Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
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.
Optical monitoring for power law fluids during spin coating.
Jardim, P L G; Michels, A F; Horowitz, F
2012-01-30
Optical monitoring is applied, in situ and in real time, to non-newtonian, power law fluids in the spin coating process. An analytical exact solution is presented for thickness evolution that well fits to most measurement data. As result, typical rheological parameters are obtained for several CMC (carboximetilcelullose) concentrations and rotation speeds. Optical monitoring thus precisely indicates applicability of the model to power law fluids under spin coating.
MHD micropumping of power-law fluids: A numerical solution
NASA Astrophysics Data System (ADS)
Moghaddam, Saied
2013-02-01
The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.
Relaxation Dynamics of Non-Power-Law Fluids
NASA Astrophysics Data System (ADS)
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong
2013-12-01
The relaxation of non-Newtonian liquids with non-power-law rheology on partially wetted surfaces is rarely investigated. This study assesses the relaxation behavior of 14 partial wetting systems with non-power-law fluids by sessile drop method. These systems are two carboxymethylcellulose sodium solutions on two kinds of slides, cover glass, and silicon wafer surfaces; three polyethylene glycol (PEG400) + silica nanoparticle suspensions on polymethyl methacrylate and polystyrene surfaces. The dynamic contact angle and moving velocity of contact line relationship data for relaxation drops of the 14 tested systems demonstrate a power-law fluid-like behavior, and the equivalent power exponent for a certain fluid on different solid substrates are uniform. By analyzing the relationship between the equivalent power exponent and shear rate, it is proposed that a fluid regime with shear rates of a few tens of s controls relaxation dynamics.
Electrokinetically modulated peristaltic transport of power-law fluids.
Goswami, Prakash; Chakraborty, Jeevanjyoti; Bandopadhyay, Aditya; Chakraborty, Suman
2016-01-01
The electrokinetically modulated peristaltic transport of power-law fluids through a narrow confinement in the form of a deformable tube is investigated. The fluid is considered to be divided into two regions - a non-Newtonian core region (described by the power-law behavior) which is surrounded by a thin wall-adhering layer of Newtonian fluid. This division mimics the occurrence of a wall-adjacent cell-free skimming layer in blood samples typically handled in microfluidic transport. The pumping characteristics and the trapping of the fluid bolus are studied by considering the effect of fluid viscosities, power-law index and electroosmosis. It is found that the zero-flow pressure rise is strongly dependent on the relative viscosity ratio of the near-wall depleted fluid and the core fluid as well as on the power-law index. The effect of electroosmosis on the pressure rise is strongly manifested at lower occlusion values, thereby indicating its importance in transport modulation for weakly peristaltic flow. It is also established that the phenomenon of trapping may be controlled on-the-fly by tuning the magnitude of the electric field: the trapping vanishes as the magnitude of the electric field is increased. Similarly, the phenomenon of reflux is shown to disappear due to the action of the applied electric field. These findings may be applied for the modulation of pumping in bio-physical environments by means of external electric fields.
Coalescence of Drops of a Power-law Fluid
NASA Astrophysics Data System (ADS)
Kamat, Pritish; Thete, Sumeet; Basaran, Osman
2014-11-01
Drop coalescence is crucial in a host of industrial, household, and natural processes that involve dispersions. Coalescence is a rate-controlling process in breaking emulsions and strongly influences drop-size-distributions in sprays. In a continuum approach, coalescence begins by the formation of a microscopic, non-slender bridge connecting the two drops. Indefinitely large axial curvature at the neck results in local lowering of pressure that drives fluid from the bulk of the drops toward the neck, thereby causing the bridge radius r (t) and height z (t) to increase in time t. The coalescence of Newtonian drops in air has heretofore been thoroughly studied. Here, we extend these earlier studies by analyzing the coalescence of drops of power-law fluids because many fluids encountered in real applications, including cosmetic creams, shampoos, grease, and paint, exhibit power-law (deformation-rate thinning) rheology. On account of the non-slender geometry of the liquid bridge connecting the two drops (z << r) , we analyze the resulting free surface flow problem by numerical simulation. Among other results, we present and discuss the nature of flows and scaling behaviors for r and z as functions of the initial viscosity and power-law index (0 < n <= 1) .
Spreading of completely wetting, non-Newtonian fluids with non-power-law rheology.
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong; Su, Ay
2010-08-01
Spreading non-Newtonian liquids with non-power-law rheology on completely wetting surfaces are seldom investigated. This study assessed the wetting behavior of polydimethylsiloxane (PDMS), a Newtonian fluid, two carboxymethylcellulose (CMC) sodium solutions, a PDMS+2%w/w silica nanoparticle suspension and three polyethylene glycol (PEG400)+5-10%w/w silica nanoparticle suspensions (non-power-law fluids) on a mica surface. The theta(D)-U and R-t data for spreading drops of the six tested, non-power-law fluids can be described by power-law wetting models. We propose that this behavior is attributable to a uniform shear rate (a few tens to a few hundreds of s(-1)) distributed over the thin-film regime that controls spreading dynamics. Estimated film thickness was below the resolution of an optical microscope for direct observation. Approximating a general non-Newtonian fluid spreading as a power-law fluid greatly simplifies theoretical analysis and data interpretation.
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.
A generalization of the power law distribution with nonlinear exponent
NASA Astrophysics Data System (ADS)
Prieto, Faustino; Sarabia, José María
2017-01-01
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts
NASA Astrophysics Data System (ADS)
Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.
The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.
