of the power-law exponent.
Yamamoto, Ken
2014-04-01
We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
International Nuclear Information System (INIS)
Oliveira, Gilson F. de; Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de
2014-01-01
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
Flow of a power-law fluid with memory past an infinite plate ...
African Journals Online (AJOL)
We examined the flow of a power law fluid with a non-constant relaxation λtb past an infinite plate. When λ is zero the fluid is pseudoplastic and when the power law exponent is 1, the fluid is a Maxwell fluid. It is shown that the problem has a solution when 0 < n ≤ 1. Moreover, we show that momentum penetration ...
Fractal approach towards power-law coherency to measure cross-correlations between time series
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2017-01-01
Roč. 50, č. 1 (2017), s. 193-200 ISSN 1007-5704 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : power-law coherency * power-law cross-correlations * correlations Subject RIV: AH - Economics OBOR OECD: Applied Economics, Econometrics Impact factor: 2.784, year: 2016 http://library.utia.cas.cz/separaty/2017/E/kristoufek-0473066.pdf
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.
Teka, Wondimu; Stockton, David; Santamaria, Fidel
2016-03-01
We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.
Directory of Open Access Journals (Sweden)
Yan Zhang
2011-01-01
Full Text Available The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.
Electrohydrodynamic stability of two stratified power law liquid in couette flow
International Nuclear Information System (INIS)
Eldabe, N.T.
1988-01-01
Consideration is given to the stability of the flow of two power law liquids under the influence of normal electric field between two infinite parallel planes when one of the planes moves with constant velocity in its own plane. It is found that the electric fields have a dramatic effect and can be chosen to stabilize or destabilize the flow. The effects of the power law parameters on the problem are examinated
Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method
International Nuclear Information System (INIS)
Wei, H.L.; Billings, S.A.
2009-01-01
Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.
Around power law for PageRank components in Buckley-Osthus model of web graph
Gasnikov, Alexander; Zhukovskii, Maxim; Kim, Sergey; Noskov, Fedor; Plaunov, Stepan; Smirnov, Daniil
2017-01-01
In the paper we investigate power law for PageRank components for the Buckley-Osthus model for web graph. We compare different numerical methods for PageRank calculation. With the best method we do a lot of numerical experiments. These experiments confirm the hypothesis about power law. At the end we discuss real model of web-ranking based on the classical PageRank approach.
Mixed-correlated ARFIMA processes for power-law cross-correlations
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2013-01-01
Roč. 392, č. 24 (2013), s. 6484-6493 ISSN 0378-4371 R&D Projects: GA ČR GA402/09/0965 Institutional support: RVO:67985556 Keywords : power- law cross-correlations * long-term memory * econophysics Subject RIV: AH - Economics Impact factor: 1.722, year: 2013 http://library.utia.cas.cz/separaty/2013/E/kristoufek-mixed-correlated arfima processes for power- law cross-correlations.pdf
Power-law and intermediate inflationary models in f(T)-gravity
Energy Technology Data Exchange (ETDEWEB)
Rezazadeh, K. [Department of Physics, University of Kurdistan,Pasdaran St., Sanandaj (Iran, Islamic Republic of); Abdolmaleki, A. [Research Institute for Astronomy Astrophysics of Maragha (RIAAM),P.O. Box 55134-441, Maragha (Iran, Islamic Republic of); Karami, K. [Department of Physics, University of Kurdistan,Pasdaran St., Sanandaj (Iran, Islamic Republic of)
2016-01-21
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{sup 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{sup 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.
Power-law and intermediate inflationary models in f(T)-gravity
International Nuclear Information System (INIS)
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.
Evapotranspiration Power Law in Self-Organized and Human-Managed Ecosystems
Zeng, R.; Cai, X.
2017-12-01
Natural systems display a profound degree of self-organization, often apparent even to the untrained eye. However, in this age of increased coupling among human and natural systems, it is unclear to what degree natural organization principles continue to govern human-managed landscapes. Here we present an emerging characteristic of terrestrial evapotranspiration (ET), one of the key components of the water cycle and energy budget, adhered to by both naturally organized and intensively managed landscapes. We find that ET variance and ET mean for ecosystems throughout the world with diverse climate conditions, vegetation structures, and land covers and land uses organize themselves according to a specific power law curve. From multi-source observations, the ET power law curve stands true through varying spatial scales, from field to region. Moreover, a phenomenon of similar ecosystems gravitating toward particular segments of the power law curve, suggests that the feature of self-optimization of ecosystems establishes the ET power law together with climatic conditions. Perhaps surprisingly, we find that landscapes persistently follow the power law curve even upon human-induced transition from rain-fed to irrigated agriculture in the American High Plains and from wetland to agricultural land in American Midwest. As such, the ET power law can be an informative tool for predicting consequences of anthropogenic disturbances to the hydrologic cycle and understanding constraints to sustainable land use.
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.
The hard X-ray view of the young supernova remnant G1.9+0.3
DEFF Research Database (Denmark)
Zoglauer, Andreas; Reynolds, Stephen P.; An, Hongjun
2015-01-01
steepens with energy. The spectral shape can be well fitted with synchrotron emission from a power-law electron energy distribution with an exponential cutoff with no additional features. It can also be described by a purely phenomenological model such as a broken power law or a power law...
Converging cylindrical magnetohydrodynamic shock collapse onto a power-law-varying line current
Mostert, W.
2016-03-16
We investigate the convergence behaviour of a cylindrical, fast magnetohydrodynamic (MHD) shock wave in a neutrally ionized gas collapsing onto an axial line current that generates a power law in time, azimuthal magnetic field. The analysis is done within the framework of a modified version of ideal MHD for an inviscid, non-dissipative, neutrally ionized compressible gas. The time variation of the magnetic field is tuned such that it approaches zero at the instant that the shock reaches the axis. This configuration is motivated by the desire to produce a finite magnetic field at finite shock radius but a singular gas pressure and temperature at the instant of shock impact. Our main focus is on the variation with shock radius, as, of the shock Mach number and pressure behind the shock as a function of the magnetic field power-law exponent, where gives a constant-in-time line current. The flow problem is first formulated using an extension of geometrical shock dynamics (GSD) into the time domain to take account of the time-varying conditions ahead of the converging shock, coupled with appropriate shock-jump conditions for a fast, symmetric MHD shock. This provides a pair of ordinary differential equations describing both and the time evolution on the shock, as a function of, constrained by a collapse condition required to achieve tuned shock convergence. Asymptotic, analytical results for and are obtained over a range of for general, and for both small and large . In addition, numerical solutions of the GSD equations are performed over a large range of, for selected parameters using . The accuracy of the GSD model is verified for some cases using direct numerical solution of the full, radially symmetric MHD equations using a shock-capturing method. For the GSD solutions, it is found that the physical character of the shock convergence to the axis is a strong function of . For μ≤0.816, and both approach unity at shock impact owing to the dominance of the strong
Directory of Open Access Journals (Sweden)
Mahroo Vojdani
2012-09-01
Conclusion: Reinforcement of the conventional heat-cured acrylic resin with 2.5 wt% Al2O3 powder significantly increased its flexural strength and hardness with no adverse effects on the surface roughness.
Directory of Open Access Journals (Sweden)
Ahmed Omran Alhareb
2017-01-01
Conclusion: The reinforced PMMA denture bases are significantly different in IS and KIC between study groups (P = 0.001. However, the Vickers hardness (VH is statistically not significantly different (P > 0.05.
A stable and robust calibration scheme of the log-periodic power law model
Filimonov, V.; Sornette, D.
2013-09-01
We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time tc, defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.
The invariances of power law size distributions [version 2; referees: 2 approved
Directory of Open Access Journals (Sweden)
Steven A. Frank
2016-11-01
Full Text Available Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances.
International Nuclear Information System (INIS)
Cybulski, Hubert; Bielski, Andrzej; Ciuryło, Roman; Szudy, Józef; Trawiński, Ryszard S.
2013-01-01
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 Distributions in the Experiment for Adjustment of the Ion Source of the NBI System
International Nuclear Information System (INIS)
Han Xiaopu; Hu Chundong
2005-01-01
The experiential adjustment process in an experiment on the ion source of the neutral beam injector system for the HT-7 Tokamak is reported in this paper. With regard to the data obtained in the same condition, in arranging the arc current intensities of every shot with a decay rank, the distributions of the arc current intensity correspond to the power laws, and the distribution obtained in the condition with the cryo-pump corresponds to the double Pareto distribution. Using the similar study method, the distributions of the arc duration are close to the power laws too. These power law distributions are formed rather naturally instead of being the results of purposeful seeking
Ormerod, Paul; Mounfield, Craig
2001-04-01
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 indeed follow power law like behaviour for a significant proportion of the data (demonstrating the existence of cooperative phenomena amongst economic agents). Crucially, however, there are systematic deviations from this behaviour when one considers the frequency of occurrence of large recessions. Under these circumstances the power law scaling breaks down. It is argued that it is the adaptive behaviour of the agents (their ability to recognise the changing economic environment) which modifies their cooperative behaviour.
Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays
Energy Technology Data Exchange (ETDEWEB)
Sibatov, R T, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy Street, Ulyanovsk (Russian Federation)
2011-08-01
A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.
Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays
International Nuclear Information System (INIS)
Sibatov, R T
2011-01-01
A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
International Nuclear Information System (INIS)
Eliazar, Iddo
2015-01-01
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
Stability of a power law relation between characteristics of earthquakes and electric precursors
Directory of Open Access Journals (Sweden)
E. Dologlou
2012-05-01
Full Text Available New data were used to test the credibility of a previously reported power law relation between the stress drop of earthquakes and the lead time of precursory SES. Here, we found that the critical exponent of this power law is very sensitive and remains stable around 0.33 only for appropriate sets of data. This value is in full agreement with the reported one in literature for critical phenomena. That means this power law is not an artifact, but probably implies that real physical dynamic processes evolving to criticality are present in the pre-focal area when the SES is emitted. An attempt to advance the underlying physics of the interconnection of the stress drop and the lead time of the precursory SES is still in progress.
Two-phase flow in porous media: power-law scaling of effective permeability
Energy Technology Data Exchange (ETDEWEB)
Groeva, Morten; Hansen, Alex, E-mail: Morten.Grova@ntnu.no, E-mail: Alex.Hansen@ntnu.no [Department of Physics, NTNU, NO-7491 Trondheim (Norway)
2011-09-15
A recent experiment has reported power-law scaling of effective permeability of two-phase flow with respect to capillary number for a two-dimensional model porous medium. In this paper, we consider the simultaneous flow of two phases through a porous medium under steady-state conditions, fixed total flow-rate and saturation, using a two-dimensional network simulator. We obtain power-law exponents for the scaling of effective permeability with respect to capillary number. The simulations are performed both for viscosity matched fluids and for a high viscosity ratio resembling that of air and water. Good power-law behaviour is found for both cases. Different exponents are found, depending on saturation.
Duality in Power-Law Localization in Disordered One-Dimensional Systems
Deng, X.; Kravtsov, V. E.; Shlyapnikov, G. V.; Santos, L.
2018-03-01
The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1 /ra . For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of a >0 . Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops (a 1 ), in which the wave function amplitude falls off algebraically with the same power γ from the localization center.
Power-law X-ray and gamma-ray emission from relativistic thermal plasmas
Zdziarski, A. A.
1985-01-01
A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.
Effective velocity power laws for electron-neutral collision frequencies. [in ionosphere
Comfort, R. H.
1975-01-01
Calculations of electron transport coefficients in the ionosphere are simplified if the electron-neutral collision frequency can be expressed as a power law in velocity. A new method for determining the effective power law representation for electron-neutral collision frequencies of arbitrary velocity dependence is presented. This method is applied to ionospheric gases in a model calculation. Comparison with similar results of Schunk and Walker and with exact calculations of transport coefficient correction factors demonstrates this technique to be more accurate than the other. Effective power law indexes are computed for both Banks' and Itikawa's collision frequencies. Relative differences between these indexes are found to be considerably larger than the differences between the collision frequencies themselves; however, the effects on transport calculations are shown to be smaller.
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2015-04-15
Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.
Timing of continuous motor imagery: the two-thirds power law originates in trajectory planning.
Karklinsky, Matan; Flash, Tamar
2015-04-01
The two-thirds power law, v = γκ(-1/3), expresses a robust local relationship between the geometrical and temporal aspects of human movement, represented by curvature κ and speed v, with a piecewise constant γ. This law is equivalent to moving at a constant equi-affine speed and thus constitutes an important example of motor invariance. Whether this kinematic regularity reflects central planning or peripheral biomechanical effects has been strongly debated. Motor imagery, i.e., forming mental images of a motor action, allows unique access to the temporal structure of motor planning. Earlier studies have shown that imagined discrete movements obey Fitts's law and their durations are well correlated with those of actual movements. Hence, it is natural to examine whether the temporal properties of continuous imagined movements comply with the two-thirds power law. A novel experimental paradigm for recording sparse imagery data from a continuous cyclic tracing task was developed. Using the likelihood ratio test, we concluded that for most subjects the distributions of the marked positions describing the imagined trajectory were significantly better explained by the two-thirds power law than by a constant Euclidean speed or by two other power law models. With nonlinear regression, the β parameter values in a generalized power law, v = γκ(-β), were inferred from the marked position records. This resulted in highly variable yet mostly positive β values. Our results imply that imagined trajectories do follow the two-thirds power law. Our findings therefore support the conclusion that the coupling between velocity and curvature originates in centrally represented motion planning. Copyright © 2015 the American Physiological Society.
Hard scattering and gauge/string duality.
Polchinski, Joseph; Strassler, Matthew J
2002-01-21
We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions.
Dilatonic BTZ black holes with power-law field
International Nuclear Information System (INIS)
Hendi, S.H.; Eslam Panah, B.; Panahiyan, S.; Sheykhi, A.
2017-01-01
Motivated by low energy effective action of string theory and numerous applications of BTZ black holes, we will consider minimal coupling between dilaton and nonlinear electromagnetic fields in three dimensions. The main goal is studying thermodynamical structure of black holes in this set up. Temperature and heat capacity of these black holes are investigated and a picture regarding their phase transitions is given. In addition, the role and importance of studying the mass of black holes is highlighted. We will see how different parameters modify thermodynamical quantities, hence thermodynamical structure of these black holes. In addition, geometrical thermodynamics is used to investigate thermodynamical properties of these black holes. In this regard, the successful method is presented and the nature of interaction around bound and phase transition points is studied.
An explanation for the universal 3.5 power-law observed in currency markets
Directory of Open Access Journals (Sweden)
Nicholas A. Johnson
Full Text Available 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. Keywords: Complex systems, Econophysics, Collective, Power law
Numerical Modeling of the Flow of a Power Law Ceramic Slurry in the Tape Casting Process
DEFF Research Database (Denmark)
Jabbari, Masoud; Hattel, Jesper Henri
2012-01-01
Multilayer ceramics and their application have increased recently. One of the most common ways used to produce these products is tape casting. In this process the wet tape thickness is one of the most determining parameters affecting the final properties of the product and it is therefore of great...... 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...
Effect of Body Perturbations on Hypersonic Flow Over Slender Power Law Bodies
Mirels, Harold; Thornton, Philip R.
1959-01-01
Hypersonic-slender-body theory, in the limit as the free-stream Mach number becomes infinite, is used to find the effect of slightly perturbing the surface of slender two-dimensional and axisymmetric power law bodies, The body perturbations are assumed to have a power law variation (with streamwise distance downstream of the nose of the body). Numerical results are presented for (1) the effect of boundary-layer development on two dimensional and axisymmetric bodies, (2) the effect of very small angles of attack (on tow[dimensional bodies), and (3) the effect of blunting the nose of very slender wedges and cones.
Determining Rheological Parameters of Generalized Yield-Power-Law Fluid Model
Directory of Open Access Journals (Sweden)
Stryczek Stanislaw
2004-09-01
Full Text Available The principles of determining rheological parameters of drilling muds described by a generalized yield-power-law are presented in the paper. Functions between tangent stresses and shear rate are given. The conditions of laboratory measurements of rheological parameters of generalized yield-power-law fluids are described and necessary mathematical relations for rheological model parameters given. With the block diagrams, the methodics of numerical solution of these relations has been presented. Rheological parameters of an exemplary drilling mud have been calculated with the use of this numerical program.
On the dynamics of the power law inflation due to an exponential potential
International Nuclear Information System (INIS)
Yokohama, Jun'ichi; Maeda, Kei-ichi; Tokyo Univ.
1988-01-01
The power law inflationary universe model induced by a scalar field with an exponential potential is studied. A dissipation term due to particle creation is introduced in the inflation's classical equation of motion. It is shown that the power index of the inflation increases prominently with an adequate viscosity. Consequently, even in theories with a rather steep exponential such as some supergravity or superstring models, it turns out that a 'realistic' power law inflation (with a power index p> or approx.10) is possible. (orig.)
Spectro-Timing Study of GX 339-4 in a Hard Intermediate State
DEFF Research Database (Denmark)
Fürst, F.; Grinberg, V.; Tomsick, J. A.
2016-01-01
We present an analysis of Nuclear Spectroscopic Telescope Array observations of a hard intermediate state of the transient black hole GX 339-4 taken in 2015 January. With the source softening significantly over the course of the 1.3 day long observation we split the data into 21 sub-sets and find...... that the spectrum of all of them can be well described by a power-law continuum with an additional relativistically blurred reflection component. The photon index increases from ∼1.69 to ∼1.77 over the course of the observation. The accretion disk is truncated at around nine gravitational radii in all spectra. We...
International Nuclear Information System (INIS)
Brandl, Erhard; Schoberth, Achim; Leyens, Christoph
2012-01-01
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.
Mathematical analysis of the global dynamics of a power law model ...
African Journals Online (AJOL)
We analyze a mathematical power law model that describes HIV infection of CD4+ T cells. We report that the number of critical points depends on , where is a positive integer. We show that for any positive integer the infection – free equilibrium is asymptotically stable if the reproduction number R0 1.
Influence of power-law index on an unsteady exothermic reaction ...
African Journals Online (AJOL)
This study presents the solution of an unsteady Arrhenius exothermic reaction where we reduced the exponential term to a power-law approximation. A numerical solution of the problem is obtained using shooting technique with second order Runge-Kuta scheme. It is shown that the temperature of the reactant depends on ...
Asymptotic expansion of unsteady gravity flow of a power-law fluid ...
African Journals Online (AJOL)
We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...
Directory of Open Access Journals (Sweden)
Pablo D. Mininni
2012-01-01
Full Text Available In the context of tackling the ill-posed inverse problem of motion estimation from image sequences, we propose to introduce prior knowledge on flow regularity given by turbulence statistical models. Prior regularity is formalised using turbulence power laws describing statistically self-similar structure of motion increments across scales. The motion estimation method minimises the error of an image observation model while constraining second-order structure function to behave as a power law within a prescribed range. Thanks to a Bayesian modelling framework, the motion estimation method is able to jointly infer the most likely power law directly from image data. The method is assessed on velocity fields of 2-D or quasi-2-D flows. Estimation accuracy is first evaluated on a synthetic image sequence of homogeneous and isotropic 2-D turbulence. Results obtained with the approach based on physics of fluids outperform state-of-the-art. Then, the method analyses atmospheric turbulence using a real meteorological image sequence. Selecting the most likely power law model enables the recovery of physical quantities, which are of major interest for turbulence atmospheric characterisation. In particular, from meteorological images we are able to estimate energy and enstrophy fluxes of turbulent cascades, which are in agreement with previous in situ measurements.
Axial annular flow of power-law fluids - applicability of the limiting cases
Czech Academy of Sciences Publication Activity Database
Filip, Petr; David, Jiří
2007-01-01
Roč. 52, č. 4 (2007), s. 365-371 ISSN 0001-7043 R&D Projects: GA ČR GA103/06/1033 Institutional research plan: CEZ:AV0Z20600510 Keywords : Concentric annuli * Poiseuile flow * annular flow * power- law fluids * flow rate * pressure drop Subject RIV: BK - Fluid Dynamics
Power-law cosmic expansion in f(R) gravity models
International Nuclear Information System (INIS)
Goheer, Naureen; Larena, Julien; Dunsby, Peter K. S.
2009-01-01
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R n gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
MHD free convection flow of a non-Newtonian power-law fluid over ...
African Journals Online (AJOL)
... flow have been presented for various parameters such as Prandtl number, flow behavior index (n), porous plate parameter and magnetic parameter. The local Nusselt number and skin friction coefficient is also presented graphically. Keywords: Magnetohydrodynamic flow; free convection flow; Non-Newtonian power-law
DEFF Research Database (Denmark)
Jørgensen, Bent; Demétrio, Clarice G. B.; Kristensen, Erik
2011-01-01
Estimation of Taylor’s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating...
Influence of power-law exponent on an unsteady endothermic reaction
African Journals Online (AJOL)
In [6], the solution of a steady Arrhenious endothermic chemical reaction where the exponential term was reduced to a power-law approximation was studied. A numerical solution obtained using a shooting technique with second order Runge-Kutta scheme showed that the minimum temperature of the reactant increases as ...
Mathematical analysis of the global dynamics of a power law model ...
African Journals Online (AJOL)
We analyze a mathematical power law model that describes HIV infection of CD4+ T cells. We report that the number of critical points depends on n , where n is a positive integer. We show that for any positive integer n the infection – free equilibrium is asymptotically stable if the reproduction number R0 < 1 and unstable if ...
Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?
Bauer, Ben
2009-01-01
Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less…
Finite sample properties of power-law cross-correlations estimators
Czech Academy of Sciences Publication Activity Database
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: 1.785, year: 2015 http://library.utia.cas.cz/separaty/2014/E/kristoufek-0433530.pdf
Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence
The binary power law (BPL) has been successfully used to characterize heterogeneity (over dispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial...
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
Thelwall, Mike; Wilkinson, David
2003-01-01
Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)
Spatial and Temporal Stability of the Estimated Parameters of the Binary Power Law
The binary power law has become a standard approach for describing and quantifying spatial patterns of disease incidence and summarizing the spatial dynamics of disease over the course of an epidemic. However, the portability and temporal stability of parameter estimates of the binary form of the p...
High energy power-law tail in X-ray binaries and bulk ...
Indian Academy of Sciences (India)
NAGENDRA KUMAR
2018-02-10
Feb 10, 2018 ... and the wind launching radius decreases with increas- ing wind speed (Díaz Trigo & Boirin 2016; Miller et al. 2016; Ponti et al. 2012; Tombesi et al. 2012, 2015). In this work, our primary motivation is to investigate the outflow geometries which can generate the high energy power-law tail. As it was earlier ...
Quantum dots with indirect band gap: power-law photoluminescence decay
Czech Academy of Sciences Publication Activity Database
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
Power laws reveal phase transitions in landscape controls of fire regimes
Donald McKenzie; Maureen C. Kennedy
2012-01-01
Understanding the environmental controls on historical wildfires, and how they changed across spatial scales, is difficult because there are no surviving explicit records of either weather or vegetation (fuels). Here we show how power laws associated with fire-event time series arise in limited domains of parameters that represent critical transitions in the controls...
A framework for evaluating statistical dependencies and rank correlations in power law graphs
Volkovich, Y.; Litvak, Nelli; Zwart, B.
We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. To the best of our knowledge, this is the first attempt to apply the well developed theory of regular variation to graph
Power-Law Indices of Time Properties on Energy Zhao-Yang Peng
Indian Academy of Sciences (India)
well-separated long-duration γ-ray burst (GRB) pulse sample is demon- strated here. We argue that the ... Correlations of the three power-law indices vs. analytic lags t31 as well as relative spectral lags t31,rel,3. ... This work was supported by the National Natural Science Foundation of China. (No. 11263006), the Yunnan ...
Czech Academy of Sciences Publication Activity Database
Keil, P.; Herben, Tomáš; Rosindell, J.; Storch, D.
2010-01-01
Roč. 265, č. 1 (2010), s. 68-86 ISSN 0022-5193 R&D Projects: GA MŠk LC06073 Institutional research plan: CEZ:AV0Z60050516 Keywords : Taylor´s power law * density dependence * pink noise Subject RIV: EF - Botanics Impact factor: 2.371, year: 2010
Propagation of Gravity Currents of non-Newtonian Power-Law Fluids in Porous Media
Di Federico, V.; Longo, S.; Ciriello, V.; Chiapponi, L.