General 2.5 power law of metallic glasses
Zeng, Qiaoshi; Lin, Yu; Liu, Yijin; Zeng, Zhidan; Shi, Crystal Y.; Zhang, Bo; Lou, Hongbo; Sinogeikin, Stanislav V.; Kono, Yoshio; Kenney-Benson, Curtis; Park, Changyong; Yang, Wenge; Wang, Weihua; Sheng, Hongwei; Mao, Ho-kwang; Mao, Wendy L.
2016-01-01
Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its “disordered” structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous “composition” change of 4f-localized “big Ce” to 4f-itinerant “small Ce,” indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs. PMID:26831105
Interception efficiency in flow of power-law fluids past confined porous bodies
NASA Astrophysics Data System (ADS)
Shahsavari, Setareh; McKinley, Gareth
2014-11-01
Understanding the flow of power-law fluids through porous media is important for a wide range of filtration and sedimentation processes. In this study, the mobility of power-law fluids through porous media is investigated numerically and we use parametric studies to systematically understand the individual roles of geometrical characteristics, rheological properties as well as flow conditions. In addition, an analytical solution is presented that can be used as a modified Darcy law for generalized Newtonian fluids. Building on this modified Darcy law, the incompressible laminar flow of power-law and Carreau fluids past a confined porous body is modeled numerically. From the simulations we calculate the flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector. Finally, the interception efficiency of power-law fluids are compared with the case of a Newtonian fluid. The focus of this work is principally for flow of inelastic fluids in fibrous media; however, the methodology can also be extended to other porous media.
Passive mechanical behavior of human neutrophils: power-law fluid.
Tsai, M A; Frank, R S; Waugh, R E
1993-01-01
= 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid. Images FIGURE 1 FIGURE 4 PMID:8298037
Mobility of power-law and Carreau fluids through fibrous media.
Shahsavari, Setareh; McKinley, Gareth H
2015-12-01
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
Vertical-channel free convection with a power-law fluid
Irvine, T.F. Jr.; Wu, K.C.; Schneider, W.J.
1982-01-01
A finite-difference solution is presented of the velocity and temperature fields for the flow of an Ostwald-de-Waele (power law) fluid between two vertical isothermal parallel plates under the influence of free convection. Two quantities are of particular interest: the total heat transferred from the plates and the average velocity between the plates. Although these quantities can be presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers, there is an important difference compared to the similar problem involving Newtonian fluids. In the present case, the generalized Prandtl number is not a fluid property but contains a geometric factor and thus the geometry of the system must be specified before the Prandtl number is fixed. The results and the manner in which they can be used are illustrated by a numerical example.
Hydrodynamics of Newtonian and power-law fluids in microchannel with superhydrophobic wall
NASA Astrophysics Data System (ADS)
Vagner, S. A.; Patlazhan, S. A.
2016-11-01
The flow peculiarities of the Newtonian and Carreau-Yasuda power-law fluids in a microchannel with the striped superhydrophobic wall is studied numerically. The driving forces leading to deviation of streamlines from the channel axis are analyzed.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock
NASA Astrophysics Data System (ADS)
Fareo, A. G.; Mason, D. P.
2016-06-01
Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.
Contracting bubbles in Hele-Shaw cells with a power-law fluid
NASA Astrophysics Data System (ADS)
McCue, Scott W.; King, John R.
2011-02-01
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.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows
NASA Astrophysics Data System (ADS)
Anbarlooei, H. R.; Cruz, D. O. A.; Ramos, F.; Silva Freire, A. P.
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
Finite and Infinite Width Stokes Layers in a Power-Law Fluid
NASA Astrophysics Data System (ADS)
Wilson, Stephen; Pritchard, David; McArdle, Catriona
2011-11-01
Self-similar solutions for the oscillatory boundary layer (the ``Stokes layer'') in a semi-infinite power-law fluid bounded by an oscillating wall (the so-called Stokes problem) are obtained and analysed. These semi-analytical solutions differ qualitatively from the classical solution for a Newtonian fluid, both in the non-sinusoidal form of the velocity oscillations and in the manner at which their amplitude decays with distance from the wall. In particular, for shear-thickening fluids the velocity reaches zero at a finite distance from the wall, and for shear-thinning fluids it decays algebraically with distance, in contrast to the exponential decay for a Newtonian fluid. We demonstrate numerically that these self-similar solutions provide a good approximation to the flow driven by a sinusoidally oscillating wall. Further details can be found in the recent paper by D. Pritchard, C. R. McArdle and S. K. Wilson entitled ``The Stokes boundary layer for a power-law fluid,'' in Journal of Non-Newtonian Fluid Mechanics 166, 745-753 (2011).
Viscous-elastic dynamics of power-law fluids within an elastic cylinder
NASA Astrophysics Data System (ADS)
Gat, Amir; Boyko, Evgeniy; Bercovici, Moran
2016-11-01
We study the fluid-structure interaction dynamics of non-Newtonian flow through a slender linearly elastic cylinder at the creeping flow regime. Specifically, considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a non-homogeneous p-Laplacian equation governing the viscous-elastic dynamics. We obtain exact solutions for the pressure and deformation fields for various initial and boundary conditions, for both shear thinning and shear thickening fluids. In particular, impulse or a step in inlet pressure yield self-similar solutions, which exhibit a compactly supported propagation front solely for shear thinning fluids. Applying asymptotic expansions, we provide approximations for weakly non-Newtonian behavior showing good agreement with the exact solutions sufficiently far from the front.