2014-12-01
A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by k; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, α; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters ω and β. Scalings for current length and thickness are derived in self similar form coupling the modified Darcy's law accounting for the fluid rheology with the mass balance equation. The length, thickness, and aspect ratio of the current are studied as functions of model parameters; several different critical values of α emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times.
PLNoise: a package for exact numerical simulation of power-law noises
Milotti, Edoardo
2006-08-01
Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell, ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press, Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case
Power laws and self-organized criticality in theory and nature
Marković, Dimitrije; Gros, Claudius
2014-03-01
Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real
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.
Komatsu, Nobuyoshi
2017-11-01
A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the α th power of the Hubble parameter, where α is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constantlike when α is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.
MHD boundary layer flow of a power-law nanofluid with new mass flux condition
Directory of Open Access Journals (Sweden)
Masood Khan
2016-02-01
Full Text Available An analysis is carried out to study the magnetohydrodynamic MHD boundary layer flow of power-law nanofluid over a non-linear stretching sheet. In the presence of a transverse magnetic field, the flow is generated due to non-linear stretching sheet. By using similarity transformations, the governing boundary layer equations are reduced into a system of ordinary differential equations. A recently proposed boundary condition requiring zero nanoparticle mass flux is employed in the flow analysis of power-law fluid. The reduced coupled differential equations are then solved numerically by the shooting method. The variations of dimensionless temperature and nanoparticle concentration with various parameters are graphed and discussed in detail. Numerical values of physical quantities such as the skin-friction coefficient and the reduced local Nusselt number are computed in tabular form.
Linear current fluctuations in the power-law region of metallic carbon nanotubes
Talukdar, D.; Yotprayoonsak, P.; Herranen, O.; Ahlskog, M.
2013-09-01
We study low-frequency noise in a non-Ohmic region of metallic single walled and multiwalled carbon nanotubes. The generalized relative noise appears to be independent of applied bias in the power-law regime of the tubes and in agreement with theoretical predictions. Beyond the power-law regime the suppression of conductance due to scattering with optical phonons is accompanied by a reduction of relative noise by an order of magnitude. Mobility fluctuations in the tubes due to optical phonon scattering cause the unexpected reduction in the relative noise magnitude which is modeled using a modified mobility fluctuation picture. The findings have important implications for metallic nanotubes being used as interconnects in nanoelectronic devices.
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.
How Power-Laws Re-Write The Rules Of Cyber Warfare
Directory of Open Access Journals (Sweden)
David L. Bibighaus
2015-12-01
Full Text Available All warfare contains and element of randomness. This article will argue that, the kind uncertainty encountered in cyber warfare (Power-Law randomness is fundamentally different from the uncertainty the military has evolved to deal with in the physical world (Gaussian-Randomness. The article will explain the difference between these two kinds of randomness, and how cyber weapons appear to operate under Power-Law randomness. It then will show how in cyberspace, key aspects of strategic thought are based on a flaws assumption of randomness. Finally, this article shall argue that if the American military is going to be effective in cyberspace, it must re-examine the way the military assumes risk, recruits is forces, plans for war and maintains the peace.
Weighted scale-free networks with variable power-law exponents
Tanaka, Takuma; Aoyagi, Toshio
2008-06-01
We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model.
On the origin of power-law distributions in systems with constrained phase space
Directory of Open Access Journals (Sweden)
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.
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.
Using Power-Law Degree Distribution to Accelerate PageRank
Directory of Open Access Journals (Sweden)
Zhaoyan Jin
2012-12-01
Full Text Available The PageRank vector of a network is very important, for it can reflect the importance of a Web page in the World Wide Web, or of a people in a social network. However, with the growth of the World Wide Web and social networks, it needs more and more time to compute the PageRank vector of a network. In many real-world applications, the degree and PageRank distributions of these complex networks conform to the Power-Law distribution. This paper utilizes the degree distribution of a network to initialize its PageRank vector, and presents a Power-Law degree distribution accelerating algorithm of PageRank computation. Experiments on four real-world datasets show that the proposed algorithm converges more quickly than the original PageRank algorithm.
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 ...
The dynamics of power laws: Fitness and aging in preferential attachment trees
Garavaglia, Alessandro; van der Hofstad, Remco; Woeginger, Gerhard
2017-01-01
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. ...
The power laws of violence against women: rescaling research and policies.
Directory of Open Access Journals (Sweden)
Karolin E Kappler
Full Text Available BACKGROUND: Violence against Women -despite its perpetuation over centuries and its omnipresence at all social levels- entered into social consciousness and the general agenda of Social Sciences only recently, mainly thanks to feminist research, campaigns, and general social awareness. The present article analyzes in a secondary analysis of German prevalence data on Violence against Women, whether the frequency and severity of Violence against Women can be described with power laws. PRINCIPAL FINDINGS: Although the investigated distributions all resemble power-law distributions, a rigorous statistical analysis accepts this hypothesis at a significance level of 0.1 only for 1 of 5 cases of the tested frequency distributions and with some restrictions for the severity of physical violence. Lowering the significance level to 0.01 leads to the acceptance of the power-law hypothesis in 2 of the 5 tested frequency distributions and as well for the severity of domestic violence. The rejections might be mainly due to the noise in the data, with biases caused by self-reporting, errors through rounding, desirability response bias, and selection bias. CONCLUSION: Future victimological surveys should be designed explicitly to avoid these deficiencies in the data to be able to clearly answer the question whether Violence against Women follows a power-law pattern. This finding would not only have statistical implications for the processing and presentation of the data, but also groundbreaking consequences on the general understanding of Violence against Women and policy modeling, as the skewed nature of the underlying distributions makes evident that Violence against Women is a highly disparate and unequal social problem. This opens new questions for interdisciplinary research, regarding the interplay between environmental, experimental, and social factors on victimization.
The distance-decay function of geographical gravity model: Power law or exponential law?
International Nuclear Information System (INIS)
Chen, Yanguang
2015-01-01
Highlights: •The distance-decay exponent of the gravity model is a fractal dimension. •Entropy maximization accounts for the gravity model based on power law decay. •Allometric scaling relations relate gravity models with spatial interaction models. •The four-parameter gravity models have dual mathematical expressions. •The inverse power law is the most probable distance-decay function. -- Abstract: 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 reasonably explained with the ideas from Euclidean geometry. This results in a dimension dilemma in geographical analysis. Consequently, a negative exponential function was used to replace the inverse power function to serve for a distance-decay function. But a new puzzle arose that the exponential-based gravity model goes against the first law of geography. This paper is devoted for solving these kinds of problems by mathematical reasoning and empirical analysis. New findings are as follows. First, the distance exponent of the gravity model is demonstrated to be a fractal dimension using the geometric measure relation. Second, the similarities and differences between the gravity models and spatial interaction models are revealed using allometric relations. Third, a four-parameter gravity model possesses a symmetrical expression, and we need dual gravity models to describe spatial flows. The observational data of China's cities and regions (29 elements indicative of 841 data points) in 2010 are employed to verify the theoretical inferences. A conclusion can be reached that the geographical gravity model based on power-law decay is more suitable for analyzing large, complex, and scale-free regional and urban systems. This study lends further support to the suggestion that the underlying rationale of fractal structure is entropy maximization. Moreover
Comparison of generalized Reynolds and Navier Stokes equations for flow of a power law fluid
Mullen, R. L.; Prekwas, A.; Braun, M. J.; Hendricks, R. C.
1987-01-01
This paper compares a finite element solution of a modified Reynolds equation with a finite difference solution of the Navier-Stokes equation for a power law fluid. Both the finite element and finite difference formulation are reviewed. Solutions to spiral flow in parallel and conical geometries are compared. Comparison with experimental results are also given. The effects of the assumptions used in the Reynolds equation are discussed.
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
Howell, L. W., Jr.
2003-01-01
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
Power-law distributions for a trapped ion interacting with a classical buffer gas.
DeVoe, Ralph G
2009-02-13
Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment.
Comments on Marken and Shaffer: The power law of movement: an example of a behavioral illusion.
Taylor, M M
2018-02-21
Many researchers who have studied movements along curved paths, under a variety of conditions, by different organisms, mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential (along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cR k , where k is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and in which the power law fails badly). Marken and Shaffer (Exp Brain Res 235:1835-1842; 2017), following a challenge by Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations from this value occur because researchers have omitted a critical correction "cross-product" factor that the authors label "D". This note questions the logic of the analysis offered by Marken and Shaffer, and argues that even had the analysis been correct, it would not affect future research into the reasons why and when the power law is observed and the circumstances that determine the value of the power found when it is observed.
Laboratory constraints on chameleon dark energy and power-law fields
Steffen, Jason H.; Upadhye, Amol; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; Weltman, Amanda; Wester, William
2010-01-01
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 betw...
Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields
International Nuclear Information System (INIS)
Steffen, J. H.; Baumbaugh, A.; Chou, A. S.; Mazur, P. O.; Tomlin, R.; Wester, W.; Upadhye, A.; Weltman, A.
2010-01-01
We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Design of Linear CMOS Transconductance Elements for Alpha-Power Law Based MOSFETs
Bhaskar Gopalan
2015-01-01
A model on alpha-power law MOSFETs based source-coupled differential pair (SCDP) is discussed and a simple design procedure for realizing a linear CMOS SCDP transconductance element is proposed. The modified SCDP circuit using this procedure is an alternative to that of conventional SCDP and the circuit discussed has superior linearity than the conventional SCDP for a wide range of input differential voltage. The modified SCDP also includes the circuitry needed to suppress the variation in th...
Javidani, M.; Arreguin-Zavala, J.; Danovitch, J.; Tian, Y.; Brochu, M.
2017-04-01
This paper aims to study the manufacturing of the AlSi10Mg alloy with direct energy deposition (DED) process. Following fabrication, the macro- and microstructural evolution of the as-processed specimens was initially investigated using optical microscopy and scanning electron microscopy. Columnar dendritic structure was the dominant solidification feature of the deposit; nevertheless, detailed microstructural analysis revealed cellular morphology near the substrate and equiaxed dendrites at the top end of the deposit. Moreover, the microstructural morphology in the melt pool boundary of the deposit differed from the one in the core of the layers. The remaining porosity of the deposit was evaluated by Archimedes' principle and by image analysis of the polished surface. Crystallographic texture in the deposit was also assessed using electron backscatter diffraction and x-ray diffraction analysis. The dendrites were unidirectionally oriented at an angle of 80° to the substrate. EPMA line scans were performed to evaluate the compositional variation and elemental segregation in different locations. Eventually, microhardness (HV) tests were conducted in order to study the hardness gradient in the as-DED-processed specimen along the deposition direction. The presented results, which exhibited a deposit with an almost defect free structure, indicate that the DED process can suitable for the deposition of Al-Si-based alloys with a highly consolidated structure.
Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile.
O'Boy, Daniel J; Bowyer, Elizabeth P; Krylov, Victor V
2011-06-01
The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor. © 2011 Acoustical Society of America
Dust-acoustic waves and stability in the permeating dusty plasma. II. Power-law distributions
International Nuclear Information System (INIS)
Gong Jingyu; Du Jiulin; Liu Zhipeng
2012-01-01
The dust-acoustic waves and the stability theory for the permeating dusty plasma with power-law distributions are studied by using nonextensive q-statistics. In two limiting physical cases, when the thermal velocity of the flowing dusty plasma is much larger than, and much smaller than the phase velocity of the waves, we derived the dust-acoustic wave frequency, the instability growth rate, and the instability critical flowing velocity. As compared with the formulae obtained in part I [Gong et al., Phys. Plasmas 19, 043704 (2012)], all formulae of the present cases and the resulting plasma characteristics are q-dependent, and the power-law distribution of each plasma component of the permeating dusty plasma has a different q-parameter and thus has a different nonextensive effect. Further, we make numerical analyses of an example that a cometary plasma tail is passing through the interplanetary space dusty plasma and we show that these power-law distributions have significant effects on the plasma characteristics of this kind of plasma environment.
Power-law behavior in complex organizational communication networks during crisis
Uddin, Shahadat; Murshed, Shahriar Tanvir Hasan; Hossain, Liaquat
2011-08-01
Communication networks can be described as patterns of contacts which are created due to the flow of messages and information shared among participating actors. Contemporary organizations are now commonly viewed as dynamic systems of adaptation and evolution containing several parts, which interact with one another both in internal and in external environment. Although there is limited consensus among researchers on the precise definition of organizational crisis, there is evidence of shared meaning: crisis produces individual crisis, crisis can be associated with positive or negative conditions, crises can be situations having been precipitated quickly or suddenly or situations that have developed over time and are predictable etc. In this research, we study the power-law behavior of an organizational email communication network during crisis from complexity perspective. Power law simply describes that, the probability that a randomly selected node has k links (i.e. degree k) follows P(k)∼k, where γ is the degree exponent. We used social network analysis tools and techniques to analyze the email communication dataset. We tested two propositions: (1) as organization goes through crisis, a few actors, who are prominent or more active, will become central, and (2) the daily communication network as well as the actors in the communication network exhibit power-law behavior. Our preliminary results support these two propositions. The outcome of this study may provide significant advancement in exploring organizational communication network behavior during crisis.
Accuracy analysis of measurements on a stable power-law distributed series of events
International Nuclear Information System (INIS)
Matthews, J O; Hopcraft, K I; Jakeman, E; Siviour, G B
2006-01-01
We investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined. The model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events. This leads to a scale-free discrete random process where customary measures, such as mean value and variance, do not exist. However, converting the number of events occurring in fixed time intervals to a 1-bit 'clipped' process allows the construction of well-behaved statistics that still retain vestiges of the original power-law and fluctuation properties. These statistics include the clipped mean and correlation function, from measurements of which both the power-law index of the distribution of events and the time constant of its fluctuations can be deduced. We report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process. This indicates that, for a fixed experiment time, the error on measurements of the sample mean is minimized by an optimum choice of the number of samples. It is shown furthermore that this choice is sensitive to the power-law index and that the approach to Poisson statistics is dominated by rare events or 'outliers'. Our results are supported by numerical simulation
Multiplicative processes and power laws in human reaction times derived from hyperbolic functions
International Nuclear Information System (INIS)
Medina, José M.
2012-01-01
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.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Decomposition of Heart Rate Variability Spectrum into a Power-Law Function and a Residual Spectrum.
Kuo, Jane; Kuo, Cheng-Deng
2016-01-01
The power spectral density (PSD) of heart rate variability (HRV) contains a power-law relationship that can be obtained by plotting the logarithm of PSD against the logarithm of frequency. The PSD of HRV can be decomposed mathematically into a power-law function and a residual HRV (rHRV) spectrum. Almost all rHRV measures are significantly smaller than their corresponding HRV measures except the normalized high-frequency power (nrHFP). The power-law function can be characterized by the slope and Y-intercept of linear regression. Almost all HRV measures except the normalized low-frequency power have significant correlations with the Y-intercept, while almost all rHRV measures except the total power [residual total power (rTP)] do not. Though some rHRV measures still correlate significantly with the age of the subjects, the rTP, high-frequency power (rHFP), nrHFP, and low-/high-frequency power ratio (rLHR) do not. In conclusion, the clinical significances of rHRV measures might be different from those of traditional HRV measures. The Y-intercept might be a better HRV measure for clinical use because it is independent of almost all rHRV measures. The rTP, rHFP, nrHFP, and rLHR might be more suitable for the study of age-independent autonomic nervous modulation of the subjects.
Comment on "Time needed to board an airplane: a power law and the structure behind it".
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the "back-to-front" strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.
Chahtour, C.; Ben Hamed, H.; Beji, H.; Guizani, A.; Alimi, W.
2018-01-01
We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.
Interacting cosmic fluids in power-law Friedmann-Robertson-Walker cosmological models
International Nuclear Information System (INIS)
Cataldo, Mauricio; Mella, Patricio; Minning, Paul; Saavedra, Joel
2008-01-01
We provide a detailed description for power-law scaling Friedmann-Robertson-Walker cosmological scenarios dominated by two interacting perfect fluid components during the expansion. As a consequence of the mutual interaction between the two fluids, neither component is conserved separately and the energy densities are proportional to 1/t 2 . It is shown that in flat FRW cosmological models there can exist interacting superpositions of two perfect fluids (each of them having a positive energy density) which accelerate the expansion of the universe. In this family there also exist flat power-law cosmological scenarios where one of the fluids may have a 'cosmological constant' or 'vacuum energy' equation of state (p=-ρ) interacting with the other component; this scenario exactly mimics the behavior of the standard flat Friedmann solution for a single fluid with a barotropic equation of state. These possibilities of combining interacting perfect fluids do not exist for the non-interacting mixtures of two perfect cosmic fluids, where the general solution for the scale factor is not described by power-law expressions and has a more complicated behavior. In this study is considered also the associated single fluid model interpretation for the interaction between two fluids
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
The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees
Garavaglia, Alessandro; van der Hofstad, Remco; Woeginger, Gerhard
2017-09-01
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.
Distributed power-law seismicity changes and crustal deformation in the SW Hellenic ARC
Directory of Open Access Journals (Sweden)
A. Tzanis
2003-01-01
Full Text Available A region of definite accelerating seismic release rates has been identified at the SW Hellenic Arc and Trench system, of Peloponnesus, and to the south-west of the island of Kythera (Greece. The identification was made after detailed, parametric time-to-failure modelling on a 0.1° square grid over the area 20° E – 27° E and 34° N–38° N. The observations are strongly suggestive of terminal-stage critical point behaviour (critical exponent of the order of 0.25, leading to a large earthquake with magnitude 7.1 ± 0.4, to occur at time 2003.6 ± 0.6. In addition to the region of accelerating seismic release rates, an adjacent region of decelerating seismicity was also observed. The acceleration/deceleration pattern appears in such a well structured and organised manner, which is strongly suggestive of a causal relationship. An explanation may be that the observed characteristics of distributed power-law seismicity changes may be produced by stress transfer from a fault, to a region already subjected to stress inhomogeneities, i.e. a region defined by the stress field required to rupture a fault with a specified size, orientation and rake. Around a fault that is going to rupture, there are bright spots (regions of increasing stress and stress shadows (regions relaxing stress; whereas acceleration may be observed in bright spots, deceleration may be expected in the shadows. We concluded that the observed seismic release patterns can possibly be explained with a family of NE-SW oriented, left-lateral, strike-slip to oblique-slip faults, located to the SW of Kythera and Antikythera and capable of producing earthquakes with magnitudes MS ~ 7. Time-to-failure modelling and empirical analysis of earthquakes in the stress bright spots yield a critical exponent of the order 0.25 as expected from theory, and a predicted magnitude and critical time perfectly consistent with the figures given above. Although we have determined an approximate location
Kumar, Jagadish; Ananthakrishna, G
2018-01-01
Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum
On the interplay between short and long term memory in the power-law cross-correlations setting
Kristoufek, Ladislav
2015-03-01
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equal to an average of separate Hurst exponents of the analyzed processes. Strength of short term memory has no effect on these asymptotic properties. Implications of these findings for the power-law cross-correlations concept are further discussed.
Bruce, Susan; DiNatale, Patrice; Ford, Jeremiah
2008-01-01
According to even the most conservative estimates, at least a quarter of deaf children have additional disabilities. Most teacher preparation programs do not sufficiently prepare teacher candidates for the challenges posed by these children. This article describes a professional development effort to prepare in-service educators of the deaf to work with students with additional disabilities. Over a 3-year period, teachers selected these in-service topics: etiologies, vision conditions, behavior, transition, sensory integration, seizures, alternate assessment, and instructional strategies. In-class consultation was requested for support in the areas of formal assessment instruments, behavior, and student performance. Elements of effective professional development programs, such as honoring teachers' choices about topics and participation, responding to teachers' immediate classroom concerns, and providing in-class follow-up support, facilitated the success of this effort.
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2014-01-01
Full Text Available This work studies the pressure transient of power-law fluids in porous media embedded with a tree-shaped fractal network. A pressure transient model was created based on the fractal properties of tree-shaped capillaries, generalized Darcy’s law and constitutive equation for power-law fluids. The dimensionless pressure model was developed using the Laplace transform and Stehfest numerical inversion method. According to the model’s solution, the bi-logarithmic type curves of power-law fluids in porous media embedded with a tree-shaped fractal network are illustrated. The influences of different fractal factors and Power-law fluids parameters on pressure transient responses are discussed.
Fantazzini, Dean; Geraskin, Petr
2011-01-01
Sornette et al. (1996), Sornette and Johansen (1997), Johansen et al. (2000) and Sornette (2003a) proposed that, prior to crashes, the mean function of a stock index price time series is characterized by a power law decorated with log-periodic oscillations, leading to a critical point that describes the beginning of the market crash. This paper reviews the original Log-Periodic Power Law (LPPL) model for financial bubble modelling, and discusses early criticism and recent generalizations prop...
Hard electronics; Hard electronics
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-03-01
Hard material technologies were surveyed to establish the hard electronic technology which offers superior characteristics under hard operational or environmental conditions as compared with conventional Si devices. The following technologies were separately surveyed: (1) The device and integration technologies of wide gap hard semiconductors such as SiC, diamond and nitride, (2) The technology of hard semiconductor devices for vacuum micro- electronics technology, and (3) The technology of hard new material devices for oxides. The formation technology of oxide thin films made remarkable progress after discovery of oxide superconductor materials, resulting in development of an atomic layer growth method and mist deposition method. This leading research is expected to solve such issues difficult to be easily realized by current Si technology as high-power, high-frequency and low-loss devices in power electronics, high temperature-proof and radiation-proof devices in ultimate electronics, and high-speed and dense- integrated devices in information electronics. 432 refs., 136 figs., 15 tabs.
Langlois, Dominic; Cousineau, Denis; Thivierge, J P
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane.
Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco
2015-06-07
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
Transition in the Flow of Power-Law Fluids through Isotropic Porous Media.
Zami-Pierre, F; de Loubens, R; Quintard, M; Davit, Y
2016-08-12
We use computational fluid dynamics to explore the creeping flow of power-law fluids through isotropic porous media. We find that the flow pattern is primarily controlled by the geometry of the porous structure rather than by the nonlinear effects in the rheology of the fluid. We further highlight a macroscale transition between a Newtonian and a non-Newtonian regime, which is the signature of a coupling between the viscosity of the fluid and the structure of the porous medium. These complex features of the flow can be condensed into an effective length scale, which defines both the non-Newtonian transition and the Newtonian permeability.
Studying laminar flows of power-law fluids in the annular channel with eccentricity
Zhigarev, V. A.; Neverov, A. L.; Guzei, D. V.; Pryazhnikov, M. I.
2017-09-01
The paper deals with numerical and experimental investigation of non-Newtonian flow of modeling drilling fluids in the annular channel. The Reynolds number was ranged from 100 to 1500. The parameters of the power-law model of drilling fluids were varied within the following ranges: n = 0.43-0.49, K = 0.22-0.89. The eccentricity was changed from 0 to 1. We have measured pressure drop in the annular channel and compared calculations with experimental data, achieving good agreement between calculations and experiment.
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.
Highly excited bound-state resonances of short-range inverse power-law potentials
Hod, Shahar
2017-11-01
We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form V(r)=-β _n r^{-n} with n>2. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius R, we derive a compact analytical formula for the threshold energy E^{ {max}}_l=E^{ {max}}_l(n,β _n,R), which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.
International Nuclear Information System (INIS)
Ding Zhonghai; Chen, Goong; Lin, Chang-Shou
2010-01-01
The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schroedinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schroedinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.
DUGDALE-MAUGIS ADHESIVE NORMAL CONTACT OF AXISYMMETRIC POWER-LAW GRADED ELASTIC BODIES
Directory of Open Access Journals (Sweden)
Emanuel Willert
2018-02-01
Full Text Available A closed-form general analytic solution is presented for the adhesive normal contact of convex axisymmetric power-law graded elastic bodies using a Dugdale-Maugis model for the adhesive stress. The case of spherical contacting bodies is studied in detail. The known JKR- and DMT-limits can be derived from the general solution, whereas the transition between both can be captured introducing a generalized Tabor parameter depending on the material grading. The influence of the Tabor parameter and the material grading is studied.
Extended power-law scaling of air permeabilities measured on a block of tuff
Directory of Open Access Journals (Sweden)
M. Siena
2012-01-01
Full Text Available We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M, Extended Self-Similarity (ESS and a generalized version thereof (G-ESS. All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q, of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q with q, are consistent with a view of these data as a sample from a truncated version (tfBm of self-affine fractional Brownian motion (fBm. Since in theory the scaling exponents, ξ(q, of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well
An explanation for the universal 3.5 power-law observed in currency markets
Johnson, Nicholas A.; Johnson, Neil F.
We present a mathematical theory to explain a recent empirical finding in the Physics literature (Zhao et al., 2013) in which the distributions of waiting-times between discrete events were found to exhibit power-law tails with an apparent universal exponent: α ∼ 3.5 . This new theory provides the first ever qualitative and quantitative explanation of Zhao et al.'s surprising finding. It also provides a mechanistic description of the origin of the observed universality, assigning its cause to the emergence of dynamical feedback processes between evolving clusters of like-minded agents.
Highly excited bound-state resonances of short-range inverse power-law potentials
Energy Technology Data Exchange (ETDEWEB)
Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Academic College, Jerusalem (Israel)
2017-11-15
We study analytically the radial Schroedinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form V(r) = -β{sub n}r{sup -n} with n > 2. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius R, we derive a compact analytical formula for the threshold energy E{sub l}{sup max} = E{sub l}{sup max}(n, β{sub n}, R), which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system. (orig.)
Laboratory constraints on chameleon dark energy and power-law fields
International Nuclear Information System (INIS)
Steffen, Jason H.; Upadhye, Amol; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; Weltman, Amanda; Wester, William
2010-01-01
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.
Truncation of power law behavior in 'scale-free' network models due to information filtering
International Nuclear Information System (INIS)
Mossa, Stefano; Barthelemy, Marc; Eugene Stanley, H.; Nunes Amaral, Luis A.
2002-01-01
We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the distribution of the number of incoming links to a node follows a universal scaling form, i.e., that it decays as a power law with an exponential truncation controlled not only by the system size but also by a feature not previously considered, the subset of the network 'accessible' to the node. We test our model with empirical data for the World Wide Web and find agreement
Disorder-induced power-law response of a superconducting vortex on a plane
Shapira, N.; Lamhot, Y.; Shpielberg, O.; Kafri, Y.; Ramshaw, B. J.; Bonn, D. A.; Liang, Ruixing; Hardy, W. N.; Auslaender, O. M.
2015-09-01
We report drive-response experiments on individual superconducting vortices on a plane, a realization for a (1+1)-dimensional directed polymer in random media. For this we use magnetic force microscopy to image and manipulate individual vortices trapped on a twin boundary in YBa2Cu3O7 -δ near optimal doping. We find that when we drag a vortex with the magnetic tip, it moves in a series of jumps. As theory suggests, the jump-size distribution does not depend on the applied force and is consistent with power-law behavior. The measured power is much larger than widely accepted theoretical calculations.
Power-law statistics of a landslide inventory of Wanzhou District, Three-Gorges Reservoir, China.
Gui, Lei; Yin, Kunlong; Glade, Thomas
2013-04-01
Landslides with high frequency and large property loss are one of the most well-known nature hazards in the world. The area of the Three Gorges Reservoir in China has a lot of landslide distributions due to geological factors and human activities. Analysis of frequency-size distribution of landslides has been frequently applied by numerous researchers. Hereby, Power-law statistics is a widely used method to determine the frequency-area (and -volume) distribution of landslides. In this study, we perform statistical analysis for a landslide inventory of the Wanzhou District in the Three-Gorges reservoir area of China. The goal is to prove that power-law statistics method for the frequency-size distribution of landslides is also applicable in Chinese environments. As the landslide investigation data is always incomplete, we proposed a way of dealing with incomplete data in this study in order to predict the total number of landslides in the study area. This study is carried out in Wanzhou District, the Three-Gorges Reservoir, China, where landslides occurred in high frequency. The landslide data has been received from the Three Gorges Geohazard Control Headquarters, which are based on a detailed field landslide investigation in 2010. The field observations have been carried out by the staff of the local environmental monitoring station and the local geologic prospecting agency. In this study, the power-law statistics has been focused on and the frequency-size and frequency-volume distribution of landslides have been analyzed. The data set contains 711 landslides. As it is an incomplete data, at the first the power-law relationship between the frequency and the area of landslides need to be analyzed, then the total number of landslides based on the ideal equation proved by other researchers has been predicted, and the real parameters within the equation used in the last step for this study area have been calculated. Finally the results have been compared with previous
Laboratory constraints on chameleon dark energy and power-law fields
Energy Technology Data Exchange (ETDEWEB)
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.
Power Law Inflation and the Cosmic No Hair Theorem in Brane World
Paul, B. C.; Beesham, A.
2004-01-01
The Cosmic no hair theorem is studied in anisotropic Bianchi brane models which admit power law inflation with a scalar field. We note that all Bianchi models except Bianchi type IX transit to an inflationary regime and the anisotropy washes out at a later epoch. It is found that in the brane world, the anisotropic universe approaches the isotropic phase via inflation much faster than that in the general theory of relativity. The modification in the Einstein field equations on the brane is he...
Hysteresis and creep: Comparison between a power-law model and Kuhnen's model
Energy Technology Data Exchange (ETDEWEB)
Oliveri, Alberto; Stellino, Flavio; Parodi, Mauro; Storace, Marco, E-mail: marco.storace@unige.it
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.
The over-the-limb hard X-ray events
Hudson, H. S.
Over-the-limb hard X-ray events offer a uniquely direct view of the hard X-ray emission from the solar corona during a major flare. Limb occultation at angles greater than about 10 deg (an arbitrary definition of this class of events) excludes any confusion with brighter chromospheric sources. Published observations of seven over-the-limb events, beginning with the prototype flare of March 30, 1969, are reviewed. The hard X-ray spectra appear to fall into two classes: hard events, with power-law index of about 2.0; and soft events, with power-law index about 5.4. This tendency towards bimodality is only significant at the 90-percent confidence level due to the smallness of the number of events observed to date. If borne out by future data, the bimodality would suggest the existence of two different acceleration mechanisms.
Directory of Open Access Journals (Sweden)
Rania Fathy
2010-01-01
Full Text Available The analysis of laminar boundary layer flow and heat transfer of non-Newtonian fluids over a continuous stretched surface with suction or injection has been presented.The velocity and temperature of the sheet were assumed to vary in a power-law form, that is u = U0xm, and Tw(x = T+ Cxb. The viscosity of the fluid is assumed to be inverse linear function of temperature. The resulting governing boundary-layer equations are highly non-linear and coupled form of partial differential equations and they have been solved numerically by using the Runge-Kutta method and Shooting technique. Velocity and temperature distributions as well as the Nusselt number where studied for two thermal boundary conditions: uniform surface temperature (b = 0 and cooled surface temperature (b = -1, for different parameters: variable viscosity parameter qr, temperature exponent b, blowing parameter d and Prandtl number. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.
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.
International Nuclear Information System (INIS)
Howell, L.W.
2002-01-01
The method of Maximum Likelihood (ML) is used to estimate the spectral parameters of an assumed broken power law energy spectrum from simulated detector responses. This methodology, which requires the complete specificity of all cosmic-ray detector design parameters, is shown to provide approximately unbiased, minimum variance, and normally distributed spectra information for events detected by an instrument having a wide range of commonly used detector response functions. The ML procedure, coupled with the simulated performance of a proposed space-based detector and its planned life cycle, has proved to be of significant value in the design phase of a new science instrument. The procedure helped make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope. This ML methodology is then generalized to estimate broken power law spectral parameters from real cosmic-ray data sets
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.
Transition from Exponential to Power Law Income Distributions in a Chaotic Market
Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.
A power-law model of psychological memory strength in short- and long-term recognition.
Donkin, Chris; Nosofsky, Robert M
2012-06-01
A classic law of cognition is that forgetting curves are closely approximated by power functions. This law describes relations between different empirical dependent variables and the retention interval, and the precise form of the functional relation depends on the scale used to measure each variable. In the research reported here, we conducted a recognition task involving both short- and long-term probes. We discovered that formal memory-strength parameters from an exemplar-recognition model closely followed a power function of the lag between studied items and a test probe. The model accounted for rich sets of response time (RT) data at both individual-subject and individual-lag levels. Because memory strengths were derived from model fits to choices and RTs from individual trials, the psychological power law was independent of the scale used to summarize the forgetting functions. Alternative models that assumed different functional relations or posited a separate fixed-strength working memory store fared considerably worse than the power-law model did in predicting the data.
Howell, Leonard W.
2002-01-01
The method of Maximum Likelihood (ML) is used to estimate the spectral parameters of an assumed broken power law energy spectrum from simulated detector responses. This methodology, which requires the complete specificity of all cosmic-ray detector design parameters, is shown to provide approximately unbiased, minimum variance, and normally distributed spectra information for events detected by an instrument having a wide range of commonly used detector response functions. The ML procedure, coupled with the simulated performance of a proposed space-based detector and its planned life cycle, has proved to be of significant value in the design phase of a new science instrument. The procedure helped make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope. This ML methodology is then generalized to estimate broken power law spectral parameters from real cosmic-ray data sets.
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.
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.
Emergence of power-law in a market with mixed models
Ali Saif, M.; Gade, Prashant M.
2007-10-01
We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.
Effective non-Coulombic power-law potential for the study of light and heavy mesons
International Nuclear Information System (INIS)
Barik, N.; Jena, S.N.
1982-01-01
From purely phenomenological considerations we have shown that it is possible to describe successfully the heavy meson spectra of cc-bar and bb-bar systems in the framework of an effective non-Coulombic power-law potential in the form V(r) = V 0 +ar/sup ν/ (with a,ν>0). The nonsingular short-distance behavior of this potential, which is in apparent contradiction with the predictions of quantum- chromodynamics, does not pose any problem in explaining the fine-hyperfine splitting, if we prescribe the spin dependence to be generated through this static confining potential in the form of an approximately equal admixture of scalar and vector parts with no contributions from the anomalous quark magnetic moments. This nonrelativistic formalsm, when extended to a unified study of the entire meson spectra including the ordinary light and the heavy mesons, gives a very good account of the meson masses, fine-hyperfine splittings, electromagnetic transition rates, and leptonic decay widths without reflecting any inadequacy in the short- and long-range behavior of this simple effective power-law potential
Universal correlations and power-law tails in financial covariance matrices
Akemann, G.; Fischmann, J.; Vivo, P.
2010-07-01
We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.
New version of PLNoise: a package for exact numerical simulation of power-law noises
Milotti, Edoardo
2007-08-01
In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press., Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. No. of lines in distributed program, including test data, etc.:2975 No. of bytes in distributed program, including test data, etc.:194 588 Distribution format:tar.gz Catalogue identifier of previous version: ADXV_v1_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212 Does the new version supersede the previous version?: Yes Nature of problem: Exact generation of different types of colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701
Birth and death of protein domains: A simple model of evolution explains power law behavior
Directory of Open Access Journals (Sweden)
Berezovskaya Faina S
2002-10-01
Full Text Available Abstract Background Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. Results A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i domain birth (duplication with divergence, ii death (inactivation and/or deletion, and iii innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer. This formalism can be described as a birth, death and innovation model (BDIM. The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational
Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses
Wijers, Ralph A. M. J.; Lubin, Lori M.
1994-01-01
We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.
Beskardes, G. D.; Weiss, C. J.; Everett, M. E.
2017-02-01
Electromagnetic responses reflect the interaction between applied electromagnetic fields and heterogeneous geoelectrical structures. Quantifying the relationship between multiscale electrical properties and the observed electromagnetic response is therefore important for meaningful geologic interpretation. We present here examples of near-surface electromagnetic responses whose spatial fluctuations appear on all length scales, are repeatable and fractally distributed, supporting the notion of a `rough geology' exhibiting multiscale hierarchical structure. Bounded by end member cases from homogenized isotropic and anisotropic media, we present numerical modelling results of the electromagnetic responses of textured and spatially correlated, stochastic geologic media, demonstrating that the electromagnetic response is a power law distribution, rather than a smooth response polluted with random, incoherent noise as commonly assumed. Our modelling results show that these electromagnetic responses due to spatially correlated geologic textures are examples of fractional Brownian motion. Furthermore, our results suggest that the fractal behaviour of the electromagnetic responses is correlated with degree of the spatial correlation, the contrasts in ground conductivity, and the preferred orientation of small-scale heterogeneity. In addition, the EM responses acquired across a fault zone comprising different lithological units and varying wavelengths of geologic heterogeneity also support our inferences from numerical modelling.
Power laws and self-organized criticality in theory and nature
International Nuclear Information System (INIS)
Marković, Dimitrije; Gros, Claudius
2014-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Akiba, M., E-mail: akiba@nict.go.jp [National Institute of Information and Communications Technology, 4-2-1, Nukuikitamachi, Koganei-City, Tokyo 184-8795 (Japan); Tsujino, K. [Department of Physics, School of Medicine, Tokyo Women' s Medical University, 8-1, Kawadacho, Shinjuku-ku, Tokyo 162-8666 (Japan)
2016-08-08
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.
Chakraborty, Ahana; Sensarma, Rajdeep
2018-03-01
The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.
Wavelet-based analysis and power law classification of C/NOFS high-resolution electron density data
Rino, C. L.; Carrano, C. S.; Roddy, Patrick
2014-08-01
This paper applies new wavelet-based analysis procedures to low Earth-orbiting satellite measurements of equatorial ionospheric structure. The analysis was applied to high-resolution data from 285 Communications/Navigation Outage Forecasting System (C/NOFS) satellite orbits sampling the postsunset period at geomagnetic equatorial latitudes. The data were acquired during a period of progressively intensifying equatorial structure. The sampled altitude range varied from 400 to 800 km. The varying scan velocity remained within 20° of the cross-field direction. Time-to-space interpolation generated uniform samples at approximately 8 m. A maximum segmentation length that supports stochastic structure characterization was identified. A two-component inverse power law model was fit to scale spectra derived from each segment together with a goodness-of-fit measure. Inverse power law parameters derived from the scale spectra were used to classify the scale spectra by type. The largest category was characterized by a single inverse power law with a mean spectral index somewhat larger than 2. No systematic departure from the inverse power law was observed to scales greater than 100 km. A small subset of the most highly disturbed passes at the lowest sampled altitudes could be categorized by two-component power law spectra with a range of break scales from less than 100 m to several kilometers. The results are discussed within the context of other analyses of in situ data and spectral characteristics used for scintillation analyses.
Zhao, Xiaofeng; McGough, Robert J.
2016-01-01
The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations. PMID:27250193
Scaling laws for fractional Brownian motion with power-law clock
International Nuclear Information System (INIS)
O'Malley, Daniel; Cushman, John H; Johnson, Graham
2011-01-01
We study the mean first passage time (MFPT) for fractional Brownian motion (fBm) in a finite interval with absorbing boundaries at each end. Analytical arguments are used to suggest a simple scaling law for the MFPT and numerical experiments are performed to verify its accuracy. The same approach is used to derive a scaling law for fBm with a power-law clock (fBm-plc). The MFPT scaling laws are employed to develop scaling laws for the finite-size Lyapunov exponent (FSLE) of fBm and fBm-plc. We apply these results to diffusion of a large polymer in a region with absorbing boundaries. (letter)
Chaube, M K; Tripathi, D; Bég, O Anwar; Sharma, Shashi; 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 profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth.
A power-law coupled three-form dark energy model
Yao, Yan-Hong; Yan, Yang-Jie; Meng, Xin-He
2018-02-01
We consider a field theory model of coupled dark energy which treats dark energy as a three-form field and dark matter as a spinor field. By assuming the effective mass of dark matter as a power-law function of the three-form field and neglecting the potential term of dark energy, we obtain three solutions of the autonomous system of evolution equations, including a de Sitter attractor, a tracking solution and an approximate solution. To understand the strength of the coupling, we confront the model with the latest Type Ia Supernova, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation observations, with the conclusion that the combination of these three databases marginalized over the present dark matter density parameter Ω _{m0} and the present three-form field κ X0 gives stringent constraints on the coupling constant, - 0.017< λ <0.047 (2σ confidence level), by which we present the model's applicable parameter range.
Validation of a power-law noise model for simulating small-scale breast tissue
Reiser, I.; Edwards, A.; Nishikawa, R. M.
2013-09-01
We have validated a small-scale breast tissue model based on power-law noise. A set of 110 patient images served as truth. The statistical model parameters were determined by matching the radially averaged power-spectrum of the projected simulated tissue with that of the central tomosynthesis patient breast projections. Observer performance in a signal-known exactly detection task in simulated and actual breast backgrounds was compared. Observers included human readers, a pre-whitening observer model and a channelized Hotelling observer model. For all observers, good agreement between performance in the simulated and actual backgrounds was found, both in the tomosynthesis central projections and the reconstructed images. This tissue model can be used for breast x-ray imaging system optimization. The complete statistical description of the model is provided.
The time-domain behavior of power-law noises. [of many geophysical phenomena
Agnew, Duncan C.
1992-01-01
The power spectra of many geophysical phenomena are well approximated by a power-law dependence on frequency or wavenumber. A simple expression for the root-mean-square variability of a process with such a spectrum over an interval of time or space is derived. The resulting expression yields the powerlaw time dependence characteristic of fractal processes, but can be generalized to give the temporal variability for more general spectral behaviors. The method is applied to spectra of crustal strain (to show what size of strain events can be detected over periods of months to seconds) and of sea level (to show the difficulty of extracting long-term rates from short records).
Beltrametti, M.
1980-01-01
The analytic solutions for radiatively driven winds are given for the case in which the winds are driven by absorption of line and continuum radiation. The wind solutions are analytically estimated for different parameters of the central source and for different power law spectra. For flat spectra, three sonic points can exist; it is shown, however, that only one of these sonic points is physically realistic. Parameters of the central source are given which generate winds of further interest for explaining the narrow and broad absorption lines in quasars. For the quasar model presented here, winds which could give rise to the narrow absorption lines are generated by central sources with parameters which are not realistic for quasars.
On syntheses of the X-ray background with power-law sources
De Zotti, G.; Boldt, E. A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.; Cavaliere, A.; Danese, L.; Franceschini, A.
1982-01-01
The conditions under which the combined emission from power-law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low-luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit steeper spectra at higher energies.
Power law X- and gamma-ray emission from relativistic thermal plasmas
Zdziarski, A. A.
1984-01-01
Pair equilibrium in thermal plasmas emitting power law photon spectra by repeated Compton scatterings of a soft photon source active galactic nuclei was studied. Dependence of the spectral index on optical thickness and on temperature of the plasma is discussed. The equation for pair equilibrium is solved for the maximum steady luminosity. Analytical solutions for the subrelativistic region, and for the ultrarelativistic region are found. In the transrelativistic region the solutions are expressed by single integrals over the pair production cross sections, performed numerically. The constraints on soft photon source imposed by the condition that the soft photon flux cannot exceed the black-body flux are considered. For the Comptonized synchrotron radiation model a relation between magnetic field strength and output luminosity is found.
Choi, Sung R.; Gyekenyesi, John P.
2002-01-01
The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.
Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.
Namikawa, Jun
2005-08-01
Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.
Validation of a power-law noise model for simulating small-scale breast tissue
International Nuclear Information System (INIS)
Reiser, I; Edwards, A; Nishikawa, R M
2013-01-01
We have validated a small-scale breast tissue model based on power-law noise. A set of 110 patient images served as truth. The statistical model parameters were determined by matching the radially averaged power-spectrum of the projected simulated tissue with that of the central tomosynthesis patient breast projections. Observer performance in a signal-known exactly detection task in simulated and actual breast backgrounds was compared. Observers included human readers, a pre-whitening observer model and a channelized Hotelling observer model. For all observers, good agreement between performance in the simulated and actual backgrounds was found, both in the tomosynthesis central projections and the reconstructed images. This tissue model can be used for breast x-ray imaging system optimization. The complete statistical description of the model is provided. (paper)
Modified Anderson orthogonality catastrophe power law in the presence of shell structure
Bandopadhyay, Swarnali; Hentschel, Martina
2011-01-01
We study Anderson orthogonality catastrophe (AOC) for parabolic quantum dots and focus on the effects of degeneracies, realized through the inherent shell structure of their energy levels that can be lifted through an external magnetic field, on the Anderson overlap. We find rich and interesting behaviors as a function of the strength and position of the perturbation, the system size, and the applied magnetic field. In particular, even for weak perturbations, we observe a pronounced AOC that is related to the degeneracy of energy levels. Most importantly, the power-law decay of the Anderson overlap as a function of the number of particles is modified in comparison to the metallic case due to the rearrangement of the energy-level shell structure. We support our analytical results by numerical calculations and also study the distribution of Anderson overlaps.
Sudden expansion of a one-dimensional bose gas from power-law traps.
Campbell, A S; Gangardt, D M; Kheruntsyan, K V
2015-03-27
We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.
A recommended procedure for estimating the cosmic-ray spectral parameter of a simple power law
Howell, L W
2002-01-01
A simple power law model with single spectral index alpha sub 1 is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10 sup 1 sup 3 eV. Two procedures for estimating alpha sub 1 --the method of moments and maximum likelihood (ML)--are developed and their statistical performance are compared. The ML procedure is shown to be the superior approach and is then generalized for application to real cosmic-ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution and inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic-ray detector as they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives.
Undersampling power-law size distributions: effect on the assessment of extreme natural hazards
Geist, Eric L.; Parsons, Thomas E.
2014-01-01
The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and by attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historic data.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
El Boustani, Sami; Marre, Olivier; Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves
2009-09-01
Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m) activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m) reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the "effective" connectivity responsible for the dynamical signature of the population signals measured
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
Directory of Open Access Journals (Sweden)
Sami El Boustani
2009-09-01
Full Text Available Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the "effective" connectivity responsible for the dynamical signature of the population
Musical rhythm spectra from Bach to Joplin obey a 1/f power law.
Levitin, Daniel J; Chordia, Parag; Menon, Vinod
2012-03-06
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/f(β) power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.
From the Cover: Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-03-01
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.
Effective power-law dependence of Lyapunov exponents on the central mass in galaxies
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-04-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L ∝ mp between the mean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p ≈ 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q ≈ 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x1 family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution ofx galaxies are discussed.
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
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.
Poon, R. K. L.
1980-01-01
The paper presents an empirical study of the oxygen spectrum near 60 GHz with reference to its applicability to the remote sensing of the tropospheric and lower stratospheric temperature. It is demonstrated that the absorption coefficient of oxygen at 60 GHz can be fitted to the power law form with a relative rms error of about 8%. The power law form, when used in conjunction with the weighting function, permits the definition of some basic quantities in the passive remote sensing of the atmospheric temperature. It is shown how the power law form has been utilized in processing data from the Nimbus 5 microwave spectrometer experiment. The algorithm presented can be applied to spectrometer experiments at infrared frequencies.
Directory of Open Access Journals (Sweden)
Lin Yanhai
2016-01-01
Full Text Available This paper presents an investigation on the MHD thin film flow and heat transfer of a power law fluid over an unsteady stretching sheet. The effects of power law viscosity on a temperature field are taken into account with a modified Fourier’s law Proposed by Zheng by assuming that the temperature field is similar to the velocity field. The governing equations are reduced to a system of nonlinear ordinary differential equations. The numerical solutions are obtained by using the shooting method coupled with the Runge-Kutta method. The influence of the Hartmann number, the power law exponent, the unsteadiness parameter, the thickness parameter and the generalized Prandtl number on the velocity and temperature fields are presented graphically and analyzed. Moreover, the critical formula for parameters are derived which indicated that the magnetic field has no effect on the critical value.
Directory of Open Access Journals (Sweden)
WenJun Zhang
2016-03-01
Full Text Available In present study I proposed a method for generating biological networks based on power-law (p(x=x^(-a and exponential-law (p(x=e^(-ax distribution functions. Given the parameter of power-law or exponential-law distribution function, a, the algorithm generates an expected frequency distribution according to the given parameter, thereafter creates an adjacency matrix in which (practical frequency distribution of node degrees matches the expected frequency distribution. The results showed that power-law distribution function performs much better than exponential-law distribution function in generating networks. Using the revised algorithm, tumor related networks (pathways are simulated and predicted. The results prove that the algorithm is overall effective in predicting network links (14.6%-21.2%of correctly predicted links against 0.1%-3.4% of that for random assignments. Matlab codes of the algorithms are given also.