Forces acting on a stationary sphere in power-law fluid flow near the wall
NASA Astrophysics Data System (ADS)
Bocharov, O. B.; Kushnir, D. Yu.
2016-01-01
The analysis and evaluation of the forces acting on the particle in a linear shear flow of power-law fluid (PLF) in the presence of the wall were performed. Using the results of a series of computations for a model problem with a spherical particle near a flat wall in the Reynolds number range of 0-200 and the distance to the wall from 0 to 20 particle diameters, the correlation formulas for calculating the coefficients of drag force and lift force were obtained. Special attention was paid to the behavior of the forces acting on the particle approaching the wall.
Spin-coating process evolution and reproducibility for power-law fluids.
Jardim, P L G; Michels, A F; Horowitz, F
2014-03-20
A distinct development of an exact analytical solution for power-law fluids during the spin-coating process is presented for temporal and spatial thickness evolution, after steady state conditions are attained. This solution leads to the definition of a characteristic time, related to the memory of the initial thickness profile. Previously obtained experimental data, for several rotation speeds and carboxymetilcellulose concentrations in water, are quantitatively analyzed through the evaluation of their characteristic times and compared with theoretical predictions, thus allowing better understanding of thickness profile evolution and of process reproducibility.
NASA Astrophysics Data System (ADS)
Jiao, Chengru; Zheng, Liancun; Ma, Lianxi
2015-08-01
This paper studies the magnetohydrodynamic (MHD) thermosolutal Marangoni convection heat and mass transfer of power-law fluids driven by a power law temperature and a power law concentration which is assumed that the surface tension varies linearly with both the temperature and concentration. Heat and mass transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection-diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient and the mass diffusion depends non-linearly on both the concentration and the concentration gradient with modified Fourier heat conduction for power law fluid. The governing equations are reduced to nonlinear ordinary differential equations by using suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM). The transport characteristics of velocity, temperature and concentration fields are analyzed in detail.
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. PMID:27057132
Inertial migration of elastic particles in a pressure-driven power-law fluid
NASA Astrophysics Data System (ADS)
Bowie, Samuel; Alexeev, Alexander
2016-11-01
Using three-dimensional computer simulations, we study the cross-stream migration of deformable particles in a channel filled with a non-Newtonian fluid driven by a pressure gradient. Our numerical approach integrates lattice Boltzmann method and lattice spring method in order to model fluid structural interactions of the elastic particle and the surrounding power fluid in the channel. The particles are modeled as elastic shells filled with a viscous fluid that are initially spherical. We focus on the regimes where the inertial effects cannot be neglected and cause cross-stream drift of particles. We probe the flow with different power law indexes including both the shear thickening and thinning fluids. We also examine migration of particles of with different elasticity and relative size. To isolate the non-Newtonian effects on particle migration, we compare the results with the inertial migration results found in the case where the channel is filled with a simple Newtonian fluid. The results can be useful for applications requiring high throughput separation, sorting, and focusing of both synthetic particles and biological cells in microfluidic devices. Financial support provided by National Science Foundation (NSF) Grant No. CMMI1538161.
Lee, S.R.; Irvine, T.F. Jr.; Greene, G.A.
1998-04-01
An implicit finite difference method was applied to analyze laminar natural convection in a vertical channel with a modified power law fluid. This fluid model was chosen because it describes the viscous properties of a pseudoplastic fluid over the entire shear rate range likely to be found in natural convection flows since it covers the shear rate range from Newtonian through transition to simple power law behavior. In addition, a dimensionless similarity parameter is identified which specifies in which of the three regions a particular system is operating. The results for the average channel velocity and average Nusselt number in the asymptotic Newtonian and power law regions are compared with numerical data in the literature. Also, graphical results are presented for the velocity and temperature fields and entrance lengths. The results of average channel velocity and Nusselt number are given in the three regions including developing and fully developed flows. As an example, a pseudoplastic fluid (carboxymethyl cellulose) was chosen to compare the different results of average channel velocity and Nusselt number between a modified power law fluid and the conventional power law model. The results show, depending upon the operating conditions, that if the correct model is not used, gross errors can result.
Propagation of Gravity Currents of non-Newtonian Power-Law Fluids in Porous Media
NASA Astrophysics Data System (ADS)
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.
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.
Brey, J Javier; Ruiz-Montero, M J
2015-01-01
The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power-law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power-law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored.
Sliding friction in the hydrodynamic lubrication regime for a power-law fluid
NASA Astrophysics Data System (ADS)
Warren, P. B.
2017-02-01
A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning regime is mechanically unstable if the power-law index n < 1/2, where n is the exponent that relates the shear stress to the shear rate. Consequently the Stribeck (friction) curve should be discontinuous, with possible hysteresis. Further analysis suggests that normal stress and flow transience (stress overshoot) do not destroy this basic picture, although they may provide stabilising mechanisms at higher shear rates. Extensional viscosity is also expected to be insignificant unless the Trouton ratio is large. A possible application to shear thickening in non-Brownian particulate suspensions is indicated.
Power-law rheology and flow behavior of low-invasion coring fluids
McGuire, P.L.
1981-08-01
An improved pressure coring system has been developed in which an extremely viscous polymer mud is extruded by the core and is used to seal and protect the core from flushing by drilling fluids. The polymer mud must be extremely viscous to minimize invasion, yet must be extruded through a long, narrow annular gap with a minimum of pressure buildup. A highly non-Newtonian shear-thinning polymer is utilized in the low invasion coring fluid. This paper describes the measurement and modeling of non-Newtonian rheology from rotary viscometer data in detail since the simplified equations which are generally used with these instruments can be grossly in error. The development of both an approximate analytical solution and an exact numerical solution of the non-Newtonian extrusion process is presented. These solutions were used to optimize the non-Newtonian rheology of the low-invasion fluid which will be used in actual coring operations.
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.
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.
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
NASA Astrophysics Data System (ADS)
Rabbi, Khan Md.; Rakib, Tawfiqur; Das, Sourav; Mojumder, Satyajit; Saha, Sourav
2016-07-01
This paper demonstrates magneto-hydrodynamic (MHD) mixed convection flow through a channel with a rectangular obstacle at the entrance region using non-Newtonian power law fluid. The obstacle is kept at uniformly high temperature whereas the inlet and top wall of the channel are maintained at a temperature lower than obstacle temperature. Poiseuille flow is implemented as the inlet velocity boundary condition. Grid independency test and code validation are performed to justify the computational accuracy before solving the present problem. Galerkin weighted residual method has been appointed to solve the continuity, momentum and energy equations. The problem has been solved for wide range of pertinent parameters like Richardson number (Ri = 0.1 - 10) at a constant Reynolds number (Re = 100), Hartmann number (Ha = 0 - 100), power index (n = 0.6 - 1.6). The flow and thermal field have been thoroughly discussed through streamline and isothermal lines respectively. The heat transfer performance of the given study has been illustrated by average Nusselt number plots. It is observed that increment of Hartmann number (Ha) tends to decrease the heat transfer rate up to a critical value (Ha = 20) and then let increase the heat transfer performance. Thus maximum heat transfer rate has been recorded for higher Hartmann number and Rayleigh number in case of pseudo-plastic (n = 0.6) non-Newtonian fluid flow.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Daboul, Jamil
1995-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
NASA Astrophysics Data System (ADS)
Caputi, K. I.
2013-05-01
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 galaxies with S ν(24 μm)>80 μJy and spectroscopic redshifts z spec > 1 in the Chandra Deep Field South, for which I study the rest-frame UV/optical/near-IR spectral energy distributions (SEDs), after subtracting a hot-dust, PL component with three possible spectral indices α = 1.3, 2.0, and 3.0. I obtain that 35% of these 24 μm sources are power-law composite galaxies (PLCGs), which I define as those galaxies for which the SED fitting with stellar templates, without any previous PL subtraction, can be rejected with >2σ confidence. Subtracting the PL component from the PLCG SEDs produces stellar mass correction factors <1.5 in >80% of cases. The PLCG incidence is especially high (47%) at 1.0 < z < 1.5. To unveil which PLCGs host AGNs, I conduct a combined analysis of 4 Ms X-ray data, galaxy morphologies, and a graybody modeling of the hot dust. I find that (1) 77% of all the X-ray AGNs in my 24 μm sample at 1.0 < z < 1.5 are recognized by the PLCG criterion; (2) PLCGs with α = 1.3 or 2.0 have regular morphologies and T dust >~ 1000 K, indicating nuclear activity. Instead, PLCGs with α = 3.0 are characterized by disturbed galaxy dynamics, and a hot interstellar medium can explain their dust temperatures T dust ~ 700-800 K. Overall, my results indicate that the fraction of AGNs among 24 μm sources is between ~30% and 52% at 1.0 < z < 1.5.
Patil, A.G.
2000-02-01
Results of an experimental investigation of heat transfer and flow friction of a generalized power-law fluid in tape generated swirl flow inside a 25.0 mm i.d. circular tube, are presented. In order to reduce excessive pressure drops associated with full width twisted tapes, with less corresponding reduction in heat transfer coefficients, reduced width twisted tapes of widths ranging from 11.0 to 23.8 mm, which are lower than the tube inside diameter are used. Reduced width twisted tape inserts give 18%--56% lower isothermal friction factors than the full width tapes. Uniform wall temperature Nusselt numbers decrease only slightly by 5%--25%, for tape widths of 19.7 and 11.0 mm, respectively. Based on the constant pumping power criterion, the tapes of width 19.7 mm perform more or less like full width tapes. Correlations are presented for isothermal and heating friction factors and Nusselt numbers (under uniform wall temperature condition) for a fully developed laminar swirl flow, which are applicable to full width as well as reduced width twisted tapes, using a modified twist ratio as pitch to width ratio of the tape. The reduced width tapes offer 20%--50% savings in the tape material as compared to the full width tapes.
NASA Astrophysics Data System (ADS)
Kishan, N.; Shashidar Reddy, B.
2013-06-01
The problem of a magneto-hydro dynamic flow and heat transfer to a non-Newtonian power-law fluid flow past a continuously moving flat porous plate in the presence of sucion/injection with heat flux by taking into consideration the viscous dissipation is analysed. The non-linear partial differential equations governing the flow and heat transfer are transformed into non-linear ordinary differential equations using appropriate transformations and then solved numerically by an implicit finite difference scheme. The solution is found to be dependent on various governing parameters including the magnetic field parameter M, power-law index n, suction/injection parameter ƒw, Prandtl number Pr and Eckert number Ec. A systematical study is carried out to illustrate the effects of these major parameters on the velocity profiles, temperature profile, skin friction coefficient and rate of heat transfer and the local Nusslet number.