Directory of Open Access Journals (Sweden)
Jawad Ahmed
Full Text Available This paper examines the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions. A uniform magnetic field is applied transversely to the direction of the flow. The governing time dependent nonlinear boundary layer equations are reduced into nonlinear ordinary differential equations with the help of similarity transformations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM and numerically by shooting procedure. Effects of various governing parameters like, power law index n, magnetic parameter M, unsteadiness A, suction/injection S, Biot number γ and generalized Prandtl number Pr on velocity, temperature, local skin friction and the local Nusselt number are studied and discussed. It is found from the analysis that the magnetic parameter diminishes the velocity profile and the corresponding thermal boundary layer thickness. Keywords: Axisymmetric flow, Power law fluid, Unsteady stretching, Convective boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Luna, N. [Secretaria de Energia, Direccion de Operacion Petrolera, Mexico DF (Mexico); Mendez, F. [UNAM, Facultad de Ingenieria, Mexico DF (Mexico); Bautista, O. [ITESM, Division de Ingenieria y Arquitectura, Mexico DF (Mexico)
2005-05-01
We treat numerically in this paper, the transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluids is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the transverse and longitudinal heat conduction effects are taken into account. The numerical results for the temporal evolution of the average temperature of the tube wall, {theta}{sub av,} is plotted for different nondimensional parameters such as conduction parameter, {alpha}, the aspect ratios of the tube, {epsilon} and {epsilon}{sub 0} and the index of power-law fluid, n. (orig.)
Directory of Open Access Journals (Sweden)
Medhat M. Helal
2013-10-01
Full Text Available The problem of heat and mass transfer in a power law, two-dimensional, laminar, boundary layer flow of a viscous incompressible fluid over an inclined plate with heat generation and thermophoresis is investigated by the characteristic function method. The governing non-linear partial differential equations describing the flow and heat transfer problem are transformed into a set of coupled non-linear ordinary differential equation which was solved using Runge–Kutta shooting method. Exact solutions for the dimensionless temperature and concentration profiles, are presented graphically for different physical parameters and for the different power law exponents 0 0.5.
Directory of Open Access Journals (Sweden)
Srinivasacharya D.
2013-01-01
Full Text Available Mixed convection heat and mass transfer along a vertical plate embedded in a power-law fluid saturated Darcy porous medium with Soret and Dufour effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using shooting method. The effect of Soret and Dufour parameters, power law index and mixed convection parameter on non-dimensional velocity, temperature and concentration fields are discussed. The variation of different parameters on heat and mass transfer rates is presented in tabular form.
Discovery of Power-Law Growth in the Self-Renewal of Heterogeneous Glioma Stem Cell Populations.
Sugimori, Michiya; Hayakawa, Yumiko; Boman, Bruce M; Fields, Jeremy Z; Awaji, Miharu; Kozano, Hiroko; Tamura, Ryoi; Yamamoto, Seiji; Ogata, Toru; Yamada, Mitsuhiko; Endo, Shunro; Kurimoto, Masanori; Kuroda, Satoshi
2015-01-01
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
Garanina, O. S.; Romanovsky, M. Yu.
2015-06-01
A multi-parametric family of exponential distributions with various power law tails is introduced and is shown to describe adequately the known distributions of incomes and wealth as well as the recently measured distributions of new car sales. The three or four-parametric families are characterized by effective temperature in the exponential part, the power exponent in the power-law asymptotic part, the coefficient for the transition between the above two parts, and the starting value, if it is not equal to zero. Since the new car sales distributions are found to correspond to known distributions of incomes, the latter may be inferred from the former.
Discovery of Power-Law Growth in the Self-Renewal of Heterogeneous Glioma Stem Cell Populations.
Directory of Open Access Journals (Sweden)
Michiya Sugimori
Full Text Available Accumulating evidence indicates that cancer stem cells (CSCs drive tumorigenesis. This suggests that CSCs should make ideal therapeutic targets. However, because CSC populations in tumors appear heterogeneous, it remains unclear how CSCs might be effectively targeted. To investigate the mechanisms by which CSC populations maintain heterogeneity during self-renewal, we established a glioma sphere (GS forming model, to generate a population in which glioma stem cells (GSCs become enriched. We hypothesized, based on the clonal evolution concept, that with each passage in culture, heterogeneous clonal sublines of GSs are generated that progressively show increased proliferative ability.To test this hypothesis, we determined whether, with each passage, glioma neurosphere culture generated from four different glioma cell lines become progressively proliferative (i.e., enriched in large spheres. Rather than monitoring self-renewal, we measured heterogeneity based on neurosphere clone sizes (#cells/clone. Log-log plots of distributions of clone sizes yielded a good fit (r>0.90 to a straight line (log(% total clones = k*log(#cells/clone indicating that the system follows a power-law (y = xk with a specific degree exponent (k = -1.42. Repeated passaging of the total GS population showed that the same power-law was maintained over six passages (CV = -1.01 to -1.17. Surprisingly, passage of either isolated small or large subclones generated fully heterogeneous populations that retained the original power-law-dependent heterogeneity. The anti-GSC agent Temozolomide, which is well known as a standard therapy for glioblastoma multiforme (GBM, suppressed the self-renewal of clones, but it never disrupted the power-law behavior of a GS population.Although the data above did not support the stated hypothesis, they did strongly suggest a novel mechanism that underlies CSC heterogeneity. They indicate that power-law growth governs the self-renewal of heterogeneous
DEFF Research Database (Denmark)
Moreno, Y.; Vázquez-Prada, M.; Pacheco, A.F.
2003-01-01
to the heterogeneity of the system. In one regime, a characteristic event is observed while for the second regime a power-law spectrum of avalanches is obtained reminiscent of self-organized criticality. We find that both regimes are different when predicting large avalanches and that, in the second regime...
Power-law modulation of the scalar power spectrum from a heavy field with a monomial potential
Huang, Qing-Guo; Pi, Shi
2018-04-01
The effects of heavy fields modulate the scalar power spectrum during inflation. We analytically calculate the modulations of the scalar power spectrum from a heavy field with a separable monomial potential, i.e. V(phi)~ phin. In general the modulation is characterized by a power-law oscillation which is reduced to the logarithmic oscillation in the case of n=2.
Caputi, K. I.
2013-01-01
5 I present a generalized power-law (PL) diagnostic which allows one to identify the presence of active galactic nuclei (AGNs) in infrared (IR) galaxies at z > 1, down to flux densities at which the extragalactic IR background is mostly resolved. I derive this diagnostic from the analysis of 174
In-Degree and PageRank of web pages: why do they follow similar power laws?
Litvak, Nelli; Scheinhardt, Willem R.W.; Volkovich, Y.
2009-01-01
PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is
In-degree and pageRank of web pages: Why do they follow similar power laws?
Litvak, Nelli; Scheinhardt, Willem R.W.; Volkovich, Y.
The PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that the PageRank obeys a 'power law' with the same exponent as the In-Degree. This paper presents a novel mathematical model that explains this phenomenon. The relation between the PageRank and In-Degree
DEFF Research Database (Denmark)
Jørgensen, Bent; Demétrio, Clarice G.B.; Kristensen, Erik
2011-01-01
Estimation of Taylor’s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating...
Wann, J; Nimmo-Smith, I; Wing, A M
1988-11-01
Unconstrained hand movements typically display a decrease in hand speed around highly curved sections of a trajectory. It has been suggested that this relation between tangential velocity and radius of curvature conforms to a one-third power law. We demonstrate that a one-third power law can be explained by models taking account of trajectory costs such as a minimum-jerk model. Data were analyzed from 6 subjects performing elliptical drawing movements of varying eccentricities. Conformity to the one-third power law in the average was obtained but is shown to be artifactual. It is demonstrated that asymmetric velocity profiles may result in consistent departures from a one-third power law but that such differences may be masked by inappropriate analysis procedures. We introduce a modification to the original minimum-jerk model by replacing the assumption of a Newtonian point-mass with a visco-elastic body. Simulations with the modified model identify a basis for asymmetry of velocity profiles and thereby predict departures from a one-third law commensurate with the empirical findings.
Directory of Open Access Journals (Sweden)
Yakup YÄ±ldÄ±rÄ±m
Full Text Available In this study, we perform the extended Kudryashov method to nonlinear SchrÃ¶dinger equation (NLSE with spatio-temporal dispersion that arises in a propagation of light in nonlinear optical fibers, planar waveguides, BoseâEinstein condensate theory. Four types of nonlinearity â Kerr law, power law, parabolic law and dual-power law â are being considered for the model. By using this scheme, the topological, singular soliton and rational solutions are obtained. In addition, some graphical simulations of solutions are provided.It is demonstrated that the proposed algorithm is effective and can be handled for many other nonlinear complex differential equations. Keywords: Solitons, Nonlinear SchrÃ¶dinger equation with spatio-temporal dispersion, Extended Kudryashovâs method
Arata, Yukinobu; Takagi, Hiroaki; Sako, Yasushi; Sawa, Hitoshi
2014-01-01
Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and power law relationship is conserved in Xenopus and C. elegans, while the absolute powers in C. elegans were different from that in Xenopus. Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic C. elegans cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Energy Technology Data Exchange (ETDEWEB)
Nieto, M.M. [Los Alamos National Lab., NM (United States); Daboul, J. [Ben Gurion Univ. of the Negev, Beer Sheva (Israel)
1994-07-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = {minus}{gamma}/r{sup {nu}}, {gamma} > 0 and {minus}{infinity} < {nu} < {infinity}. When the angular momentum is non-zero, these solutions lead to the classical orbits {rho}(t) = [cos {mu}({var_phi}(t) {minus} {var_phi}{sub 0}(t))]{sup 1/{mu}}, with {mu} = {nu}/2 {minus} 1 {ne} 0. For {nu} > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when {nu} > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed.
The flow of power law fluids in elastic networks and porous media.
Sochi, Taha
2016-02-01
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
Wosnitza, Jan Henrik; Denz, Cornelia
2013-09-01
We employ the log-periodic power law (LPPL) to analyze the late-2000 financial crisis from the perspective of critical phenomena. The main purpose of this study is to examine whether LPPL structures in the development of credit default swap (CDS) spreads can be used for default classification. Based on the different triggers of Bear Stearns’ near bankruptcy during the late-2000 financial crisis and Ford’s insolvency in 2009, this study provides a quantitative description of the mechanism behind bank runs. We apply the Johansen-Ledoit-Sornette (JLS) positive feedback model to explain the rise of financial institutions’ CDS spreads during the global financial crisis 2007-2009. This investigation is based on CDS spreads of 40 major banks over the period from June 2007 to April 2009 which includes a significant CDS spread increase. The qualitative data analysis indicates that the CDS spread variations have followed LPPL patterns during the global financial crisis. Furthermore, the univariate classification performances of seven LPPL parameters as default indicators are measured by Mann-Whitney U tests. The present study supports the hypothesis that discrete scale-invariance governs the dynamics of financial markets and suggests the application of new and fast updateable default indicators to capture the buildup of long-range correlations between creditors.
Enhanced dust emissivity power-law index along the western Hα filament of NGC 1569
Suzuki, T.; Kaneda, H.; Onaka, T.; Yamagishi, M.; Ishihara, D.; Kokusho, T.; Tsuchikawa, T.
2018-03-01
We used a data set from AKARI and Herschel images at wavelengths from 7 μm to 500 μm to catch the evidence of dust processing in galactic winds in NGC 1569. Images show a diffuse infrared (IR) emission extending from the galactic disk into the halo region. The most prominent filamentary structure seen in the diffuse IR emission is spatially in good agreement with the western Hα filament (western arm). The spatial distribution of the F350/F500 map shows high values in regions around the super-star clusters (SSCs) and towards the western arm, which are not found in the F250/F350 map. The color-color diagram of F250/F350-F350/F500 indicates high values of the emissivity power-law index (βc) of the cold dust component in those regions. From a spectral decomposition analysis on a pixel-by-pixel basis, a βc map shows values ranging from ˜1 to ˜2 over the whole galaxy. In particular, high βc values of ˜2 are only observed in the regions indicated by the color-color diagram. Since the average cold dust temperature in NGC 1569 is ˜30 K, βc starburst activities and that those grains are blown away along the HI ridge and thus the western arm.
Cascade model of gamma-ray bursts: Power-law and annihilation-line components
Harding, A. K.; Sturrock, P. A.; Daugherty, J. K.
1988-01-01
If, in a neutron star magnetosphere, an electron is accelerated to an energy of 10 to the 11th or 12th power eV by an electric field parallel to the magnetic field, motion of the electron along the curved field line leads to a cascade of gamma rays and electron-positron pairs. This process is believed to occur in radio pulsars and gamma ray burst sources. Results are presented from numerical simulations of the radiation and photon annihilation pair production processes, using a computer code previously developed for the study of radio pulsars. A range of values of initial energy of a primary electron was considered along with initial injection position, and magnetic dipole moment of the neutron star. The resulting spectra was found to exhibit complex forms that are typically power law over a substantial range of photon energy, and typically include a dip in the spectrum near the electron gyro-frequency at the injection point. The results of a number of models are compared with data for the 5 Mar., 1979 gamma ray burst. A good fit was found to the gamma ray part of the spectrum, including the equivalent width of the annihilation line.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Nieto, Michael Martin; Daboul, Jamil
1995-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
Adjustment to Subtle Time Constraints and Power Law Learning in Rapid Serial Visual Presentation.
Shin, Jacqueline C; Chang, Seah; Cho, Yang Seok
2015-01-01
We investigated whether attention could be modulated through the implicit learning of temporal information in a rapid serial visual presentation (RSVP) task. Participants identified two target letters among numeral distractors. The stimulus-onset asynchrony immediately following the first target (SOA1) varied at three levels (70, 98, and 126 ms) randomly between trials or fixed within blocks of trials. Practice over 3 consecutive days resulted in a continuous improvement in the identification rate for both targets and attenuation of the attentional blink (AB), a decrement in target (T2) identification when presented 200-400 ms after another target (T1). Blocked SOA1s led to a faster rate of improvement in RSVP performance and more target order reversals relative to random SOA1s, suggesting that the implicit learning of SOA1 positively affected performance. The results also reveal "power law" learning curves for individual target identification as well as the reduction in the AB decrement. These learning curves reflect the spontaneous emergence of skill through subtle attentional modulations rather than general attentional distribution. Together, the results indicate that implicit temporal learning could improve high level and rapid cognitive processing and highlights the sensitivity and adaptability of the attentional system to subtle constraints in stimulus timing.
A Recommended Procedure for Estimating the Cosmic Ray Spectral Parameter of a Simple Power Law
Howell, Leonard W.; Rose, M. Franklin (Technical Monitor)
2000-01-01
A simple power law model consisting of a single spectral index a(f(sub i)) is believed to be an adequate description of the galactic cosmic ray (GQ proton flux at energies below 1013 eV. Two procedures for estimating a(f(sub i)), referred as (1) the method of moments, and (2) maximum likelihood, are developed and their statistical performance compared. I concluded that the maximum likelihood procedure attains the most desirable statistical properties and is hence the recommended statistic estimation procedure for estimating a1. The maximum likelihood procedure is then generalized for application to a set of real cosmic ray data and thereby makes this approach applicable to existing cosmic ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution, as well as inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic ray detector because they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose practical limits to the design envelope.
Contracting bubbles in Hele-Shaw cells with a power-law fluid
International Nuclear Information System (INIS)
McCue, Scott W; King, John R
2011-01-01
The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener–Hopf problem, the transition between the long thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalize the ellipses that characterize the Newtonian case being constructed by the Wiener–Hopf calculation
Role of viscous dissipation in the dynamics of lava flows with power-law rheology
Piombo, A.; Dragoni, M.
2011-09-01
We model a lava flow as a one-dimensional flow of a pseudoplastic fluid with viscous dissipation. The flow is horizontally unbounded and is driven downslope by the gravity force. We consider a power-law constitutive equation and we take into account the temperature dependence of the rheological parameters. Given an effusion rate and an initial temperature at the eruption vent, the flow is assumed to cool down by heat radiation. We calculate the heat produced by viscous dissipation as a function of lava temperature and effusion rate. The cooling rate is calculated as a function of the surface temperature and flow rate. Viscous dissipation reduces the cooling rate by an amount which is independent of flow rate. We evaluate the effect of viscous dissipation on the flow thickness and velocity. The effect of dissipation is to decrease the flow thickness and to increase the flow velocity. The effect on flow thickness is greater for smaller flow rates, while the effect on velocity is greater for larger effusion rates. In principle, the model provides a method for estimating the flow rate from in-field measurements of distances and temperatures.
Friction losses in valves and fittings for power-law fluids
Directory of Open Access Journals (Sweden)
Polizelli M.A.
2003-01-01
Full Text Available Data on pressure drop were obtained in stainless steel, sanitary fittings and valves during laminar and turbulent flow of aqueous solutions of sucrose and xanthan gum, which were selected as model fluids. The rheological properties of these solutions were determined and the power-law model provided the best fit for experimental data. Friction losses were measured in fully and partially open butterfly and plug valves, bends and unions. Values of loss coefficients (k f were calculated and correlated as a function of the generalized Reynolds number by the two-k method. The model adjustment was satisfactory and was better in the laminar flow range (0.976 < r² < 0.999 than in the turbulent flow range (0.774 < r² < 0.989. In order to test the adequacy of the results for predicting loss coefficients during flow of real fluids, experiments were conducted with coffee extract. Comparison between experimental and predicted loss coefficients showed very good agreement.
A unified econophysics explanation for the power-law exponents of stock market activity
Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, Eugene
2007-08-01
We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.
Particle Swarm Optimization with Power-Law Parameter Based on the Cross-Border Reset Mechanism
Directory of Open Access Journals (Sweden)
WANG, H.
2017-11-01
Full Text Available In order to improve the performance of traditional particle swarm optimization, this paper introduces the principle of Levy flight and cross-border reset mechanism. In the proposed particle swarm optimization, the dynamic variation of parameters meets the power-law distribution and the pattern of particles transition conforms to the Levy flight in the process of algorithm optimization. It means the particles make long distance movements in the search space with a small probability and make short distance movements with a large probability. Therefore, the particles can jump out of local optimum more easily and coordinate the global search and local search of particle swarm optimization. This paper also designs the cross-border reset mechanism to make particles regain optimization ability when stranding on the border of search space after a long distance movement. The simulation results demonstrate the proposed algorithms are easier to jump out of local optimum and have higher accuracy when compared with the existing similar algorithms based on benchmark test functions and handwriting character recognition system.
Can log-periodic power law structures arise from random fluctuations?
Wosnitza, Jan Henrik; Leker, Jens
2014-05-01
Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable LPPL structures. To this end, we first estimate the stochastic process underlying the DAX log-returns during the period from mid-1997 until end-2003. The employed data set contains about 3.93ṡ106 intraday DAX quotes at a sampling rate of 15 s. Our results indicate that the DAX log-returns can be described as a Markov process. As a consequence, a Langevin equation is derived. Based on this model equation, we run extensive simulations in order to generate 100 synthetic DAX trajectories each covering 3000 trading days. We find LPPL behavior in ten artificial time series. Moreover, we can establish a link between LPPL patterns and ensuing bubble bursts in seven synthetic 600-week windows. However, the LPPL components in most synthetic trajectories differ fundamentally from those LPPL structures that have previously been detected in real financial time series. Summarized, this paper demonstrates that LPPL structures are not necessarily the signature of imitative behavior among investors but can also stem from noise, even though the likelihood of this is extremely low. Thus, our findings confirm with high statistical confidence that the LPPL structures in the DAX development are rooted deeper than only in the random fluctuations of the German stock market.
Power-law creep of powder-metallurgy grade molybdenum sheet
International Nuclear Information System (INIS)
Ciulik, J.; Taleff, E.M.
2007-01-01
Creep behavior of commercial-purity, powder-metallurgy grade molybdenum (Mo) sheet has been investigated at temperatures between 1300 and 1600 deg. C (0.56-0.63 T m ) using tensile testing at controlled strain rates. Strain-rate-change tests were performed at constant-temperatures over true-strain rates from 1.0 x 10 -6 to 5.0 x 10 -4 s -1 . Results agree with previously published data indicating that Mo follows power-law creep with a stress exponent of about 5; however, the present results address a temperature range not previously documented. The activation energy for creep was determined to be 240 kJ/mol within this temperature range, which is lower than previously published values and approximately half the value reported for self-diffusion, indicating that diffusion mechanisms faster than lattice diffusion are active. It is shown that Mo creep data from a variety of investigations converge closely to a single line on a master plot of strain rate normalized using an activation energy of 240 kJ/mol when plotted against stress normalized by the temperature-dependent elastic modulus. This activation energy for creep is attributed to an effective diffusivity that fits the creep data obtained during this study as well as from previously published creep data from commercial-purity molybdenum
Sparse Power-Law Network Model for Reliable Statistical Predictions Based on Sampled Data
Directory of Open Access Journals (Sweden)
Alexander P. Kartun-Giles
2018-04-01
Full Text Available A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model that does not depend on the order in which nodes are sampled. Despite a large variety of non-equilibrium (growing and equilibrium (static sparse complex network models that are widely used in network science, how to reconcile sparseness (constant average degree with the desired statistical properties of projectivity and exchangeability is currently an outstanding scientific problem. Here we propose a network process with hidden variables which is projective and can generate sparse power-law networks. Despite the model not being exchangeable, it can be closely related to exchangeable uncorrelated networks as indicated by its information theory characterization and its network entropy. The use of the proposed network process as a null model is here tested on real data, indicating that the model offers a promising avenue for statistical network modelling.
Stochastic models with power-law tails the equation X = AX + B
Buraczewski, Dariusz; Mikosch, Thomas
2016-01-01
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the c...
Cockmartin, L; Bosmans, H; Marshall, N W
2013-08-01
This work characterizes three candidate mammography phantoms with structured background in terms of power law analysis in the low frequency region of the power spectrum for 2D (planar) mammography and digital breast tomosynthesis (DBT). The study was performed using three phantoms (spheres in water, Voxmam, and BR3D CIRS phantoms) on two DBT systems from two different vendors (Siemens Inspiration and Hologic Selenia Dimensions). Power spectra (PS) were calculated for planar projection, DBT projection, and reconstructed images and curve fitted in the low frequency region from 0.2 to 0.7 mm(-1) with a power law function characterized by an exponent β and magnitude κ. The influence of acquisition dose and tube voltage on the power law parameters was first explored. Then power law parameters were calculated from images acquired with the same anode∕filter combination and tube voltage for the three test objects, and compared with each other. Finally, PS curves for automatic exposure controlled acquisitions (anode∕filter combination and tube voltages selected by the systems based on the breast equivalent thickness of the test objects) were compared against PS analysis performed on patient data (for Siemens 80 and for Hologic 48 mammograms and DBT series). Dosimetric aspects of the three test objects were also examined. The power law exponent (β) was found to be independent of acquisition dose for planar mammography but varied more for DBT projections of the sphere-phantom. Systematic increase of tube voltage did not affect β but decreased κ, both in planar and DBT projection phantom images. Power spectra of the BR3D phantom were closer to those of the patients than these of the Voxmam phantom; the Voxmam phantom gave high values of κ compared to the other phantoms and the patient series. The magnitude of the PS curves of the BR3D phantom was within the patient range but β was lower than the average patient value. Finally, PS magnitude for the sphere
Global Scale Analysis of the Stream Power Law Parameters based on Worldwide 10Be Denudation Rates
Harel, M. A.; Mudd, S. M.; Attal, M.
2015-12-01
The stream power law, expressed as E = KAmSn where E is erosion rate [LT-1], K is erodibility [T-1L(1-2m)], A is drainage area [L2], S is channel gradient [L/L] and m and n are constants, is the most widely used model for bedrock channel incision. Despite its simplicity and limitations, the model has proved useful for a large number of applications such as topographic evolution, knickpoint migration, palaeotopography reconstruction, and the determination of uplift patterns and rates. However, the unknown parameters K, m and n are often fixed arbitrarily or are based on assumptions about the physics of the erosion processes that are not always valid, which considerably alters the use and interpretation of the model. In this study, we compile published 10Be basin-wide erosion rates (N= 1423) in order to assess the m/n ratio (or concavity index), the slope exponent n and erodibility coefficient K using the integral method of channel profile analysis. These three parameters are calculated for 67 areas and allow for a global scale analysis in terms of climatic, tectonic and environmental settings. Our results suggest that (i) many sites are too noisy or do not have enough data to predict n and K with a satisfying level of confidence; (ii) the slope exponent is predominantly greater than one, meaning that the relationship between erosion rate and the channel gradient is non-linear, supporting the idea that incision is a threshold controlled process. Furthermore, a multi-regression analysis and the calculation of n and K using a reference concavity index m/n = 0.45 demonstrates that (iii) many intuitive or previously demonstrated local-scale trends, such as the correlation between erosion rate and climate, do not appear at a global scale.
Directory of Open Access Journals (Sweden)
Anthony Papadopoulos
Full Text Available The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.
Correction: MAXI J1543-564 in hard intermediate state
Kennea, J. A.; Motta, S.; Curran, P.; Krimm, P. A. Evans. H. A.; Romano, P.; Mangano, V.; Yamaoka, K.; Negoro, H.
2011-09-01
A correction to Kennea et al. (ATEL #3662): With a measured photon index of ~2.7, the Swift/XRT spectrum of MAXI J1543-564 is currently consistent with the source being in the hard intermediate state, or under the Remillard and McClintock (2006) definition, the steep power-law state. We apologize for this error, and thank Tomaso Belloni for bringing it to our attention.
Spectral Variability in Hard X-rays and the Evidence for a 13.5 Years ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
A single power law fit in the X-ray and gamma ray energy bands points to a common origin of these photons and the absence of spectral break around 1 MeV as suggested in literature. We have reanalyzed the available data to study the temporal variability of the spectrum in the hard X-ray band. Our analysis reveals that.
DEFF Research Database (Denmark)
Freltoft, T.; Kjems, Jørgen; Sinha, S. K.
1986-01-01
Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/cm3. Assuming power-law correlations between particles and a finite correlation length ξ......, the authors derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension df corresponding to the power-law correlation was 2.61±0.1 for all dry samples, and 2...
Recalling items from a category for 1 hour: an inquiry into power-law behavior and memory foraging.
Rhodes, Theo
2013-07-01
There are two complementary approaches to characterizing performance in a free recall task (retrieving items from a specified category). The historic, or top down approach, considers the overall structure of the produced responses, generally as the parameters of a fitted cumulative recall curve. Alternatively, free recall can be considered as a time series of recalls or inter-recall intervals. Earlier work employing this approach (Rhodes & Turvey, 2007) suggested power law behavior. Long trial durations (1 hour) are employed to more rigorously test for the presence of power law behavior and more generally, the hypothesis that the dynamics of free recall reflect complex, multiplicative processes. The outlined empirical methods are also employed to test predictions about the relative structure of differently sized categories. Consequences for an asymptotic curve based understanding of free recall and foraging metaphors of retrieval are discussed.
Chen, W.; Holm, S.
2004-04-01
Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.
DEFF Research Database (Denmark)
Wiuf, Carsten Henrik; Feliu, Elisenda
2013-01-01
is derived from the determinant of the Jacobian of the species formation rate function. Using this characterization, we further derive similar determinant criteria applicable to general sets of kinetics. The criteria are conceptually simple, computationally tractable, and easily implemented. Our approach...... embraces and extends previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or noncatalytic kinetics, and also work based on graphical analysis of the interaction graph associated with the system. Further, we interpret the criteria...... and how the species influence each reaction. We characterize families of so-called power-law kinetics for which the associated species formation rate function is injective within each stoichiometric class and thus the network cannot exhibit multistationarity. The criterion for power-law kinetics...
A MODEL FOR THE NON-UNIVERSAL POWER LAW OF THE SOLAR WIND SUB-ION-SCALE MAGNETIC SPECTRUM
International Nuclear Information System (INIS)
Passot, T.; Sulem, P. L.
2015-01-01
A phenomenological turbulence model for kinetic Alfvén waves in a magnetized collisionless plasma that is able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere is presented. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition from large-scale weak turbulence to smaller scale strong turbulence is captured and nonlocal interactions, relevant in the case of steep spectra, are accounted for
Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
On the interplay between short and long term memory in the power-law cross-correlations setting
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2015-01-01
Roč. 421, č. 1 (2015), s. 218-222 ISSN 0378-4371 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : Power - law cross-correlations * Long term memory * Short term memory Subject RIV: AH - Economics Impact factor: 1.785, year: 2015 http://library.utia.cas.cz/separaty/2015/E/kristoufek-0452316.pdf
Wu, P.; Wang, H.; van der Wal, W.
2006-12-01
Modern geodetic measurements from GPS, satellite altimetry, tide-gauges, Satellite Laser Ranging (SLR) and space-borne gravimetry (such as GRACE) have been used to monitor global change. Since these measurements contain contributions from glacial isostatic adjustment (GIA) and other tectonic processes, they must be modeled and removed in order to observe current climate change. In the past, most GIA models assumed that the earth is laterally homogeneous and the rheology is linear. The aim of this paper is to investigate the effects of lateral heterogeneity and Power-Law rheology on GIA induced land uplift rate, horizontal velocities, relative sealevels, J-dot and the secular gravity rate of change in the southern part of Hudson Bay, which is detected by the GRACE mission. Here, GIA is modeled with a spherical, self-gravitating, compressible viscoelastic, laterally heterogeneous earth using the Finite-Element Method. The effect of gravitationally self-consistent sea levels in realistic oceans is also included. Lateral variations in mantle viscosities and lithospheric thickness are inferred from the seismic tomography model S20A using well known scaling relationships. Power-Law rheologies in the whole mantle or in combination with linear rheologies in the upper or lower mantle are also investigated. Both ICE-5G and ICE-4G deglaciation models are used to investigate their effect on the pattern of rebound. Preliminary results show that both lateral heterogeneity and power-law rheology have strong effects on the direction and magnitude of horizontal velocities. The effects of lateral heterogeneity and power-law rheology are also large enough to be detected in land uplift rate, relative sealevels, J-dot and gravity rate of change. Their implication on observing the effects of global warming will also be discussed.
Sazuka, Naoya; Inoue, Jun-Ichi
2007-03-01
A Weibull distribution with power-law tails is confirmed as a good candidate to describe the first passage time process of foreign currency exchange rates. The Lorentz curve and the corresponding Gini coefficient for a Weibull distribution are derived analytically. We show that the coefficient is in good agreement with the same quantity calculated from the empirical data. We also calculate the average waiting time which is an important measure to estimate the time for customers to wait until the next price change after they login to their computer systems. By assuming that the first passage time distribution might change its shape from the Weibull to the power-law at some critical time, we evaluate the averaged waiting time by means of the renewal-reward theorem. We find that our correction of tails of the distribution makes the averaged waiting time much closer to the value obtained from empirical data analysis. We also discuss the deviation from the estimated average waiting time by deriving the waiting time distribution directly. These results make us conclude that the first passage process of the foreign currency exchange rates is well described by a Weibull distribution with power-law tails.
Howard, Robert W
2014-09-01
The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. Copyright © 2014 Elsevier B.V. All rights reserved.
Langbein, John O.
2012-01-01
Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.
Rossberg, Axel G.; Farnsworth, Keith D.; Satoh, Keisuke; Pinnegar, John K.
2011-01-01
A central question in community ecology is how the number of trophic links relates to community species richness. For simple dynamical food-web models, link density (the ratio of links to species) is bounded from above as the number of species increases; but empirical data suggest that it increases without bounds. We found a new empirical upper bound on link density in large marine communities with emphasis on fish and squid, using novel methods that avoid known sources of bias in traditional approaches. Bounds are expressed in terms of the diet-partitioning function (DPF): the average number of resources contributing more than a fraction f to a consumer's diet, as a function of f. All observed DPF follow a functional form closely related to a power law, with power-law exponents independent of species richness at the measurement accuracy. Results imply universal upper bounds on link density across the oceans. However, the inherently scale-free nature of power-law diet partitioning suggests that the DPF itself is a better defined characterization of network structure than link density. PMID:21068048
Power-law versus log-law in wall-bounded turbulence: A large-eddy simulation perspective
Cheng, W.
2014-01-29
The debate whether the mean streamwise velocity in wall-bounded turbulent flows obeys a log-law or a power-law scaling originated over two decades ago, and continues to ferment in recent years. As experiments and direct numerical simulation can not provide sufficient clues, in this study we present an insight into this debate from a large-eddy simulation (LES) viewpoint. The LES organically combines state-of-the-art models (the stretched-vortex model and inflow rescaling method) with a virtual-wall model derived under different scaling law assumptions (the log-law or the power-law by George and Castillo [“Zero-pressure-gradient turbulent boundary layer,” Appl. Mech. Rev.50, 689 (1997)]). Comparison of LES results for Re θ ranging from 105 to 1011 for zero-pressure-gradient turbulent boundary layer flows are carried out for the mean streamwise velocity, its gradient and its scaled gradient. Our results provide strong evidence that for both sets of modeling assumption (log law or power law), the turbulence gravitates naturally towards the log-law scaling at extremely large Reynolds numbers.
Interplay of soft and hard processes and hadron $p_{T}$ spectra in p A and AA collisions
Enke, Wang; 10.1103/PhysRevC.64.034901
2001-01-01
Motivated by a schematic model of multiple parton scattering within the Glauber formalism, the transverse momentum spectra in pA and AA collisions are analyzed in terms of a nuclear modification factor with respect to pp collisions. The existing data at the CERN Super Proton Synchrotron energies are shown to be consistent with the picture of Glauber multiple scattering in which the interplay between soft and hard processes and the effect of absorptive processes lead to nontrivial nuclear modification of the particle spectra. Relative to the additive model of incoherent hard scattering, the spectra are enhanced at large p/sub T/ (hard) by multiple scattering while suppressed at low p/sub T/ (soft) by absorptive correction with the transition occurring at around a scale p/sub 0/~1-2 GeV/c that separates soft and hard processes. Around the same scale, the p/sub T / spectra in pp collisions also change from an exponential form at low p/sub T/ to a power-law behavior at high p/sub T/. At very large p/sub T/>>p/sub...
International Nuclear Information System (INIS)
Bharti, Ram P.; Harvie, Dalton J.E.; Davidson, Malcolm R.
2009-01-01
Electroviscous effects in steady, fully developed, pressure-driven flow of power-law liquids through a uniform cylindrical microchannel have been investigated numerically by solving the Poisson-Boltzmann and the momentum equations using a finite difference method. The pipe wall is considered to have uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Electroviscous resistance reduces the velocity adjacent to the wall, relative to the velocity on the axis. The effect is shown to be greater when the liquid is shear-thinning, and less when it is shear-thickening, than it is for Newtonian flow. For overlapping electrical double layers and elevated surface charge density, the electroviscous reduction in the near-wall velocity can form an almost stationary (zero shear) layer there when the liquid is shear-thinning. In that case, the liquid behaves approximately as if it is flowing through a channel of reduced diameter. The induced axial electrical field shows only a weak dependence on the power-law index with the dependence being greatest for shear-thinning liquids. This field exhibits a local maximum as surface charge density increases from zero, even though the corresponding electrokinetic resistance increases monotonically. The magnitude of the electroviscous effect on the apparent viscosity, as measured by the ratio of the apparent and physical consistency indices, decreases monotonically as the power-law index increases. Thus, overall, the electroviscous effect is stronger in shear-thinning, and weaker in shear-thickening liquids, than it is when the liquid is Newtonian.
Gall, Andrew J; Joshi, Badal; Best, Janet; Florang, Virginia R; Doorn, Jonathan A; Blumberg, Mark S
2009-07-01
Daily amounts of sleep and wakefulness are accumulated in discrete bouts that exhibit distinct statistical properties. In adult mammals, sleep bout durations follow an exponential distribution whereas wake bout durations follow a power-law distribution. In infant Norway rats, however, wake bouts initially follow an exponential distribution and only transition to a power-law distribution beginning around postnatal day 15 (P15). Here we test the hypothesis that the locus coeruleus (LC), one of several wake-active nuclei in the brainstem, contributes to this developmental transition. At P7, rats were injected subcutaneously with saline or DSP-4, a neurotoxin that targets noradrenergic (NA) LC terminals. Then, at P21, sleep and wakefulness during the day and night were monitored. The effectiveness of DSP-4 treatment was verified by measuring NA, dopamine (DA), and serotonin (5-HT) concentration in cortical and non-cortical tissue using high performance liquid chromatography. In relation to controls, subjects treated with DSP-4 exhibited significant reductions only in cortical and non-cortical NA concentration. Consistent with our hypothesis, the wake bout durations of DSP-4 subjects more closely followed an exponential distribution, whereas those of control subjects followed the expected power-law distribution. Sleep bout distributions were unaffected by DSP-4. These results suggest that the fundamental developmental transition in the statistical structure of wake bout durations is effected in part by changes in noradrenergic LC functioning. Considered within the domain of network theory, the hub-like connectivity of the LC may have important implications for the maintenance of network function in the face of random or targeted neural degeneration.
Lagrue, Clément; Poulin, Robert; Cohen, Joel E
2015-02-10
How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor's law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution.
Lagrue, Clément; Poulin, Robert; Cohen, Joel E.
2015-01-01
How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor’s law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution. PMID:25550506
Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu
2014-03-01
We start from Gibrat's law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.
Power law specific heat divergence in Sr{sub 3}Ru{sub 2}O{sub 7}
Energy Technology Data Exchange (ETDEWEB)
Rost, A.W.; Berridge, A.M.; Mercure, J.F.; Mackenzie, A.P. [Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews (United Kingdom); Perry, R.S. [SUPA, School of Physics, University of Edinburgh (United Kingdom); Grigera, S.A. [Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews (United Kingdom); Instituto de Fisica de Liquidos y Sistemas Biologicos, UNLP-CONICET, La Plata (Argentina)
2010-03-15
We present measurement and analysis of field-dependent specific heat measurements on Sr{sub 3}Ru{sub 2}O{sub 7}, showing that, at low temperatures, an incipient divergence is cut off by the formation of a new phase previously identified to show the transport properties of an electronic nematic. We discuss how to interpret a specific heat divergence in a system with van Hove singularities, and caution against a simple-minded comparison of experimentally determined power laws with the predictions of quantum critical theories. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Allen, J. M.
1974-01-01
Analytical expressions for the effects of compressibility and heat transfer on laminar and turbulent shape factors H have been developed. Solving the turbulent equation for the power law velocity profile exponent N has resulted in a simple technique by which the N values of experimental turbulent profiles can be calculated directly from the integral parameters. Thus the data plotting, curve fitting, and slope measuring, which is the normal technique of obtaining experimental N values, is eliminated. The N values obtained by this method should be within the accuracy with which they could be measured.
The effect of power-law body forces on a thermally driven flow between concentric rotating spheres
Macaraeg, M. G.
1986-01-01
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
The effect of power law body forces on a thermally-driven flow between concentric rotating spheres
Macaraeg, M. G.
1985-01-01
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
Mehedi Faruk, Mir; Sazzad Hossain, Md.; Muktadir Rahman, Md.
2016-02-01
The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U=\\sumi=1dci\\vert xi/ai\\vertni are studied carefully. Detailed calculation of Kim et al. (J. Phys. Condens. Matter 11 (1999) 10269) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume CV are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; López-López, M. G.; Alvarado-Martínez, V. M.
2018-03-01
In this paper, the two-dimensional projectile motion was studied; for this study two cases were considered, for the first one, we considered that there is no air resistance and, for the second case, we considered a resisting medium k . The study was carried out by using fractional calculus. The solution to this study was obtained by using fractional operators with power law, exponential decay and Mittag-Leffler kernel in the range of γ \\in (0,1] . These operators were considered in the Liouville-Caputo sense to use physical initial conditions with a known physical interpretation. The range and the maximum height of the projectile were obtained using these derivatives. With the aim of exploring the validity of the obtained results, we compared our results with experimental data given in the literature. A multi-objective particle swarm optimization approach was used for generating Pareto-optimal solutions for the parameters k and γ for different fixed values of velocity v0 and angle θ . The results showed some relevant qualitative differences between the use of power law, exponential decay and Mittag-Leffler law.
Hu, Bin; Kieweg, Sarah L
2012-07-15
Gravity-driven thin film flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. There have been many prior works on gravity-driven thin films. However, the incorporation of surface tension effect has not been well studied for non-Newtonian fluids. After surface tension effect was incorporated into our 2D (i.e. 1D spreading) power-law model, we found that surface tension effect not only impacted the spreading speed of the microbicide gel, but also had an influence on the shape of the 2D spreading profile. We observed a capillary ridge at the front of the fluid bolus. Previous literature shows that the emergence of a capillary ridge is strongly related to the contact line fingering instability. Fingering instabilities during epithelial coating may change the microbicide gel distribution and therefore impact how well it can protect the epithelium. In this study, we focused on the capillary ridge in 2D flow and performed a series of simulations and showed how the capillary ridge height varies with other parameters, such as surface tension coefficient, inclination angle, initial thickness, and power-law parameters. As shown in our results, we found that capillary ridge height increased with higher surface tension, steeper inclination angle, bigger initial thickness, and more Newtonian fluids. This study provides the initial insights of how to optimize the flow and prevent the appearance of a capillary ridge and fingering instability.
The Effect of Surface Tension on the Gravity-driven Thin Film Flow of Newtonian and Power-law Fluids
Hu, Bin; Kieweg, Sarah L.
2012-01-01
Gravity-driven thin film flow is of importance in many fields, as well as for the design of polymeric drug delivery vehicles, such as anti-HIV topical microbicides. There have been many prior works on gravity-driven thin films. However, the incorporation of surface tension effect has not been well studied for non-Newtonian fluids. After surface tension effect was incorporated into our 2D (i.e. 1D spreading) power-law model, we found that surface tension effect not only impacted the spreading speed of the microbicide gel, but also had an influence on the shape of the 2D spreading profile. We observed a capillary ridge at the front of the fluid bolus. Previous literature shows that the emergence of a capillary ridge is strongly related to the contact line fingering instability. Fingering instabilities during epithelial coating may change the microbicide gel distribution and therefore impact how well it can protect the epithelium. In this study, we focused on the capillary ridge in 2D flow and performed a series of simulations and showed how the capillary ridge height varies with other parameters, such as surface tension coefficient, inclination angle, initial thickness, and power-law parameters. As shown in our results, we found that capillary ridge height increased with higher surface tension, steeper inclination angle, bigger initial thickness, and more Newtonian fluids. This study provides the initial insights of how to optimize the flow and prevent the appearance of a capillary ridge and fingering instability. PMID:23687391
Barletta, A.; Nield, D. A.
2011-01-01
The onset of the convective instability in the horizontal throughflow of a power-law fluid saturating a horizontal porous layer heated from below is studied. A linear stability analysis of the basic flow is carried out and the disturbance equations are solved analytically. The problem examined here is an extension of the classical Prats problem for Newtonian fluids. It is shown that the marginal stability condition, as well as the critical values of the wave number and of the Darcy-Rayleigh number, is affected by the value of the Péclet number associated with the basic flow, except for the special case of a Newtonian fluid. The limit of a vanishingly small Péclet number is considered leading to the special case of the Horton-Rogers-Lapwood (HRL) problem for a power-law fluid, i.e., the Prats problem with a vanishing basic throughflow. It is shown that the generalized HRL problem is always linearly stable for pseudoplastic fluids and always linearly unstable for dilatant fluids.
Power-law distributions for the areas of the basins of attraction on a potential energy landscape.
Massen, Claire P; Doye, Jonathan P K
2007-03-01
Energy landscape approaches have become increasingly popular for analyzing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy landscape into basins of attraction surrounding the minima. Here, we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids. We find that this probability distribution is a power law over a large number of decades with the lower-energy minima having larger basins of attraction. Interestingly, the exponent for this power law is approximately the same as that for a high-dimensional Apollonian packing, providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. These results suggest that the basins of attraction provide a fractal-like tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.
Amani, Roonak; Rezazadeh, Kazem; Abdolmaleki, Asrin; Karami, Kayoomars
2018-02-01
We investigate the power-law, intermediate, and logamediate inflationary models in the framework of DBI non-canonical scalar field with constant sound speed. In the DBI setting, we first represent the power spectrum of both scalar density and tensor gravitational perturbations. Then, we derive different inflationary observables including the scalar spectral index n s , the running of the scalar spectral index {{dn}}s/d{ln}k, and the tensor-to-scalar ratio r. We show that the 95% CL constraint of the Planck 2015 T + E data on the non-Gaussianity parameter {f}{NL}{DBI} leads to the sound speed bound {c}s≥slant 0.087 in the DBI inflation. Moreover, our results imply that, although the predictions of the power-law, intermediate, and logamediate inflations in the standard canonical framework (c s = 1) are not consistent with the Planck 2015 data, in the DBI scenario with constant sound speed {c}srunning of the scalar spectral index and find that it is compatible with the 95% CL constraint from the Planck 2015 TT,TE,EE+lowP data.
Hard X-ray Emission along the Z Track in GX 17+2 GQ Ding∗ & CP ...
Indian Academy of Sciences (India)
In the hard states of BHXBs, the energetic electrons are assumed to exist in the optically thin part between the black hole and an optically thick truncated disk far from the black hole, where the high-energy electrons are ... power-law (PL) distribution (Poutanen & Coppi 1998; Coppi 1999; Gierlinski et al. 1999; Zdziarski et al.
Selvam, A. M.
2017-01-01
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference
Charge and density fluctuations lock horns: ionic criticality with power-law forces
International Nuclear Information System (INIS)
Aqua, Jean-Noel; Fisher, Michael E
2004-01-01
How do charge and density fluctuations compete in ionic fluids near gas-liquid criticality when quantum mechanical effects play a role? To gain some insight, long-range Φ L ±± /r d+σ interactions (with σ > 0), which encompass van der Waals forces (when σ = d = 3), have been incorporated in exactly soluble, d-dimensional 1:1 ionic spherical models with charges ±q 0 and hard-core repulsions. In accord with previous work, when d > min{σ, 2} (and q 0 is not too large), the Coulomb interactions do not alter the (q 0 = 0) critical universality class that is characterized by density correlations at criticality decaying as 1/r d-2+η with η = max{0, 2 - σ}. But screening is now algebraic, the charge-charge correlations decaying, in general, only as 1/r d+σ+4 ; thus σ = 3 faithfully mimics known noncritical d = 3 quantal effects. But in the absence of full (+, -) ion symmetry, density and charge fluctuations mix via a transparent mechanism: then the screening at criticality is weaker by a factor r 4-2η . Furthermore, the otherwise valid Stillinger-Lovett sum rule fails at criticality whenever η = 0 (as, e.g., when σ > 2) although it remains valid if η > 0 (as for σ < 2 or in real d ≤ 3 Ising-type systems). (letter to the editor)
Edwards, Andrew M
2008-11-01
1. Ecologists are obtaining ever-increasing amounts of data concerning animal movement. A movement strategy that has been concluded for a broad variety of animals is that of Lévy flights, which are random walks whose step lengths come from probability distributions with heavy power-law tails. 2. The exponent that parameterizes the power-law tail, denoted micro, has repeatedly been found to be within the Lévy range of 1 < micro
Directory of Open Access Journals (Sweden)
Noa Slater
2015-04-01
Full Text Available Measures of allele and haplotype diversity, which are fundamental properties in population genetics, often follow heavy tailed distributions. These measures are of particular interest in the field of hematopoietic stem cell transplant (HSCT. Donor/Recipient suitability for HSCT is determined by Human Leukocyte Antigen (HLA similarity. Match predictions rely upon a precise description of HLA diversity, yet classical estimates are inaccurate given the heavy-tailed nature of the distribution. This directly affects HSCT matching and diversity measures in broader fields such as species richness. We, therefore, have developed a power-law based estimator to measure allele and haplotype diversity that accommodates heavy tails using the concepts of regular variation and occupancy distributions. Application of our estimator to 6.59 million donors in the Be The Match Registry revealed that haplotypes follow a heavy tail distribution across all ethnicities: for example, 44.65% of the European American haplotypes are represented by only 1 individual. Indeed, our discovery rate of all U.S. European American haplotypes is estimated at 23.45% based upon sampling 3.97% of the population, leaving a large number of unobserved haplotypes. Population coverage, however, is much higher at 99.4% given that 90% of European Americans carry one of the 4.5% most frequent haplotypes. Alleles were found to be less diverse suggesting the current registry represents most alleles in the population. Thus, for HSCT registries, haplotype discovery will remain high with continued recruitment to a very deep level of sampling, but population coverage will not. Finally, we compared the convergence of our power-law versus classical diversity estimators such as Capture recapture, Chao, ACE and Jackknife methods. When fit to the haplotype data, our estimator displayed favorable properties in terms of convergence (with respect to sampling depth and accuracy (with respect to diversity
Formation and relaxation of quasistationary states in particle systems with power-law interactions
Marcos, B.; Gabrielli, A.; Joyce, M.