Digilov, Rafael M
2008-12-02
The impact of non-Newtonian behavior and the dynamic contact angle on the rise dynamics of a power law liquid in a vertical capillary is studied theoretically and experimentally for quasi-steady-state flow. An analytical solution for the time evolution of the meniscus height is obtained in terms of a Gaussian hypergeometric function, which in the case of a Newtonian liquid reduces to the Lucas-Washburn equation modified by the dynamic contact angle correction. The validity of the solution is checked against experimental data on the rise dynamics of a shear-thinning cmc solution in a glass microcapillary, and excellent agreement is found.
Dhar, Jayabrata; Ghosh, Uddipta; Chakraborty, Suman
2014-03-01
We study the coupled effect of electrokinetic phenomena and fluid rheology in altering the induced streaming potential in narrow fluidic confinements, which is manifested by establishing a time periodic pressure-driven flow in presence of electrical double layer phenomenon. However, in sharp contrast with reported literature, we take into account nonelectrostatic ion-ion interactions toward estimating the same in addition to electrostatic interactions and steric effects. We employ power law based rheological model for estimating the induced streaming potential. We bring out an intricate interaction between nonelectrostatic interactions and fluid rheology on the concerned electrokinetic phenomena, bearing immense consequences toward designing of integrated lab-on-a-chip-based microdevices and nanodevices.
NASA Astrophysics Data System (ADS)
Shit, G. C.; Mondal, A.; Sinha, A.; Kundu, P. K.
2016-11-01
A mathematical model has been developed for studying the electro-osmotic flow and heat transfer of bio-fluids in a micro-channel in the presence of Joule heating effects. The flow of bio-fluid is governed by the non-Newtonian power-law fluid model. The effects of thermal radiation and velocity slip condition have been examined in the case of hydrophobic channel. The Poisson-Boltzmann equation governing the electrical double layer field and a body force generated by the applied electric potential field are taken into consideration. The results presented here pertain to the case where the height of the channel is much greater than the thickness of electrical double layer comprising the Stern and diffuse layers. The expressions for flow characteristics such as velocity, temperature, shear stress and Nusselt number have been derived analytically under the purview of the present model. The results estimated on the basis of the data available in the existing scientific literatures are presented graphically. The effects of thermal radiation have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding the heat transfer in micro-channel in the presence of electric potential. The dimensionless Joule heating parameter has a reducing impact on Nusselt number for both pseudo-plastic and dilatant fluids, nevertheless its impact on Nusselt number is more pronounced for dilatant fluid. Furthermore, the effect of viscous dissipation has a significant role in controlling heat transfer and should not be neglected.
NASA Astrophysics Data System (ADS)
Babu, D. Harish; Narayana, P. V. Satya
2016-08-01
An analysis has been carried out to study the Joule heating effect on MHD heat transfer of an incompressible Jeffrey fluid due to a stretching porous sheet with power law heat flux and heat source. A constant magnetic field is applied normal to the stretching surface. The basic governing equations are reduced into the coupled nonlinear ordinary differential equations by using similarity transformations. The resulting equations are then solved numerically by shooting method with fourth order Runge-Kutta scheme. The effects of various physical parameters entering into the problem on dimensionless velocity and temperature distribution are discussed through graphs and tables. The results reveal that the momentum and thermal boundary layer thickness are significantly influenced by Deborah number (β), ratio of relaxation and retardation times parameter (λ), heat generation parameter (β*), Eckert number (Ec) and magnetic field parameter (M). A comparison with the previously published works shows excellent agreement.
NASA Astrophysics Data System (ADS)
Khan, M.; Munir, A.; Shahzad, A.; Shah, A.
2015-03-01
A steady boundary layer flow and heat transfer over a radially stretching isothermal porous sheet is analyzed. Stretching is assumed to follow a radial power law, and the fluid is electrically conducting in the presence of a transverse magnetic field with a very small magnetic Reynolds number. The governing nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations by using appropriate similarity transformations, which are solved analytically by the homotopy analysis method (HAM) and numerically by employing the shooting method with the adaptive Runge-Kutta method and Broyden's method in the domain [0,∞). Analytical expressions for the velocity and temperature fields are derived. The influence of pertinent parameters on the velocity and temperature profiles is discussed in detail. The skin friction coefficient and the local Nusselt number are calculated as functions of several influential parameters. The results predicted by both methods are demonstrated to be in excellent agreement. Moreover, HAM results for a particular problem are also compared with exact solutions.
NASA Astrophysics Data System (ADS)
Bae, Hyeong-Ohk; Wolf, Jörg
2017-02-01
We prove the local regularity of a weak solution {\\varvec{u}} to the equations of a generalized Newtonian fluid with power law 1< q ≤ 2 if {\\varvec{u}} belongs to a suitable Lebesgue space. This result extends the well-known Serrin condition for weak solutions of the Navier-Stokes equations to the shear-thinning fluids.
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2017-02-01
Boundary-layer solutions to Banks' problem for the flow induced by power-law stretching of a plate are obtained for two generalizations that include arbitrary transverse plate shearing motion. In one extension an arbitrary transverse shearing motion is the product of the power-law stretching. In the other extension the streamwise stretching coordinate is added to an arbitrary transverse shearing and together raised to the power of stretching. In addition we find that Banks' power law stretching may be accompanied by orthogonal power-law shear. In all cases, the original boundary-value problem of Banks [1] is recovered. Results are illustrated with velocity profiles both at the plate and at fixed height in the fluid above the plate.