2017-09-01
We explore the formation and relaxation of the so-called quasistationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential V (r →∞ ) ˜1 /rγ with γ >0 , and either a soft core or hard core regularization at small r . In the first part of the paper, we generalize, for any spatial dimension d ≥2 , Chandrasekhar's approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two-body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for γ >d -1 , the rate diverges in the large particle number N (mean-field) limit, unless a sufficiently large soft core is present; for γ code, for a range of different exponents γ and soft cores leading to the formation of QSS. We find, just as for the previously well studied case of gravity (which we also revisit), excellent agreement between the parametric dependence of the observed relaxation times and our analytic predictions. Further, as in the case of gravity, we find that the results indicate that, when large impact factors dominate, the appropriate cutoff is the size of the system (rather than, for example, the mean interparticle distance). Our results provide strong evidence that the existence of QSS is robust only for long-range interactions with a large distance behavior γ
Directory of Open Access Journals (Sweden)
Omotayo Omosebi
2015-12-01
This article presents an analytic technique for interpreting pressure falloff tests of non-Newtonian Power-law fluids in wells that are located near boundaries in dual-porosity reservoirs. First, dimensionless pressure solutions are obtained and Stehfest inversion algorithm is used to develop new type curves. Subsequently, long-time analytic solutions are presented and interpretation procedure is proposed using direct synthesis. Two examples, including real field data from a heavy oil reservoir in Colombian eastern plains basin, are used to validate and demonstrate application of this technique. Results agree with conventional type-curve matching procedure. The approach proposed in this study avoids the use of type curves, which is prone to human errors. It provides a better alternative for direct estimation of formation and flow properties from falloff data.
Second-order small disturbance theory for hypersonic flow over power-law bodies. Ph.D. Thesis
Townsend, J. C.
1974-01-01
A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.
Determining the power-law wind-profile exponent under near-neutral stability conditions at sea
Hsu, S. A.; Meindl, Eric A.; Gilhousen, David B.
1994-01-01
On the basis of 30 samples from near-simultaneous overwater measurements by pairs of anemometers located at different heights in the Gulf of Mexico and off the Chesapeake Bay, Virginia, the mean and standard deviation for the exponent of the power-law wind profile over the ocean under near-neutral atmospheric stability conditions were determined to be 0.11 +/- 0.03. Because this mean value is obtained from both deep and shallow water environments, it is recommended for use at sea to adjust the wind speed measurements at different heights to the standard height of 10 m above the mean sea surface. An example to apply this P value to estimate the momentum flux or wind stress is provided.
Directory of Open Access Journals (Sweden)
Markus Hess
2016-12-01
Full Text Available Until recently, the only way of solving contact problems was to applythree-dimensional contact theories. However, this presupposes higher mathematical and numerical knowledge, which usually only research groups possess. This has changed drastically with the development of the method of dimensionality reduction (MDR, which allows every practically oriented engineer an access to the solution of contact problems. The simple and contact-type dependent rules are summarized in the first part of the user manual; they require contacts between elastically homogeneous materials. The present paper forms the second part of the user handbook and is dedicated to the solution of contact problems between power-law graded materials. All the MDR-rules are listed with which normal, tangential and adhesive contacts between such high-performance materials can be calculated in a simple manner.
Huang, Y.; Song, Q. W.; Tan, B. L.
2018-04-01
It is first proposed a theoretical scaling law respectively for the coronal magnetic field strength B and electron power-law index δ versus frequency and coronal height in solar microwave burst sources. Based on the non-thermal gyro-synchrotron radiation model (Ramaty in Astrophys. J. 158:753, 1969), B and δ are uniquely solved by the observable optically-thin spectral index and turnover (peak) frequency, the other parameters (plasma density, temperature, view angle, low and high energy cutoffs, etc.) are relatively insensitive to the calculations, thus taken as some typical values. Both of B and δ increase with increasing of radio frequency but with decreasing of coronal height above photosphere, and well satisfy a square or cubic logarithmic fitting.
Thompson, Rodger I.
2018-04-01
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar ϕ with respect to the natural log of the scale factor a, β (φ )=d φ /d ln (a). Once the beta function is specified, modulo a boundary condition, the evolution of the scalar ϕ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated "beta potential" is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are that are not calculable using only the model action. As an example this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that ΛCDM is part of the family of quintessence cosmology power law potentials with a power of zero.
Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert
2011-08-25
Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.
Directory of Open Access Journals (Sweden)
Sorribas Albert
2011-08-01
Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.
Balloon-borne hard x-ray imaging observations of non-thermal phenomena
Kunieda, Hideyo
2006-06-01
Non-thermal phenomena is now-a-days recognized as an important half of the energetics of the Universe. Hard X-ray emission from energetic particles is the most important clue to investigate the non-thermal phenomena. Hard X-ray imaging telescopes are known to improve the sensitivity of hard X-ray observations dramatically. Since hard X-rays above 25 keV can be observed at the altitude of 40 km, we are performing hard X-ray imaging balloon experiments as the path finders of future satellite missions of hard X-ray imaging. Major fields we are looking into are non-thermal components from SNR and Cluster of galaxies and the power law components from AGN even with thick column. The former are related to acceleration mechanisms of high energy particles responsible for hard X-ray power law components. The latter is the complete search of emission from massive blackholes which contribute most to the cosmic X-ray background. Our current balloon programs are InFOCμS experiment and SUMIT project. NeXT is the hard X-ray imaging mission proposed as the next Japanese X-ray mission.
International Nuclear Information System (INIS)
Dehkordi, Asghar Molaei; Mohammadi, Ali Asghar
2009-01-01
A numerical investigation was conducted on the transient behavior of a hydrodynamically, fully developed, laminar flow of power-law fluids in the thermally developing entrance region of circular ducts taking into account the effect of viscous dissipation but neglecting the effect of axial conduction. In this regard, the unsteady state thermal energy equation was solved by using a finite difference method, whereas the steady state thermal energy equation without wall heat flux was solved analytically as the initial condition of the former. The effects of the power-law index and wall heat flux on the local Nusselt number and thermal entrance length were investigated. Moreover, the local Nusselt number of steady state conditions was correlated in terms of the power-law index and wall heat flux and compared with literature data, which were obtained by an analytic solution for Newtonian fluids. Furthermore, a relationship was proposed for the thermal entrance length
Aziz, Asim; Ali, Yasir; Aziz, Taha; Siddique, J I
2015-01-01
In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.
International Nuclear Information System (INIS)
Jing Yipeng.
1989-08-01
We study the three-point correlation functions ρ(r, u, v) of clusters in the two types of explosion models by numerical simulations. The clusters are identified as the ''knots'' where three shells intersect. The shells are assumed to have the constant radii (the constant models) or have the power law radius distributions (the power law models). In both kinds of models, we find that ρ can be approximately expressed by the scaling form: ρ = Q(ξ 1 ξ 2 + ξ 2 ξ 3 + ξ 3 ξ 1 ), and Q is about 1, which are consistent with the observations. More detailed studies of r-, u- and v-dependences of Q show that Q remains constant in the constant models. In the power-law models, Q is independent of the shape parameters u and v, while it has some moderate r-dependences (variations with r about a factor of 1 or 2). (author). 27 refs, 9 figs
El-Amin, Mohamed
2010-11-27
A boundary layer analysis was presented to study the non-Darcy-free convection of a power-law fluid over a non-isothermal two-dimensional body embedded in a porous medium. The Ostwald-de Waele power-law model was used to characterize the non-Newtonian fluid behavior. Similarity solutions were obtained with variations in surface temperature or surface heat flux. In view of the fact that most of the non-Newtonian fluids have large Prandtl numbers, this study was directed toward such fluids. The effects of the porous medium parameters, k1 and k2, body shape parameter, m, and surface thermal variations parameter, p, as well as the power-law index, n, were examined. © 2010 Springer Science+Business Media B.V.
American Society for Testing and Materials. Philadelphia
2007-01-01
1.1 Conversion Table 1 presents data in the Rockwell C hardness range on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, Knoop hardness, and Scleroscope hardness of non-austenitic steels including carbon, alloy, and tool steels in the as-forged, annealed, normalized, and quenched and tempered conditions provided that they are homogeneous. 1.2 Conversion Table 2 presents data in the Rockwell B hardness range on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, Knoop hardness, and Scleroscope hardness of non-austenitic steels including carbon, alloy, and tool steels in the as-forged, annealed, normalized, and quenched and tempered conditions provided that they are homogeneous. 1.3 Conversion Table 3 presents data on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, and Knoop hardness of nickel and high-nickel alloys (nickel content o...
International Nuclear Information System (INIS)
Dan, J.P.; Boving, H.J.; Hintermann, H.E.
1993-01-01
Hard, wear resistant and low friction coatings are presently produced on a world-wide basis, by different processes such as electrochemical or electroless methods, spray technologies, thermochemical, CVD and PVD. Some of the most advanced processes, especially those dedicated to thin film depositions, basically belong to CVD or PVD technologies, and will be looked at in more detail. The hard coatings mainly consist of oxides, nitrides, carbides, borides or carbon. Over the years, many processes have been developed which are variations and/or combinations of the basic CVD and PVD methods. The main difference between these two families of deposition techniques is that the CVD is an elevated temperature process (≥ 700 C), while the PVD on the contrary, is rather a low temperature process (≤ 500 C); this of course influences the choice of substrates and properties of the coating/substrate systems. Fundamental aspects of the vapor phase deposition techniques and some of their influences on coating properties will be discussed, as well as the very important interactions between deposit and substrate: diffusions, internal stress, etc. Advantages and limitations of CVD and PVD respectively will briefly be reviewed and examples of applications of the layers will be given. Parallel to the development and permanent updating of surface modification technologies, an effort was made to create novel characterisation methods. A close look will be given to the coating adherence control by means of the scratch test, at the coating hardness measurement by means of nanoindentation, at the coating wear resistance by means of a pin-on-disc tribometer, and at the surface quality evaluation by Atomic Force Microscopy (AFM). Finally, main important trends will be highlighted. (orig.)
Revisiting the definition of local hardness and hardness kernel.
Polanco-Ramírez, Carlos A; Franco-Pérez, Marco; Carmona-Espíndola, Javier; Gázquez, José L; Ayers, Paul W
2017-05-17
An analysis of the hardness kernel and local hardness is performed to propose new definitions for these quantities that follow a similar pattern to the one that characterizes the quantities associated with softness, that is, we have derived new definitions for which the integral of the hardness kernel over the whole space of one of the variables leads to local hardness, and the integral of local hardness over the whole space leads to global hardness. A basic aspect of the present approach is that global hardness keeps its identity as the second derivative of energy with respect to the number of electrons. Local hardness thus obtained depends on the first and second derivatives of energy and electron density with respect to the number of electrons. When these derivatives are approximated by a smooth quadratic interpolation of energy, the expression for local hardness reduces to the one intuitively proposed by Meneses, Tiznado, Contreras and Fuentealba. However, when one combines the first directional derivatives with smooth second derivatives one finds additional terms that allow one to differentiate local hardness for electrophilic attack from the one for nucleophilic attack. Numerical results related to electrophilic attacks on substituted pyridines, substituted benzenes and substituted ethenes are presented to show the overall performance of the new definition.
New design concept of hard x-ray supermirrors for astronomical x-ray telescopes
Wang, Fangfang; Zhu, Jingtao; Tan, Moyan; Jiang, Li; Wang, Zhanshan
2010-10-01
A numerical and analysis method for optimizing multilayer supermirrors is developed based on the combination of the power-law method and the local optimization method of simplex algorithm. The parameters in the power-law formula are optimized by genetic algorithm. This allows a global minimization of the merit function and a many-fold decrease of the computing time. Several groups of X-ray supermirrors with the energy extended to 30 keV are successfully designed using this optimization method for a hard X-ray telescope. Tungsten and boron carbide are chosen as the multilayer materials. High reflectivity and high effective area are obtained, indicating that this numerical and analysis method is an effective tool to design hard X-ray supermirrors.
The hard x-ray spectrum of SN 1987A
International Nuclear Information System (INIS)
Trumper, J.; Reppin, C.; Pietsch, W.; Englhauser, J.; Voges, W.; Kendziorra, E.; Bezler, M.; Staubert, R.; Sunyaev, R.; Kaniovskiy, A.; Efremov, V.; Grebenev, M.; Kuznetsov, A.; Meliorazkiy, A.; Stepanov, D.; Chulkov, I.
1988-01-01
The authors report the discovery of hard x-rays in the energy range from 20 to 350 keV. The hard x-rays were first observed on August 10, 1987 and thereafter SN 1987A became the main target of the observatory. The measured spectrum is extremely hard. At high energies the photon spectrum has a power law index of ∼ 1.4. At lower energies the spectrum becomes flatter and there is indication of a cut-off below 25 keV. The luminosity in the above energy band is ∼ 2 x 10 38 erg/s. The flux shows little variation between August 10 and beginning of October
Multivariate power-law models for streamflow prediction in the Mekong Basin
Directory of Open Access Journals (Sweden)
Guillaume Lacombe
2014-11-01
New hydrological insights for the region: A combination of 3–6 explanatory variables – chosen among annual rainfall, drainage area, perimeter, elevation, slope, drainage density and latitude – is sufficient to predict a range of flow metrics with a prediction R-squared ranging from 84 to 95%. The inclusion of forest or paddy percentage coverage as an additional explanatory variable led to slight improvements in the predictive power of some of the low-flow models (lowest prediction R-squared = 89%. A physical interpretation of the model structure was possible for most of the resulting relationships. Compared to regional regression models developed in other parts of the world, this new set of equations performs reasonably well.
Does price efficiency increase with trading volume? Evidence of nonlinearity and power laws in ETFs
Caginalp, Gunduz; DeSantis, Mark
2017-02-01
Whether efficiency increases with increasing volume is an important issue that may illuminate trader strategies and distinguish between market theories. This relationship is tested using 124,236 daily observations comprising 68 large and liquid U.S. equity exchange traded funds (ETFs). ETFs have the advantage that efficiency can be measured in terms of the deviation between the trading price and the underlying net asset value that is reported each day. Our findings support the hypothesis that the relationship between volume and efficiency is nonlinear. Indeed, efficiency increases as volume increases from low to moderately high levels, but then decreases as volume increases further. The first part tends to support the idea that higher volume simply facilitates transactions and maintains efficiency, while the latter part, i.e., even higher volumes, supports the ansatz that increased volume is associated with increased speculation that ignores valuation and decreases efficiency. The results are consistent with the hypothesis that valuation is only part of the motivation for traders. Our methodology accounts for fund heterogeneity and contemporaneous correlations. Similar results are obtained when daily price volatility is introduced as an additional independent variable.
A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues.
Nicolle, S; Vezin, P; Palierne, J-F
2010-03-22
Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s(-1) to 0.7s(-1). Copyright (c) 2009 Elsevier Ltd. All rights reserved.
Scocchia, Lisa; Bolognini, Nadia; Convento, Silvia; Stucchi, Natale
2015-11-16
Human movements conform to specific kinematic laws of motion. One of such laws, the "two-thirds power law", describes the systematic co-variation between curvature and velocity of body movements. Noticeably, the same law also influences the perception of moving stimuli: the velocity of a dot moving along a curvilinear trajectory is perceived as uniform when the dot kinematics complies with the two-thirds power law. Instead, if the dot moves at constant speed, its velocity is perceived as highly non-uniform. This dynamic visual illusion points to a strong coupling between action and perception; however, how this coupling is implemented in the brain remains elusive. In this study, we tested whether the premotor cortex (PM) and the primary visual cortex (V1) play a role in the illusion by means of transcranial Direct Current Stimulation (tDCS). All participants underwent three tDCS sessions during which they received active or sham cathodal tDCS (1.5mA) over PM or V1 of the left hemisphere. During tDCS, participants were required to adjust the velocity of a dot moving along an elliptical trajectory until it looked uniform across the whole trajectory. Results show that occipital tDCS decreases the illusion variability both within and across participants, as compared to sham tDCS. This means that V1 stimulation increases individual sensitivity to the illusory motion and also increases coherence across different observers. Conversely, the illusion seems resistant to tDCS in terms of its magnitude, with cathodal stimulation of V1 or PM not affecting the amount of the illusory effect. Our results provide evidence for strong visuo-motor coupling in visual perception: the velocity of a dot moving along an elliptical trajectory is perceived as uniform only when its kinematics closely complies to the same law of motion that constrains human movement production. Occipital stimulation by cathodal tDCS can stabilize such illusory percept. Copyright © 2015 Elsevier Ireland Ltd
Shenoy, S. R.; Lookman, T.; Saxena, A.
2010-10-01
We consider ferroelastic first-order phase transitions with NOP order-parameter strains entering Landau free energies as invariant polynomials that have NV structural-variant Landau minima. The total free energy includes (seemingly innocuous) harmonic terms, in the n=6-NOP nonorder-parameter strains. Four three-dimensional (3D) transitions are considered, tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal, and cubic/orthorhombic unit-cell distortions, with, respectively, NOP=1 , 2, 3, and 2; and NV=2 , 3, 4, and 6. Five two-dimensional (2D) transitions are also considered, as simpler examples. Following Barsch and Krumhansl, we scale the free energy to absorb most material-dependent elastic coefficients into an overall prefactor, by scaling in an overall elastic energy density; a dimensionless temperature variable; and the spontaneous-strain magnitude at transition λ≪1 . To leading order in λ the scaled Landau minima become material independent, in a kind of “quasiuniversality.” The scaled minima in NOP -dimensional order-parameter space, fall at the center and at the NV corners, of a transition-specific polyhedron inscribed in a sphere, whose radius is unity at transition. The “polyhedra” for the four 3D transitions are, respectively, a line, a triangle, a tetrahedron, and a hexagon. We minimize the n terms harmonic in the nonorder-parameter strains, by substituting solutions of the “no dislocation” St Venant compatibility constraints, and explicitly obtain power-law anisotropic, order-parameter interactions, for all transitions. In a reduced discrete-variable description, the competing minima of the Landau free energies induce unit-magnitude pseudospin vectors, with NV+1 values, pointing to the polyhedra corners and the (zero-value) center. The total scaled free energies then become ZNV+1 clocklike pseudospin Hamiltonians, with temperature-dependent local Landau terms, nearest-neighbor Ginzburg couplings, and power-law St Venant
Palmer, Bradley M.; Tanner, Bertrand C.W.; Toth, Michael J.; Miller, Mark S.
2013-01-01
Viscoelastic characteristics of many materials falling under the category of soft glassy substances, including biological tissue, often exhibit a mechanical complex modulus Y(ω) well described by a fractional derivative model: Y(ω) = E(iω/ϕ)k, where E = a generalized viscoelastic stiffness; i = (−1)1/2; ω = angular frequency; ϕ = scaling factor; and k = an exponent valued between 0 and 1. The term “fractional derivative” refers to the value of k: when k = 0 the viscoelastic response is purely elastic, and when k = 1 the response is purely viscous. We provide an analytical derivation of the fractional derivative complex modulus based on the hypothesis that the viscoelastic response arises from many intermittent molecular crosslinks, whose lifetimes longer than a critical threshold lifetime, tcrit, are distributed with an inverse power law proportional to t-(k+2). We demonstrate that E is proportional to the number and stiffness of crosslinks formed at any moment; the scaling factor ϕ is equivalent to reciprocal of tcrit; and the relative mean lifetime of the attached crosslinks is inversely proportional to the parameter k. To test whether electrostatic molecular bonds could be responsible for the fractional derivative viscoelasticity, we used chemically skinned human skeletal muscle as a one-dimensional model of a soft glassy substance. A reduction in ionic strength from 175 to 110 mEq resulted in a larger E with no change in k, consistent with a higher probability of interfilament molecular interactions. Thick to thin filament spacing was reduced by applying 4% w/v of the osmolyte Dextran T500, which also resulted in a larger E, indicating a greater probability of crosslink formation in proportion to proximity. A 10°C increase in temperature resulted in an increase in k, which corresponded to a decrease in cross-bridge attachment lifetime expected with higher temperatures. These theoretical and experimental results suggest that the fractional
Luscombe, Nicholas M; Qian, Jiang; Zhang, Zhaolei; Johnson, Ted; Gerstein, Mark
2002-07-25
The sequencing of genomes provides us with an inventory of the 'molecular parts' in nature, such as protein families and folds, and their functions in living organisms. Through the analysis of such inventories, it has been shown that different genomes have very different usage of parts; for example, the common folds in the worm are very different from those in Escherichia coli. Despite these differences, we find that the genomic occurrence of generalized parts follows a well-known mathematical framework called the power law, with a few parts occurring many times and most occurring only a few times. This observation is true in a wide variety of genomic contexts. Earlier studies found power laws in a few specific cases, such as the occurrence of protein families. Here, we find many further cases of power-law behavior, for example in the occurrence of pseudogenes and in levels of gene expression. We show comprehensively that this behavior applies across many different genomes, for many different types of parts (DNA words, InterPro families, protein superfamilies and folds, pseudogene families and pseudomotifs), and for the many disparate attributes associated with these parts (their functions, interactions and expression levels). Power-law behavior provides a concise mathematical description of an important biological feature: the sheer dominance of a few members over the overall population. We present this behavior in a unified framework and propose that all these observations are connected to an underlying DNA duplication process as genomes evolved to their current state.
Catalina Segura; Davide Lazzati; Arumugam Sankarasubramanian
2013-01-01
A recent study employed a broken power-law (BPL) distribution for understanding the scaling frequency of bankfull discharge in snowmelt-dominated basins. This study, grounded from those findings, investigated the ability of a BPL function to describe the distribution of daily flows above the mean annual flow in 1217 sites across the conterminous U.S. (CONUS). The...
Directory of Open Access Journals (Sweden)
Scholkmann F.
2016-01-01
Full Text Available The recent (14 th July 2015 flyby of NASA’s New Horizons spacecraft of the dwarf planet Pluto resulted in the first high-resolution images of the geological surface- features of Pluto. Since previous studies showed that the impact crater size-frequency distribution (SFD of different celestial objects of our solar system follows power-laws, the aim of the present analysis was to determine, for the first time, the power-law scaling behavior for Pluto’s crater SFD based on the first images available in mid-September 2015. The analysis was based on a high-resolution image covering parts of Pluto’s re- gions Sputnik Planum , Al-Idrisi Montes and Voyager Terra . 83 impact craters could be identified in these regions and their diameter ( D was determined. The analysis re- vealed that the crater diameter SFD shows a statistically significant power-law scaling ( α = 2.4926±0.3309 in the interval of D values ranging from 3.75±1.14 km to the largest determined D value in this data set of 37.77 km. The value obtained for the scaling coefficient α is similar to the coefficient determined for the power-law scaling of the crater SFDs from the other celestial objects in our solar system. Further analysis of Pluto’s crater SFD is warranted as soon as new images are received from the spacecraft.
Directory of Open Access Journals (Sweden)
Gao Feng
2017-01-01
Full Text Available In this paper we address the general fractional calculus of Liouville-Weyl and Liouville-Caputo general fractional derivative types with non-singular power-law kernel for the first time. The Fourier transforms and the anomalous diffusions are discussed in detail. The formulations are adopted to describe complex phenomena of the heat transfer problems.
Contact Line Instability of Gravity-Driven Flow of Power-Law Fluids.