Carloni, Sante; Chaichian, Masud; Tureanu, Anca; Nojiri, Shin'ichi; Odintsov, Sergei D.; Oksanen, Markku
2010-09-15
We propose the most general modified first-order Horava-Lifshitz gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat Friedmann-Robertson-Walker (FRW) space-time, demonstrating many of the features of the general theory. It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent. As a large class of such theories, the modified Horava-Lifshitz F(R) gravity is introduced. The study of its ultraviolet properties shows that its z=3 version seems to be renormalizable in the same way as the original Horava-Lifshitz proposal. The Hamiltonian analysis of the modified Horava-Lifshitz F(R) gravity shows that it is in general a consistent theory. The F(R) gravity action is also studied in the fixed-gauge form, where the appearance of a scalar field is particularly illustrative. Then the spatially-flat FRW cosmology for this F(R) gravity is investigated. It is shown that a special choice of parameters for this theory leads to the same equations of motion as in the case of traditional F(R) gravity. Nevertheless, the cosmological structure of the modified Horava-Lifshitz F(R) gravity turns out to be much richer than for its traditional counterpart. The emergence of multiple de Sitter solutions indicates the possibility of unification of early-time inflation with late-time acceleration within the same model. Power-law F(R) theories are also investigated in detail. It is analytically shown that they have a quite rich cosmological structure: early-/late-time cosmic acceleration of quintessence, as well as of phantom types. Also it is demonstrated that all the four known types of finite-time future singularities may occur in the power-law Horava-Lifshitz F(R) gravity. Finally, a covariant proposal for (renormalizable) F(R) gravity within the Horava-Lifshitz spirit is presented.
Reich, Peter B.; Oleksyn, Jacek; Wright, Ian J.; Niklas, Karl J.; Hedin, Lars; Elser, James J.
2010-01-01
Scaling relations among plant traits are both cause and consequence of processes at organ-to-ecosystem scales. The relationship between leaf nitrogen and phosphorus is of particular interest, as both elements are essential for plant metabolism; their limited availabilities often constrain plant growth, and general relations between the two have been documented. Herein, we use a comprehensive dataset of more than 9300 observations of approximately 2500 species from 70 countries to examine the scaling of leaf nitrogen to phosphorus within and across taxonomical groups and biomes. Power law exponents derived from log–log scaling relations were near 2/3 for all observations pooled, for angiosperms and gymnosperms globally, and for angiosperms grouped by biomes, major functional groups, orders or families. The uniform 2/3 scaling of leaf nitrogen to leaf phosphorus exists along a parallel continuum of rising nitrogen, phosphorus, specific leaf area, photosynthesis and growth, as predicted by stoichiometric theory which posits that plants with high growth rates require both high allocation of phosphorus-rich RNA and a high metabolic rate to support the energy demands of macromolecular synthesis. The generality of this finding supports the view that this stoichiometric scaling relationship and the mechanisms that underpin it are foundational components of the living world. Additionally, although abundant variance exists within broad constraints, these results also support the idea that surprisingly simple rules regulate leaf form and function in terrestrial ecosystems. PMID:19906667
Reich, Peter B; Oleksyn, Jacek; Wright, Ian J; Niklas, Karl J; Hedin, Lars; Elser, James J
2010-03-22
Scaling relations among plant traits are both cause and consequence of processes at organ-to-ecosystem scales. The relationship between leaf nitrogen and phosphorus is of particular interest, as both elements are essential for plant metabolism; their limited availabilities often constrain plant growth, and general relations between the two have been documented. Herein, we use a comprehensive dataset of more than 9300 observations of approximately 2500 species from 70 countries to examine the scaling of leaf nitrogen to phosphorus within and across taxonomical groups and biomes. Power law exponents derived from log-log scaling relations were near 2/3 for all observations pooled, for angiosperms and gymnosperms globally, and for angiosperms grouped by biomes, major functional groups, orders or families. The uniform 2/3 scaling of leaf nitrogen to leaf phosphorus exists along a parallel continuum of rising nitrogen, phosphorus, specific leaf area, photosynthesis and growth, as predicted by stoichiometric theory which posits that plants with high growth rates require both high allocation of phosphorus-rich RNA and a high metabolic rate to support the energy demands of macromolecular synthesis. The generality of this finding supports the view that this stoichiometric scaling relationship and the mechanisms that underpin it are foundational components of the living world. Additionally, although abundant variance exists within broad constraints, these results also support the idea that surprisingly simple rules regulate leaf form and function in terrestrial ecosystems.
Power-law cosmic expansion in f(R) gravity models
Goheer, Naureen; Larena, Julien; Dunsby, Peter K. S.
2009-09-15
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R{sup n} gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
Anisotropic power-law inflation
Kanno, Sugumi; Soda, Jiro; Watanabe, Masa-aki E-mail: jiro@tap.scphys.kyoto-u.ac.jp
2010-12-01
We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.
Power-law regularities in human language
NASA Astrophysics Data System (ADS)
Mehri, Ali; Lashkari, Sahar Mohammadpour
2016-11-01
Complex structure of human language enables us to exchange very complicated information. This communication system obeys some common nonlinear statistical regularities. We investigate four important long-range features of human language. We perform our calculations for adopted works of seven famous litterateurs. Zipf's law and Heaps' law, which imply well-known power-law behaviors, are established in human language, showing a qualitative inverse relation with each other. Furthermore, the informational content associated with the words ordering, is measured by using an entropic metric. We also calculate fractal dimension of words in the text by using box counting method. The fractal dimension of each word, that is a positive value less than or equal to one, exhibits its spatial distribution in the text. Generally, we can claim that the Human language follows the mentioned power-law regularities. Power-law relations imply the existence of long-range correlations between the word types, to convey an especial idea.
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.
Fractional power-law spatial dispersion in electrodynamics
Tarasov, Vasily E.; Trujillo, Juan J.
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.
Spinning fluids in general relativity
NASA Technical Reports Server (NTRS)
Ray, J. R.; Smalley, L. L.
1982-01-01
General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.
Zipf's law, power laws and maximum entropy
NASA Astrophysics Data System (ADS)
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.
Thresholded Power law Size Distributions of Instabilities in Astrophysics
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2015-11-01
Power-law-like size distributions are ubiquitous in astrophysical instabilities. There are at least four natural effects that cause deviations from ideal power law size distributions, which we model here in a generalized way: (1) a physical threshold of an instability; (2) incomplete sampling of the smallest events below a threshold x0; (3) contamination by an event-unrelated background xb; and (4) truncation effects at the largest events due to a finite system size. These effects can be modeled in the simplest terms with a “thresholded power law” distribution function (also called generalized Pareto [type II] or Lomax distribution), N(x){dx}\\propto {(x+{x}0)}-a{dx}, where x0 > 0 is positive for a threshold effect, while x0 < 0 is negative for background contamination. We analytically derive the functional shape of this thresholded power law distribution function from an exponential growth evolution model, which produces avalanches only when a disturbance exceeds a critical threshold x0. We apply the thresholded power law distribution function to terrestrial, solar (HXRBS, BATSE, RHESSI), and stellar flare (Kepler) data sets. We find that the thresholded power law model provides an adequate fit to most of the observed data. Major advantages of this model are the automated choice of the power law fitting range, diagnostics of background contamination, physical instability thresholds, instrumental detection thresholds, and finite system size limits. When testing self-organized criticality models that predict ideal power laws, we suggest including these natural truncation effects.
Helmholtz solitons in power-law optical materials
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-09-15
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.
Power Law Distribution in Education
NASA Astrophysics Data System (ADS)
Gupta, Hari M.; Campanha, José R.; Prado, Fernando D.
We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.
Power law inflation with electromagnetism
Luo, Xianghui; Isenberg, James
2013-07-15
We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.
Systematic harmonic power laws inter-relating multiple fundamental constants
NASA Astrophysics Data System (ADS)
Chakeres, Donald; Buckhanan, Wayne; Andrianarijaona, Vola
2017-01-01
Power laws and harmonic systems are ubiquitous in physics. We hypothesize that 2, π, the electron, Bohr radius, Rydberg constant, neutron, fine structure constant, Higgs boson, top quark, kaons, pions, muon, Tau, W, and Z when scaled in a common single unit are all inter-related by systematic harmonic powers laws. This implies that if the power law is known it is possible to derive a fundamental constant's scale in the absence of any direct experimental data of that constant. This is true for the case of the hydrogen constants. We created a power law search engine computer program that randomly generated possible positive or negative powers searching when the product of logical groups of constants equals 1, confirming they are physically valid. For 2, π, and the hydrogen constants the search engine found Planck's constant, Coulomb's energy law, and the kinetic energy law. The product of ratios defined by two constants each was the standard general format. The search engine found systematic resonant power laws based on partial harmonic fraction powers of the neutron for all of the constants with products near 1, within their known experimental precision, when utilized with appropriate hydrogen constants. We conclude that multiple fundamental constants are inter-related within a harmonic power law system.
NASA Technical Reports Server (NTRS)
DiSalvo, Roberto; Deaconu, Stelu; Majumdar, Alok
2006-01-01
One of the goals of this program was to develop the experimental and analytical/computational tools required to predict the flow of non-Newtonian fluids through the various system components of a propulsion system: pipes, valves, pumps etc. To achieve this goal we selected to augment the capabilities of NASA's Generalized Fluid System Simulation Program (GFSSP) software. GFSSP is a general-purpose computer program designed to calculate steady state and transient pressure and flow distributions in a complex fluid network. While the current version of the GFSSP code is able to handle various systems components the implicit assumption in the code is that the fluids in the system are Newtonian. To extend the capability of the code to non-Newtonian fluids, such as silica gelled fuels and oxidizers, modifications to the momentum equations of the code have been performed. We have successfully implemented in GFSSP flow equations for fluids with power law behavior. The implementation of the power law fluid behavior into the GFSSP code depends on knowledge of the two fluid coefficients, n and K. The determination of these parameters for the silica gels used in this program was performed experimentally. The n and K parameters for silica water gels were determined experimentally at CFDRC's Special Projects Laboratory, with a constant shear rate capillary viscometer. Batches of 8:1 (by weight) water-silica gel were mixed using CFDRC s 10-gallon gelled propellant mixer. Prior to testing the gel was allowed to rest in the rheometer tank for at least twelve hours to ensure that the delicate structure of the gel had sufficient time to reform. During the tests silica gel was pressure fed and discharged through stainless steel pipes ranging from 1", to 36", in length and three diameters; 0.0237", 0.032", and 0.047". The data collected in these tests included pressure at tube entrance and volumetric flowrate. From these data the uncorrected shear rate, shear stress, residence time
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.
Power-law relations in random networks with communities.
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S H
2016-07-01
Most random graph models are locally tree-like-do not contain short cycles-rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ. In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ=γ-1.
Universal power law behaviors in genomic sequences and evolutionary models
NASA Astrophysics Data System (ADS)
Martignetti, Loredana; Caselle, Michele
2007-08-01
We study the length distribution of a particular class of DNA sequences known as the 5' untranslated regions exons. These exons belong to the messenger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that in both mice and humans these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model, which may explain this finding. We conjecture that this power law behavior could indeed be a general feature of higher eukaryotes.