Hu, Bin; Kieweg, Sarah L
2015-11-01
The moving contact line of a thin fluid film can often corrugate into fingers, which is also known as a fingering instability. Although the fingering instability of Newtonian fluids has been studied extensively, there are few studies published on contact line fingering instability of non-Newtonian fluids. In particular, it is still unknown how shear-thinning rheological properties can affect the formation, growth, and shape of a contact line instability. Our previous study (Hu and Kieweg, 2012) showed a decreased capillary ridge formation for more shear-thinning fluids in a 2D model (i.e. 1D thin film spreading within the scope of lubrication theory). Those results motivated this study's hypothesis: more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In this study, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. This study also showed that the distance between emerging fingers was smaller on a vertical plane than on a less-inclined plane for shear-thinning fluids, as previously shown for Newtonian fluids. For the first time for shear
Wong, Wing-Cheong; Ng, Hong-Kiat; Tantoso, Erwin; Soong, Richie; Eisenhaber, Frank
2018-02-12
Though earlier works on modelling transcript abundance from vertebrates to lower eukaroytes have specifically singled out the Zip's law, the observed distributions often deviate from a single power-law slope. In hindsight, while power-laws of critical phenomena are derived asymptotically under the conditions of infinite observations, real world observations are finite where the finite-size effects will set in to force a power-law distribution into an exponential decay and consequently, manifests as a curvature (i.e., varying exponent values) in a log-log plot. If transcript abundance is truly power-law distributed, the varying exponent signifies changing mathematical moments (e.g., mean, variance) and creates heteroskedasticity which compromises statistical rigor in analysis. The impact of this deviation from the asymptotic power-law on sequencing count data has never truly been examined and quantified. The anecdotal description of transcript abundance being almost Zipf's law-like distributed can be conceptualized as the imperfect mathematical rendition of the Pareto power-law distribution when subjected to the finite-size effects in the real world; This is regardless of the advancement in sequencing technology since sampling is finite in practice. Our conceptualization agrees well with our empirical analysis of two modern day NGS (Next-generation sequencing) datasets: an in-house generated dilution miRNA study of two gastric cancer cell lines (NUGC3 and AGS) and a publicly available spike-in miRNA data; Firstly, the finite-size effects causes the deviations of sequencing count data from Zipf's law and issues of reproducibility in sequencing experiments. Secondly, it manifests as heteroskedasticity among experimental replicates to bring about statistical woes. Surprisingly, a straightforward power-law correction that restores the distribution distortion to a single exponent value can dramatically reduce data heteroskedasticity to invoke an instant increase in
Goodman, Michael L.; Kwan, Chiman; Ayhan, Bulent; Shang, Eric L.
2017-01-01
A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model predicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q-s, above an AR dependent threshold value of Q, where 0.3952 or = E obeys the same type of distribution, N(E) / E-S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.
High energy power-law tail in X-ray binaries and bulk Comptonization due to an outflow from a disk
Kumar, Nagendra
2018-02-01
We study the high energy power-law tail emission of X-ray binaries (XRBs) by a bulk Comptonization process which is usually observed in the very high soft (VHS) state of black hole (BH) XRBs and the high soft (HS) state of the neutron star (NS) and BH XRBs. Earlier, to generate the power-law tail in bulk Comptonization framework, a free-fall converging flow into BH or NS had been considered as a bulk region. In this work, for a bulk region we consider mainly an outflow geometry from the accretion disk which is bounded by a torus surrounding the compact object. We have two choices for an outflow geometry: (i) collimated flow and (ii) conical flow of opening angle θ _b and the axis is perpendicular to the disk. We also consider an azimuthal velocity of the torus fluids as a bulk motion where the fluids are rotating around the compact object (a torus flow). We find that the power-law tail can be generated in a torus flow having large optical depth and bulk speed (>0.75 c), and in conical flow with θ _b > ˜ 30° for a low value of Comptonizing medium temperature. Particularly, in conical flow the low opening angle is more favourable to generate the power-law tail in both the HS state and the VHS state. We notice that when the outflow is collimated, then the emergent spectrum does not have power-law component for a low Comptonizing medium temperature.
Cai, PingGen; Takahashi, Ryosuke; Kuribayashi-Shigetomi, Kaori; Subagyo, Agus; Sueoka, Kazuhisa; Maloney, John M; Van Vliet, Krystyn J; Okajima, Takaharu
2017-08-08
Changes in the cytoskeletal organization within cells can be characterized by large spatial and temporal variations in rheological properties of the cell (e.g., the complex shear modulus G ∗ ). Although the ensemble variation in G ∗ of single cells has been elucidated, the detailed temporal variation of G ∗ remains unknown. In this study, we investigated how the rheological properties of individual fibroblast cells change under a spatially confined environment in which the cell translational motion is highly restricted and the whole cell shape remains unchanged. The temporal evolution of single-cell rheology was probed at the same measurement location within the cell, using atomic force microscopy-based oscillatory deformation. The measurements reveal that the temporal variation in the power-law rheology of cells is quantitatively consistent with the ensemble variation, indicating that the cell system satisfies an ergodic hypothesis in which the temporal statistics are identical to the ensemble statistics. The autocorrelation of G ∗ implies that the cell mechanical state evolves in the ensemble of possible states with a characteristic timescale. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Abdel-Khalek, S.; Berrada, K.; Alkhateeb, Sadah A.
2016-09-01
In this paper, we propose a useful quantum system to perform different tasks of quantum information and computational technologies. We explore the required optimal conditions for this system that are feasible with real experimental realization. We present an active way to control the variation of some measures of nonclassicality considering the time-dependent coupling and photon transition effects under a model that closely describes a realistic experimental scenario. We investigate qualitatively the quantum measures for a two-level atom system interacting with a quantum field initially defined in a coherent state in the framework of power-law potentials (PLPCSs). We study the nonlocal correlation in the whole system state using the negativity as a measure of entanglement in terms of the exponent parameter, number of photon transition, and phase damping effect. The influences of the different physical parameters on the statistical properties and purity of the field are also demonstrated during the time evolution. The results indicate that the preservation and enhancement of entanglement greatly benefit from the combination of the choice of the physical parameters. Finally, we explore an interesting relationship between the different quantum measures of non-classicality during the time evolution in the absence and presence of time-dependent coupling effect.
Directory of Open Access Journals (Sweden)
M. H. Yazdi
2014-01-01
Full Text Available In the present study, the first and second law analyses of power-law non-Newtonian flow over embedded open parallel microchannels within micropatterned permeable continuous moving surface are examined at prescribed surface temperature. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. The velocity, the temperature, the velocity gradient, and the temperature gradient adjacent to the wall are substituted into this equation resulting from the momentum and energy equations obtained numerically by Dormand-Prince pair and shooting method. Finally, the entropy generation numbers, as well as the Bejan number, are evaluated. It is noted that the presence of the shear thinning (pseudoplastic fluids creates entropy along the surface, with an opposite effect resulting from shear thickening (dilatant fluids.
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
Scott, James F; Evans, Donald M; Katiyar, Ram S; McQuaid, Raymond G P; Gregg, J Marty
2017-08-02
Since the 1935 work of Landau-Lifshitz and of Kittel in 1946 all ferromagnetic, ferroelectric, and ferroelastic domains have been thought to be straight-sided with domain widths proportional to the square root of the sample thickness. We show in the present work that this is not true. We also discover period doubling domains predicted by Metaxas et al (2008 Phys. Rev. Lett. 99 217208) and modeled by Wang and Zhao (2015 Sci. Rep. 5 8887). We examine non-equilibrium ferroic domain structures in perovskite oxides with respect to folding, wrinkling, and relaxation and suggest that structures are kinetically limited and in the viscous flow regime predicted by Metaxas et al in 2008 but never observed experimentally. Comparisons are made with liquid crystals and hydrodynamic instabilities, including chevrons, and fractional power-law relaxation. As Shin et al (2016 Soft Matter 12 3502) recently emphasized: 'An understanding of how these folds initiate, propagate, and interact with each other is still lacking'. Inside each ferroelastic domain are ferroelectric 90° nano-domains with 10 nm widths and periodicity in agreement with the 10 nm theoretical minima predicted by Feigl et al (2014 Nat. Commun. 5 4677). Evidence is presented for domain-width period doubling, which is common in polymer films but unknown in ferroic domains. A discussion of the folding-to-period doubling phase transition model of Wang and Zhao is included.
International Nuclear Information System (INIS)
Taghipour, Sharareh; Banjevic, Dragan
2011-01-01
Trend analysis is a common statistical method used to investigate the operation and changes of a repairable system over time. This method takes historical failure data of a system or a group of similar systems and determines whether the recurrent failures exhibit an increasing or decreasing trend. Most trend analysis methods proposed in the literature assume that the failure times are known, so the failure data is statistically complete; however, in many situations, such as hidden failures, failure times are subject to censoring. In this paper we assume that the failure process of a group of similar independent repairable units follows a non-homogenous Poisson process with a power law intensity function. Moreover, the failure data are subject to left, interval and right censoring. The paper proposes using the likelihood ratio test to check for trends in the failure data. It uses the Expectation-Maximization (EM) algorithm to find the parameters, which maximize the data likelihood in the case of null and alternative hypotheses. A recursive procedure is used to solve the main technical problem of calculating the expected values in the Expectation step. The proposed method is applied to a hospital's maintenance data for trend analysis of the components of a general infusion pump.
Directory of Open Access Journals (Sweden)
Qun Zhang
Full Text Available We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the "S&P 500 1987" bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs.
Zhang, Qun; Zhang, Qunzhi; Sornette, Didier
2016-01-01
We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the "S&P 500 1987" bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs.
Size effect and scaling power-law for superelasticity in shape-memory alloys at the nanoscale.
Gómez-Cortés, Jose F; Nó, Maria L; López-Ferreño, Iñaki; Hernández-Saz, Jesús; Molina, Sergio I; Chuvilin, Andrey; San Juan, Jose M
2017-08-01
Shape-memory alloys capable of a superelastic stress-induced phase transformation and a high displacement actuation have promise for applications in micro-electromechanical systems for wearable healthcare and flexible electronic technologies. However, some of the fundamental aspects of their nanoscale behaviour remain unclear, including the question of whether the critical stress for the stress-induced martensitic transformation exhibits a size effect similar to that observed in confined plasticity. Here we provide evidence of a strong size effect on the critical stress that induces such a transformation with a threefold increase in the trigger stress in pillars milled on [001] L2 1 single crystals from a Cu-Al-Ni shape-memory alloy from 2 μm to 260 nm in diameter. A power-law size dependence of n = -2 is observed for the nanoscale superelasticity. Our observation is supported by the atomic lattice shearing and an elastic model for homogeneous martensite nucleation.
Directory of Open Access Journals (Sweden)
Fan Li
2016-01-01
Full Text Available Software reliability growth models (SRGMs based on a nonhomogeneous Poisson process (NHPP are widely used to describe the stochastic failure behavior and assess the reliability of software systems. For these models, the testing-effort effect and the fault interdependency play significant roles. Considering a power-law function of testing effort and the interdependency of multigeneration faults, we propose a modified SRGM to reconsider the reliability of open source software (OSS systems and then to validate the model’s performance using several real-world data. Our empirical experiments show that the model well fits the failure data and presents a high-level prediction capability. We also formally examine the optimal policy of software release, considering both the testing cost and the reliability requirement. By conducting sensitivity analysis, we find that if the testing-effort effect or the fault interdependency was ignored, the best time to release software would be seriously delayed and more resources would be misplaced in testing the software.
DEFF Research Database (Denmark)
Tendulkar, Shriharsh P.; Bachetti, Matteo; Tomsick, J.
2014-01-01
frequencies. The Lorentzian has a width of 2 Hz and a fractional rms of 25+/-3%. The hard power-law index, the high energy of the cutoff, and the level of variability all are consistent with properties expected for an accreting black hole in the hard state. While we cannot completely rule out the possibility...... power-law with an exponential cutoff and a broad, asymmetric, iron emission line. The column density is (3.3+/-0.6)e22 cm-2 (using Anders & Grevesse 1989 abundances; errors on all spectral parameters are 90% confidence), the photon index is 1.46+/-0.06, and the e-folding energy is >100 keV (with...... the "cutoffpl" model in XSPEC). The unabsorbed 3-79 keV flux is 3.96e-10 erg/cm2/s with a 0.8% error. At the Galactic center distance, this corresponds to an isotropic luminosity of 3e36 erg/s. The power spectrum consists of two components: a zero-centered Lorentzian peaking near 1 Hz and a power-law at lower...
Alibardi, L
2014-10-01
The localization of specific claw beta-proteins among the 40 total corneous beta-proteins present in the lizard Anolis carolinensis is not known. The hardness of claws likely depends on glycine-cysteine-rich beta-proteins content, as suggested by previous immunoblot studies. Previous studies have indicated that glycine-cysteine-rich corneous beta-proteins in addition to cysteine-rich alpha-keratins are present in the claw. In order to detect at the ultrastructural level the presence of claw-specific corneous proteins immunofluorescence and electron microscopy immunogold have been utilized. More intense immunoreactivity is obtained for the HgGC3 beta-protein while less intense immunolabeling is seen for HgGC10 and HgG5 beta-proteins and no labeling for the cysteine-rich beta-protein HgC1. The HgGC3 beta-protein appears the prevalent type present in the claw and its numerous cysteines likely form intermolecular disulphide bonds while glycine contributes hydrophobic properties to the corneous material. Other antibodies tagging the core-box and pre-core box regions of beta-proteins label with less intensity the corneous layer. The presence of cysteine-rich alpha-keratins with high homology to some human hair keratins in the dorsal part of the claw suggests that HgGC3-like beta-proteins form numerous disulphide bonds with the larger alpha-keratins giving rise to the hard corneous material of the claw. Copyright © 2014 Elsevier Ltd. All rights reserved.
Dash, S.; Kajita, T.; Okawa, M.; Saitoh, T.; Ikenaga, E.; Saini, N. L.; Katsufuji, T.; Mizokawa, T.
2018-04-01
We have studied a charge-orbital driven metal-insulator transition (MIT) in hollandite-type BaxTi8O16 +δ by means of hard x-ray photoemission spectroscopy (HAXPES). The Ti 2 p HAXPES indicates strong Ti3 +/Ti4 + charge fluctuation in the metallic phase above the MIT temperature. The metallic phase is characterized by a power-law spectral function near the Fermi level which would be a signature of bad metal with non-Drude polaronic behavior. The power-law spectral shape is associated with the large Seebeck coefficient of the metallic phase in BaxTi8O16 +δ .
Holanda, R. F. L.; Pereira, S. H.; Jain, Deepak
2017-11-01
In this work, by using strong gravitational lensing (SGL) observations along with Type Ia Supernovae (Union2.1) and gamma-ray burst data (GRBs), we propose a new method to study a possible redshift evolution of γ(z), the mass density power-law index of strong gravitational lensing systems. In this analysis, we assume the validity of cosmic distance duality relation and the flat universe. In order to explore the γ(z) behaviour, three different parametrizations are considered, namely: (P1) γ(zl) = γ0 + γ1zl; (P2) γ(zl) = γ0 + γ1zl/(1 + zl); and (P3) γ(zl) = γ0 + γ1ln (1 + zl), where zl corresponds to lens redshift. If γ0 = 2 and γ1 = 0, the singular isothermal sphere model is recovered. Our method is performed on SGL sub-samples defined by different lens redshifts and velocity dispersions. For the former case, the results are in full agreement with each other, while a 1σ tension between the sub-samples with low (≤250 km s-1) and high (>250 km s-1) velocity dispersions was obtained on the (γ0-γ1) plane. By considering the complete SGL sample, we obtain γ0 ≈ 2 and γ1 ≈ 0 within 1σ c.l. for all γ(z) parametrizations. However, we find the following best-fitting values of γ1: -0.085; -0.16; and -0.12 for P1, P2 and P3 parametrizations, respectively, suggesting a mild evolution for γ(z). By repeating the analysis with Type Ia Supernovae from Joint Light Analysis compilation, GRBs and SGL systems this mild evolution is reinforced.
Chen, Lin; Boone, John M.; Nosratieh, Anita; Abbey, Craig K.
2011-03-01
Digital mammography is the current standard for breast cancer screening, however breast tomosynthesis and breast CT (bCT) have been studied in clinical trials. At our institution, 30 women (BIRADS 4 and 5) underwent IRB-approved imaging by mammography, breast tomosynthesis, and bCT on the same day. Twenty three data sets were used for analysis. The 2D noise power spectrum (NPS) was computed and averaged for each data set. The NPS was computed for different slice thicknesses of dx × N, where dx ~ 0.3 mm and N=1-64, on the bCT data. Each 2D NPS was radially averaged, and the 1D data were fit using a power law function as proposed by Burgess: NPS(f) = αf-β. The value of β was determined over a range of frequencies corresponding to anatomical noise, for each patient and each modality. Averaged over the 30 women (26 for bCT, 28 for tomosynthesis, 28 for mammography), for mammography β=3.06 (0.25), for CC tomosynthesis β=2.91 (0.35), and for axial bCT β=1.72 (0.47). For sagittal bCT β=1.77 (0.36) and for coronal bCT, β=1.88 (0.45). The computation of β versus slice thickness on the coronal bCT data set led to β~1.7 for N=1, asymptotically reaching β ~ 3 for larger slice thickness. These results suggest that there is a fundamental difference in breast anatomic noise as characterized by β, between thin slices (<2 mm) and thicker slices. Tomosynthesis was found to have anatomic noise properties closer to mammography than breast CT, most likely due to the relatively thick slice sensitivity profile of tomosynthesis.
Temperature-dependent power-law analysis of capacitance-voltage for GaN-based pn junction
Wang, Chun An; Fu, Silie; Liu, Liu; Li, Junxian; Bao, Jiayi
2018-04-01
Capacitance-voltage (C-V) measurement is an effective method that has been widely used to study the electronic characteristics of the pn junction. In this paper, the C-V measurement is used to study the effect of the temperature on the structural type of the GaN-based pn junction. The C-2-V and C-3-V curves, combined with power-law index k, are used to determine the structural type of the GaN-based pn junction when the temperature is set at 25 °C, -50 °C, -100 °C, -150 °C, and -195 °C. Our experimental results show that the C-2-V curve is a clear linear relation, and the index k is 0.5 when the temperature is set at 25 °C and -50 °C. This shows an abrupt junction when the temperature ranges from 25 °C to -50 °C. When the temperature is dropped to -100 °C, the structural type of the pn junction begins to change and the index k becomes 0.45. When the temperature is decreased further to T = -150 °C and -195 °C, the index k becomes 0.30 and 0.28, respectively, corresponding to a non-abrupt and non-linear junction. Possible explanations of this phenomenon are: the low-temperature carrier freeze-out effect and the localized space charge region that is produced by crystal defects and interface states. The enhancement of the inhomogeneous and localized space charge region further affects the structural type of the pn junction in a low temperature environment.
Dias, W. S.; Bertrand, D.; Lyra, M. L.
2017-06-01
Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d >4 .
Dias, W S; Bertrand, D; Lyra, M L
2017-06-01
Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.
Directory of Open Access Journals (Sweden)
D. Srinivasacharya
2016-01-01
Full Text Available Mixed convection heat and mass transfer along a vertical plate embedded in a power-law fluid saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically.
International Nuclear Information System (INIS)
Lima, M.L.; Mignaco, J.A.
1985-01-01
It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt
International Nuclear Information System (INIS)
Lima, M.L.; Mignaco, J.A.
1985-01-01
It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt
Oldenburg, Amy L; Yu, Xiao; Gilliss, Thomas; Alabi, Oluwafemi; Taylor, Russell M; Troester, Melissa A
2015-10-20
The progression of breast cancer is known to be affected by stromal cells within the local microenvironment. Here we study the effect of stromal fibroblasts on the in-place motions (motility) of mammary epithelial cells within organoids in 3D co-culture, inferred from the speckle fluctuation spectrum using optical coherence tomography (OCT). In contrast to Brownian motion, mammary cell motions exhibit an inverse power-law fluctuation spectrum. We introduce two complementary metrics for quantifying fluctuation spectra: the power-law exponent and a novel definition of the motility amplitude, both of which are signal- and position-independent. We find that the power-law exponent and motility amplitude are positively ( p <0.001) and negatively ( p <0.01) correlated with the density of stromal cells in 3D co-culture, respectively. We also show how the hyperspectral data can be visualized using these metrics to observe heterogeneity within organoids. This constitutes a simple and powerful tool for detecting and imaging cellular functional changes with OCT.
Oldenburg, Amy L.; Yu, Xiao; Gilliss, Thomas; Alabi, Oluwafemi; Taylor, Russell M.; Troester, Melissa A.
2015-01-01
The progression of breast cancer is known to be affected by stromal cells within the local microenvironment. Here we study the effect of stromal fibroblasts on the in-place motions (motility) of mammary epithelial cells within organoids in 3D co-culture, inferred from the speckle fluctuation spectrum using optical coherence tomography (OCT). In contrast to Brownian motion, mammary cell motions exhibit an inverse power-law fluctuation spectrum. We introduce two complementary metrics for quantifying fluctuation spectra: the power-law exponent and a novel definition of the motility amplitude, both of which are signal- and position-independent. We find that the power-law exponent and motility amplitude are positively (p<0.001) and negatively (p<0.01) correlated with the density of stromal cells in 3D co-culture, respectively. We also show how the hyperspectral data can be visualized using these metrics to observe heterogeneity within organoids. This constitutes a simple and powerful tool for detecting and imaging cellular functional changes with OCT. PMID:26973862
Ashby, G. C., Jr.
1974-01-01
Experimental data have been obtained for two series of bodies at Mach 6 and Reynolds numbers, based on model length, from 1.4 million to 9.5 million. One series consisted of axisymmetric power-law bodies geometrically constrained for constant length and base diameter with values of the exponent n of 0.25, 0.5, 0.6, 0.667, 0.75, and 1.0. The other series consisted of positively and negatively cambered bodies of polygonal cross section, each having a constant longitudinal area distribution conforming to that required for minimizing zero-lift wave drag at hypersonic speeds under the geometric constraints of given length and volume. At the highest Reynolds number, the power-law body for minimum drag is blunter (exponent n lower) than predicted by inviscid theory (n approximately 0.6 instead of n = 0.667); however, the peak value of lift-drag ratio occurs at n = 0.667. Viscous effects were present on the bodies of polygonal cross section but were less pronounced than those on the power-law bodies. The trapezoidal bodies with maximum width at the bottom were found to have the highest maximum lift-drag ratio and the lowest mimimum drag.
Directory of Open Access Journals (Sweden)
Q. Cheng
2010-10-01
Full Text Available This contribution introduces a fractal filtering technique newly developed on the basis of a spectral energy density vs. area power-law model in the context of multifractal theory. It can be used to map anisotropic singularities of geochemical landscapes created from geochemical concentration values in various surface media such as soils, stream sediments, tills and water. A geochemical landscape can be converted into a Fourier domain in which the spectral energy density is plotted against the area (in wave number units, and the relationship between the spectrum energy density (S and the area (A enclosed by the above-threshold spectrum energy density can be fitted by power-law models. Mixed geochemical landscape patterns can be fitted with different S-A power-law models in the frequency domain. Fractal filters can be defined according to these different S-A models and used to decompose the geochemical patterns into components with different self-similarities. The fractal filtering method was applied to a geochemical dataset from 7,349 stream sediment samples collected from Gejiu mineral district, which is famous for its word-class tin and copper production. Anomalies in three different scales were decomposed from total values of the trace elements As, Sn, Cu, Zn, Pb, and Cd. These anomalies generally correspond to various geological features and geological processes such as sedimentary rocks, intrusions, fault intersections and mineralization.
Directory of Open Access Journals (Sweden)
Payam Hooshmand
2017-03-01
Full Text Available Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power law shear thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium are considered. The temperature dependent heat sources, Joule heating, and viscous heating are considered as the source terms in the energy balance. The non-dimensional boundary layer equations are solved numerically in terms of similarity variable. A parameter study on the Nusselt number, viscous components of entropy generation, and thermal components of entropy generation in fluid is performed as a function of thermal radiation parameter (0 to 2, Brinkman number (0 to 10, Prandtl number (0 to 10, Hartmann number (0 to 1, power law index (0 to 1, and heat source coefficient (0 to 0.1.
Sathyachandran, S.; Roy, D. P.; Boschetti, L.
2010-12-01
Spatially and temporally explicit mapping of the amount of biomass burned by fire is needed to estimate atmospheric emissions of green house gases and aerosols. The instantaneous Fire Radiative Power (FRP) [units: W] is retrieved at active fire detections from mid-infrared wavelength remotely sensed data and can be used to estimate the rate of biomass consumed. Temporal integration of FRP measurements over the duration of the fire provides the Fire Radiative Energy (FRE) [units: J] that has been shown to be linearly related to the total biomass burned [units: g]. However, FRE, and thus biomass burned retrieval, is sensitive to the satellite spatial and temporal sampling of FRP which can be sparse under cloudy conditions and with polar orbiting sensors such as MODIS. In this paper the FRE is derived in a new way as the product of the fire duration and the first moment of the FRP power law probability distribution. MODIS FRP data retrieved over savanna fires in Australia and deforestation fires in Brazil are shown to have power law distributions with different scaling parameters that are related to the fire energy in these two contrasting systems. The FRE derived burned biomass estimates computed using this new method are compared to estimates using the conventional temporal FRP integration method and with literature values. The results of the comparison suggest that the new method may provide more reliable burned biomass estimates under sparse satellite sampling conditions if the fire duration and the power law distribution parameters are characterized a priori.
High spectral resolution measurements of a solar flare hard X-ray burst
International Nuclear Information System (INIS)
Lin, R.P.; Schwartz, R.A.; NASA, Goddard Space Flight Center, Greenbelt, MD)
1987-01-01
Observations are reported of an intense solar flare hard X-ray burst on June 27, 1980, made with a balloon-borne array of liquid nitrogen-cooled Ge detector which provided unprecedented spectral resolution (no more than 1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 0.1-1 billion K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting about 3-15 sec, which have a hard spectrum and a break energy of 30-65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 kev to at least 100 keV through the event. The double power-law shape indicates that DC electric field acceleration, similar to that occurring in the earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. 39 references
Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles
Energy Technology Data Exchange (ETDEWEB)
Effenberger, Frederic; Costa, Fatima Rubio da; Petrosian, Vahé [Department of Physics and KIPAC, Stanford University, Stanford, CA 94305 (United States); Oka, Mitsuo; Saint-Hilaire, Pascal; Krucker, Säm [Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450 (United States); Liu, Wei [Bay Area Environmental Research Institute, 625 2nd Street, Suite 209, Petaluma, CA 94952 (United States); Glesener, Lindsay, E-mail: feffen@stanford.edu, E-mail: frubio@stanford.edu [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States)
2017-02-01
Flares close to the solar limb, where the footpoints are occulted, can reveal the spectrum and structure of the coronal looptop source in X-rays. We aim at studying the properties of the corresponding energetic electrons near their acceleration site, without footpoint contamination. To this end, a statistical study of partially occulted flares observed with Reuven Ramaty High-Energy Solar Spectroscopic Imager is presented here, covering a large part of solar cycles 23 and 24. We perform detailed spectra, imaging, and light curve analyses for 116 flares and include contextual observations from SDO and STEREO when available, providing further insights into flare emission that were previously not accessible. We find that most spectra are fitted well with a thermal component plus a broken power-law, non-thermal component. A thin-target kappa distribution model gives satisfactory fits after the addition of a thermal component. X-ray imaging reveals small spatial separation between the thermal and non-thermal components, except for a few flares with a richer coronal source structure. A comprehensive light curve analysis shows a very good correlation between the derivative of the soft X-ray flux (from GOES ) and the hard X-rays for a substantial number of flares, indicative of the Neupert effect. The results confirm that non-thermal particles are accelerated in the corona and estimated timescales support the validity of a thin-target scenario with similar magnitudes of thermal and non-thermal energy fluxes.
Directory of Open Access Journals (Sweden)
Chun-Kuei Su
2018-03-01
Full Text Available Nitric oxide (NO is a diffusible gas and has multifarious effects on both pre- and postsynaptic events. As a consequence of complex excitatory and inhibitory integrations, NO effects on neuronal activities are heterogeneous. Using in vitro preparations of neonatal rats that retain the splanchnic sympathetic nerves and the thoracic spinal cord as an experimental model, we report here that either enhancement or attenuation of NO production in the neonatal rat spinal cords could increase, decrease, or not change the spontaneous firing behaviors recorded from splanchnic sympathetic single fibers. To elucidate the mathematical features of NO-mediated heterogeneous responses, the ratios of changes in firing were plotted against their original firing rates. In log-log plots, a linear data distribution demonstrated that NO-mediated heterogeneity in sympathetic firing responses was well described by a power function. Selective antagonists were applied to test if glycinergic, GABAergic, glutamatergic, and cholinergic neurotransmission in the spinal cord are involved in NO-mediated power-law firing modulations (plFM. NO-mediated plFM diminished in the presence of mecamylamine (an open-channel blocker of nicotinic cholinergic receptors, indicating that endogenous nicotinic receptor activities were essential for plFM. Applications of strychnine (a glycine receptor blocker, gabazine (a GABAA receptor blocker, or kynurenate (a broad-spectrum ionotropic glutamate receptor blocker also caused plFM. However, strychnine- or kynurenate-induced plFM was diminished by L-NAME (an NO synthase inhibitor pretreatments, indicating that the involvements of glycine or ionotropic glutamate receptor activities in plFM were secondary to NO signaling. To recapitulate the arithmetic natures of the plFM, the plFM were simulated by firing changes in two components: a step increment and a fractional reduction of their basal firing activities. Ionotropic glutamate receptor
Su, Chun-Kuei; Chen, Yi-Yin; Ho, Chiu-Ming
2018-01-01
Nitric oxide (NO) is a diffusible gas and has multifarious effects on both pre- and postsynaptic events. As a consequence of complex excitatory and inhibitory integrations, NO effects on neuronal activities are heterogeneous. Using in vitro preparations of neonatal rats that retain the splanchnic sympathetic nerves and the thoracic spinal cord as an experimental model, we report here that either enhancement or attenuation of NO production in the neonatal rat spinal cords could increase, decrease, or not change the spontaneous firing behaviors recorded from splanchnic sympathetic single fibers. To elucidate the mathematical features of NO-mediated heterogeneous responses, the ratios of changes in firing were plotted against their original firing rates. In log-log plots, a linear data distribution demonstrated that NO-mediated heterogeneity in sympathetic firing responses was well described by a power function. Selective antagonists were applied to test if glycinergic, GABAergic, glutamatergic, and cholinergic neurotransmission in the spinal cord are involved in NO-mediated power-law firing modulations (plFM). NO-mediated plFM diminished in the presence of mecamylamine (an open-channel blocker of nicotinic cholinergic receptors), indicating that endogenous nicotinic receptor activities were essential for plFM. Applications of strychnine (a glycine receptor blocker), gabazine (a GABA A receptor blocker), or kynurenate (a broad-spectrum ionotropic glutamate receptor blocker) also caused plFM. However, strychnine- or kynurenate-induced plFM was diminished by L-NAME (an NO synthase inhibitor) pretreatments, indicating that the involvements of glycine or ionotropic glutamate receptor activities in plFM were secondary to NO signaling. To recapitulate the arithmetic natures of the plFM, the plFM were simulated by firing changes in two components: a step increment and a fractional reduction of their basal firing activities. Ionotropic glutamate receptor activities were found
Testan, Peter R.
1987-04-01
A number of Color Hard Copy (CHC) market drivers are currently indicating strong growth in the use of CHC technologies for the business graphics marketplace. These market drivers relate to product, software, color monitors and color copiers. The use of color in business graphics allows more information to be relayed than is normally the case in a monochrome format. The communicative powers of full-color computer generated output in the business graphics application area will continue to induce end users to desire and require color in their future applications. A number of color hard copy technologies will be utilized in the presentation graphics arena. Thermal transfer, ink jet, photographic and electrophotographic technologies are all expected to be utilized in the business graphics presentation application area in the future. Since the end of 1984, the availability of color application software packages has grown significantly. Sales revenue generated by business graphics software is expected to grow at a compound annual growth rate of just over 40 percent to 1990. Increased availability of packages to allow the integration of text and graphics is expected. Currently, the latest versions of page description languages such as Postscript, Interpress and DDL all support color output. The use of color monitors will also drive the demand for color hard copy in the business graphics market place. The availability of higher resolution screens is allowing color monitors to be easily used for both text and graphics applications in the office environment. During 1987, the sales of color monitors are expected to surpass the sales of monochrome monitors. Another major color hard copy market driver will be the color copier. In order to take advantage of the communications power of computer generated color output, multiple copies are required for distribution. Product introductions of a new generation of color copiers is now underway with additional introductions expected
Mir, Mehedi Faruk; Muktadir Rahman, Md.; Dwaipayan, Debnath; Sakhawat Hossain Himel, Md.
2016-04-01
Energy fluctuation of ideal Fermi gas trapped under generic power law potential U=\\sumi=1d ci \\vertxi/ai \\vert n_i has been calculated in arbitrary dimensions. Energy fluctuation is scrutinized further in the degenerate limit μ ≫ KBT with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can not only exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d = 3 but also can describe the outcome for any power law potential in arbitrary dimension.
Hardness variability in commercial technologies
International Nuclear Information System (INIS)
Shaneyfelt, M.R.; Winokur, P.S.; Meisenheimer, T.L.; Sexton, F.W.; Roeske, S.B.; Knoll, M.G.
1994-01-01
The radiation hardness of commercial Floating Gate 256K E 2 PROMs from a single diffusion lot was observed to vary between 5 to 25 krad(Si) when irradiated at a low dose rate of 64 mrad(Si)/s. Additional variations in E 2 PROM hardness were found to depend on bias condition and failure mode (i.e., inability to read or write the memory), as well as the foundry at which the part was manufactured. This variability is related to system requirements, and it is shown that hardness level and variability affect the allowable mode of operation for E 2 PROMs in space applications. The radiation hardness of commercial 1-Mbit CMOS SRAMs from Micron, Hitachi, and Sony irradiated at 147 rad(Si)/s was approximately 12, 13, and 19 krad(Si), respectively. These failure levels appear to be related to increases in leakage current during irradiation. Hardness of SRAMs from each manufacturer varied by less than 20%, but differences between manufacturers are significant. The Qualified Manufacturer's List approach to radiation hardness assurance is suggested as a way to reduce variability and to improve the hardness level of commercial technologies
Non-thermal Hard X-Ray Emission from Coma and Several Abell Clusters
International Nuclear Information System (INIS)
Correa, C
2004-01-01
We report results of hard X-Ray observations of the clusters Coma, Abell 496, Abell754, Abell 1060, Abell 1367, Abell2256 and Abell3558 using RXTE data from the NASA HEASARC public archive. Specifically we searched for clusters with hard x-ray emission that can be fitted by a power law because this would indicate that the cluster is a source of non-thermal emission. We are assuming the emission mechanism proposed by Vahk Petrosian where the inter cluster space contains clouds of relativistic electrons that by themselves create a magnetic field and emit radio synchrotron radiation. These relativistic electrons Inverse-Compton scatter Microwave Background photons up to hard x-ray energies. The clusters that were found to be sources of non-thermal hard x-rays are Coma, Abell496, Abell754 and Abell 1060
Standard test methods for rockwell hardness of metallic materials
American Society for Testing and Materials. Philadelphia
2008-01-01
1.1 These test methods cover the determination of the Rockwell hardness and the Rockwell superficial hardness of metallic materials by the Rockwell indentation hardness principle. This standard provides the requirements for Rockwell hardness machines and the procedures for performing Rockwell hardness tests. 1.2 This standard includes additional requirements in annexes: Verification of Rockwell Hardness Testing Machines Annex A1 Rockwell Hardness Standardizing Machines Annex A2 Standardization of Rockwell Indenters Annex A3 Standardization of Rockwell Hardness Test Blocks Annex A4 Guidelines for Determining the Minimum Thickness of a Test Piece Annex A5 Hardness Value Corrections When Testing on Convex Cylindrical Surfaces Annex A6 1.3 This standard includes nonmandatory information in appendixes which relates to the Rockwell hardness test. List of ASTM Standards Giving Hardness Values Corresponding to Tensile Strength Appendix X1 Examples of Procedures for Determining Rockwell Hardness Uncertainty Appendix X...
Standard test methods for rockwell hardness of metallic materials
American Society for Testing and Materials. Philadelphia
2011-01-01
1.1 These test methods cover the determination of the Rockwell hardness and the Rockwell superficial hardness of metallic materials by the Rockwell indentation hardness principle. This standard provides the requirements for Rockwell hardness machines and the procedures for performing Rockwell hardness tests. 1.2 This standard includes additional requirements in annexes: Verification of Rockwell Hardness Testing Machines Annex A1 Rockwell Hardness Standardizing Machines Annex A2 Standardization of Rockwell Indenters Annex A3 Standardization of Rockwell Hardness Test Blocks Annex A4 Guidelines for Determining the Minimum Thickness of a Test Piece Annex A5 Hardness Value Corrections When Testing on Convex Cylindrical Surfaces Annex A6 1.3 This standard includes nonmandatory information in appendixes which relates to the Rockwell hardness test. List of ASTM Standards Giving Hardness Values Corresponding to Tensile Strength Appendix X1 Examples of Procedures for Determining Rockwell Hardness Uncertainty Appendix X...
The XMM-SSC survey of hard-spectrum XMM-Newton sources - I. Optically bright sources
Page, M. J.; Lehmann, I.; Boller, Th.; Watson, M. G.; Dwelly, T.; Hess, S.; Matute, I.; Loaring, N. S.; Rosen, S.; Ziaeepour, H.; Schwope, A.; Lamer, G.; Carrera, F. J.; Tedds, J.; Della Ceca, R.; Severgnini, P.; McMahon, R. G.; Yuan, W.
2007-07-01
We present optical and X-ray data for a sample of serendipitous XMM-Newton sources that are selected to have 0.5-2 versus 2-4.5 keV X-ray hardness ratios which are harder than the X-ray background. The sources have 2-4.5 keV X-ray flux >=10-14 erg cm-2 s-1, and in this paper we examine a subsample of 42 optically bright (r 1044 erg s-1, and two of these sources have optical spectra which are dominated by narrow emission lines, that is, are type 2 QSOs. Only a small fraction of the sources (7/42) show broad optical emission lines, and all of these have NH 100 times the Galactic gas-to-dust ratio are rare in AGN absorbers (at most a few per cent of the population), and may be restricted to broad absorption line QSOs. Seven objects appear to have an additional soft X-ray component in addition to the heavily absorbed power law; all seven are narrow emission-line objects with z 4 per cent of broad-line AGN (BLAGN) have ionized absorbers that attenuate their soft X-ray flux by >50 per cent. In at least one of the X-ray-absorbed BLAGN in our sample the X-ray spectrum requires an ionized absorber, consistent with this picture.
DEFF Research Database (Denmark)
Mori, Kaya; Hailey, Charles J.; Krivonos, Roman
2015-01-01
self-consistently determined their intrinsic column density (similar to 10(23) cm(-2)), primary X-ray spectra (power-laws with Gamma similar to 2) and set a lower limit of the X-ray luminosity of Sgr A* flare illuminating the Sgr A clouds to L-X >= 10(38) erg s(-1). Above similar to 20 keV, hard X......We present the first sub-arcminute images of the Galactic Center above 10 keV, obtained with NuSTAR. NuSTAR resolves the hard X-ray source IGR J17456-2901 into non-thermal X-ray filaments, molecular clouds, point sources, and a previously unknown central component of hard X-ray emission (CHXE). Nu......STAR detects four non-thermal X-ray filaments, extending the detection of their power-law spectra with Gamma similar to 1.3-2.3 up to similar to 50 keV. A morphological and spectral study of the filaments suggests that their origin may be heterogeneous, where previous studies suggested a common origin in young...
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Gadadhar; Maitra, Sarit [Department of Mathematics, National Institute of Technology Durgapur, Durgapur (India)
2015-04-15
Sagdeev's pseudopotential method is used to study small as well as arbitrary amplitude dust acoustic solitons in a dusty plasma with kappa distributed electrons and ions with dust grains having power law size distribution. The existence of potential well solitons has been shown for suitable parametric region. The criterion for existence of soliton is derived in terms of upper and lower limit for Mach numbers. The numerical results show that the size distribution can affect the existence as well as the propagation characteristics of the dust acoustic solitons. The effect of kappa distribution is also highlighted.
Thermodynamic hardness and the maximum hardness principle.
Franco-Pérez, Marco; Gázquez, José L; Ayers, Paul W; Vela, Alberto
2017-08-21
An alternative definition of hardness (called the thermodynamic hardness) within the grand canonical ensemble formalism is proposed in terms of the partial derivative of the electronic chemical potential with respect to the thermodynamic chemical potential of the reservoir, keeping the temperature and the external potential constant. This temperature dependent definition may be interpreted as a measure of the propensity of a system to go through a charge transfer process when it interacts with other species, and thus it keeps the philosophy of the original definition. When the derivative is expressed in terms of the three-state ensemble model, in the regime of low temperatures and up to temperatures of chemical interest, one finds that for zero fractional charge, the thermodynamic hardness is proportional to T -1 (I-A), where I is the first ionization potential, A is the electron affinity, and T is the temperature. However, the thermodynamic hardness is nearly zero when the fractional charge is different from zero. Thus, through the present definition, one avoids the presence of the Dirac delta function. We show that the chemical hardness defined in this way provides meaningful and discernible information about the hardness properties of a chemical species exhibiting integer or a fractional average number of electrons, and this analysis allowed us to establish a link between the maximum possible value of the hardness here defined, with the minimum softness principle, showing that both principles are related to minimum fractional charge and maximum stability conditions.
Varotsos, C. A.; Efstathiou, M. N.
2018-03-01
In this paper we investigate the evolution of the energy emitted by CO2 and NO from the Earth's thermosphere on a global scale using both observational and empirically derived data. In the beginning, we analyze the daily power observations of CO2 and NO received from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) equipment on the NASA Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite for the entire period 2002-2016. We then perform the same analysis on the empirical daily power emitted by CO2 and NO that were derived recently from the infrared energy budget of the thermosphere during 1947-2016. The tool used for the analysis of the observational and empirical datasets is the detrended fluctuation analysis, in order to investigate whether the power emitted by CO2 and by NO from the thermosphere exhibits power-law behavior. The results obtained from both observational and empirical data do not support the establishment of the power-law behavior. This conclusion reveals that the empirically derived data are characterized by the same intrinsic properties as those of the observational ones, thus enhancing the validity of their reliability.
Bhattacharjee, Saikat; Mondal, Mrinmoy; De, Sirshendu
2017-05-01
Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye-Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential -73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Bigger, J. T. Jr; Steinman, R. C.; Rolnitzky, L. M.; Fleiss, J. L.; Albrecht, P.; Cohen, R. J.
1996-01-01
BACKGROUND. The purposes of the present study were (1) to establish normal values for the regression of log(power) on log(frequency) for, RR-interval fluctuations in healthy middle-aged persons, (2) to determine the effects of myocardial infarction on the regression of log(power) on log(frequency), (3) to determine the effect of cardiac denervation on the regression of log(power) on log(frequency), and (4) to assess the ability of power law regression parameters to predict death after myocardial infarction. METHODS AND RESULTS. We studied three groups: (1) 715 patients with recent myocardial infarction; (2) 274 healthy persons age and sex matched to the infarct sample; and (3) 19 patients with heart transplants. Twenty-four-hour RR-interval power spectra were computed using fast Fourier transforms and log(power) was regressed on log(frequency) between 10(-4) and 10(-2) Hz. There was a power law relation between log(power) and log(frequency). That is, the function described a descending straight line that had a slope of approximately -1 in healthy subjects. For the myocardial infarction group, the regression line for log(power) on log(frequency) was shifted downward and had a steeper negative slope (-1.15). The transplant (denervated) group showed a larger downward shift in the regression line and a much steeper negative slope (-2.08). The correlation between traditional power spectral bands and slope was weak, and that with log(power) at 10(-4) Hz was only moderate. Slope and log(power) at 10(-4) Hz were used to predict mortality and were compared with the predictive value of traditional power spectral bands. Slope and log(power) at 10(-4) Hz were excellent predictors of all-cause mortality or arrhythmic death. To optimize the prediction of death, we calculated a log(power) intercept that was uncorrelated with the slope of the power law regression line. We found that the combination of slope and zero-correlation log(power) was an outstanding predictor, with a
Design of grazing-incidence multilayer supermirrors for hard-X-ray reflectors
DEFF Research Database (Denmark)
Joensen, K. D.; Voutov, P.; Szentgyorgyi, A.
1995-01-01
-X-ray reflector and a hard-X-ray telescope) shows that an improved performance can be obtained. A multilayer whose bilayer thicknesses are given by a power law expression is found to provide the best solution; however, it is only slightly better than some of the adapted neutron designs......Extremely broadband grazing-incidence multilayers for hard-X-ray reflection can be obtained by a gradual change of the layer thicknesses down through the structure. Existing approaches for designing similar neutron optics, called supermirrors, are shown to provide respectable performance when...... applied to X-ray multilayers. However, none of these approaches consider the effects of imperfect layer interfaces and absorption in the overlying layers. Adaptations of neutron designs that take these effects into account are presented, and a thorough analysis of two specific applications (a single hard...
Free energy landscape and cooperatively rearranging region in a hard sphere glass
Yoshidome, Takashi; Yoshimori, Akira; Odagaki, Takashi
2007-08-01
Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density. Analyzing the relaxation process in the CRR, we also find that the string motion is the elementary process for the structural relaxation, which leads to the natural definition of the simultaneously rearranging region as the particles displaced in the string motion.
Energy Technology Data Exchange (ETDEWEB)
Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.; Clifton Johnson, L.; Beerman, Lori C.; Williams, Benjamin F. [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States); Hogg, David W.; Foreman-Mackey, Daniel T. [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Rix, Hans-Walter; Gouliermis, Dimitrios [Max Planck Institute for Astronomy, Koenigstuhl 17, D-69117 Heidelberg (Germany); Dolphin, Andrew E. [Raytheon Company, 1151 East Hermans Road, Tucson, AZ 85756 (United States); Lang, Dustin [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Bell, Eric F. [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States); Gordon, Karl D.; Kalirai, Jason S. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Skillman, Evan D., E-mail: dweisz@astro.washington.edu [Minnesota Institute for Astrophysics, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States)
2013-01-10
We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the
International Nuclear Information System (INIS)
Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.; Clifton Johnson, L.; Beerman, Lori C.; Williams, Benjamin F.; Hogg, David W.; Foreman-Mackey, Daniel T.; Rix, Hans-Walter; Gouliermis, Dimitrios; Dolphin, Andrew E.; Lang, Dustin; Bell, Eric F.; Gordon, Karl D.; Kalirai, Jason S.; Skillman, Evan D.
2013-01-01
We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M ∼> 1 M ☉ ). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, α, are unbiased and that the uncertainty, Δα, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on α, and provide an analytic approximation for Δα as a function of the observed number of stars and mass range. Comparison with literature studies shows that ∼3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield (α) = 2.46, with a 1σ dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF
Pines, V.; Zlatkowski, M.; Chait, A.
1990-01-01
The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.
Ashby, G. C., Jr.; Harris, J. E.
1974-01-01
Wave and skin-friction drag have been numerically calculated for a series of power-law bodies at a Mach number of 6 and Reynolds numbers, based on body length, from 1.5 million to 9.5 million. Pressure distributions were computed on the nose by the inverse method and on the body by the method of characteristics. These pressure distributions and the measured locations of boundary-layer transition were used in a nonsimilar-boundary-layer program to determine viscous effects. A coupled iterative approach between the boundary-layer and pressure-distribution programs was used to account for boundary-layer displacement-thickness effects. The calculated-drag coefficients compared well with previously obtained experimental data.
Olanrewaju, P. O.; Fenuga, O. J.; Gbadeyan, J. A.; Okedayo, T. G.
2013-01-01
In this paper, the influence of thermal and thermo diffusion on convection heat and mass transfer in an electrically conducting power law flow over a heated porous plate in the presence of magnetic field has been considered. The similarity solution is used to transform the system of partial differential equations into a boundary value problem of coupled ordinary differential equations. Runge Kutta of sixth order has been used along with a shooting method for better accuracy. The results were presented as velocity, temperature, and concentration fields for pseudoplastic and dilatant fluids for different values of the embedded flow parameters. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interests are significantly influenced by these parameters.
Bahauddin, Shah Mohammad; Mehedi Faruk, Mir
2016-09-01
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.