General Transient Fluid Flow Algorithm
Amsden, A. A.; Ruppel, H. M.; Hirt, C. W.
1992-03-12
SALE2D calculates two-dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a two-dimensional network of quadrilateral cells for either cylindrical or Cartesian coordinates, and a variety of user-selectable boundary conditions are provided in the program.
Deformation of a Capsule in a Power-Law Shear Flow
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values. PMID:27840656
NASA Astrophysics Data System (ADS)
Ullah, Saif; Ullah, Arshad; Iqbal, Mohsan
2015-12-01
This investigation deals with analytical solutions of thin film flow for withdrawal and drainage of an incompressible generalized Oldroyd-B fluid on a vertical cylinder under the influence of non-isothermal effects. The derived solutions are presented under series form for velocity profile, temperature distribution, volume flux, average film velocity and shear stress in both cases. These solutions satisfy both the governing equations and all imposed initial and boundary conditions. The corresponding exact solutions for Newtonian fluid are also obtained as a special case of our derived solutions. Moreover, solutions for generalized Maxwell fluid and Power Law model, performing the same motion, can be obtained as limiting cases of our general solutions. The influence of pertinent parameters on the fluid motion is also underlined by graphical illustration.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks.
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
Hierarchical networks, power laws, and neuronal avalanches.
Friedman, Eric J; Landsberg, Adam S
2013-03-01
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
Extension of Generalized Fluid System Simulation Program's Fluid Property Database
NASA Technical Reports Server (NTRS)
Patel, Kishan
2011-01-01
This internship focused on the development of additional capabilities for the General Fluid Systems Simulation Program (GFSSP). GFSSP is a thermo-fluid code used to evaluate system performance by a finite volume-based network analysis method. The program was developed primarily to analyze the complex internal flow of propulsion systems and is capable of solving many problems related to thermodynamics and fluid mechanics. GFSSP is integrated with thermodynamic programs that provide fluid properties for sub-cooled, superheated, and saturation states. For fluids that are not included in the thermodynamic property program, look-up property tables can be provided. The look-up property tables of the current release version can only handle sub-cooled and superheated states. The primary purpose of the internship was to extend the look-up tables to handle saturated states. This involves a) generation of a property table using REFPROP, a thermodynamic property program that is widely used, and b) modifications of the Fortran source code to read in an additional property table containing saturation data for both saturated liquid and saturated vapor states. Also, a method was implemented to calculate the thermodynamic properties of user-fluids within the saturation region, given values of pressure and enthalpy. These additions required new code to be written, and older code had to be adjusted to accommodate the new capabilities. Ultimately, the changes will lead to the incorporation of this new capability in future versions of GFSSP. This paper describes the development and validation of the new capability.
COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS
Mota, David F.; Winther, Hans A.
2011-05-20
In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to {Lambda}CDM, but can in some special cases enhance the growth of the linear 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.
Heat transfer analysis in an annular cone subjected to power law variations
NASA Astrophysics Data System (ADS)
Salman Ahmed, N. J.; Al-Rashed, Abdullah A. A. A.; Yunus Khan, T. M.; Kamangar, Sarfaraz; Athani, Abdulgaphur; Anjum Badruddin, Irfan
2016-09-01
Present study deals with the analysis of heat transfer and fluid flow behavior in an annular cone fixed with saturated porous medium. The inner surface of the cone is assumed to have power law variable wall temperature. The governing partial differential equations are solved using well known Finite Element Method (FEM). The coupled nonlinear differential equations are converted into the algebraic equations by using Galerkin method. A 3 noded triangular element is used to divide the porous domain into smaller segments. The effects of various geometrical parameters on the cone angle are presented. It is found that the effect of cone angle on the heat transfer characteristics and fluid flow behavior is considerably significant. The fluid moment is found to shift towards the upper side of cone with increase in the power law coefficient. The fluid velocity decreases with increase in the power law coefficient.
Spectrum of power laws for curved hand movements.
Huh, Dongsung; Sejnowski, Terrence J
2015-07-21
In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.
Scaling range of power laws that originate from fluctuation analysis
NASA Astrophysics Data System (ADS)
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Scaling range of power laws that originate from fluctuation analysis.
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R^{2} of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Fractal power law in literary English
NASA Astrophysics Data System (ADS)
Gonçalves, L. L.; Gonçalves, L. B.
2006-02-01
We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.
Relativity, nonextensivity, and extended power law distributions.
Silva, R; Lima, J A S
2005-11-01
A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.
Power laws governing epidemics in isolated populations
NASA Astrophysics Data System (ADS)
Rhodes, C. J.; Anderson, R. M.
1996-06-01
TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1-11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12-14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16-19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.
NASA Astrophysics Data System (ADS)
Sochi, Taha
2015-05-01
We continue our investigation to the use of the variational method to derive flow relations for generalized Newtonian fluids in confined geometries. While in the previous investigations we used the straight circular tube geometry with eight fluid rheological models to demonstrate and establish the variational method, the focus here is on the plane long thin slit geometry using those eight rheological models, namely: Newtonian, power law, Ree-Eyring, Carreau, Cross, Casson, Bingham and Herschel-Bulkley. We demonstrate how the variational principle based on minimizing the total stress in the flow conduit can be used to derive analytical expressions, which are previously derived by other methods, or used in conjunction with numerical procedures to obtain numerical solutions which are virtually identical to the solutions obtained previously from well established methods of fluid dynamics. In this regard, we use the method of Weissenberg-Rabinowitsch- Mooney-Schofield (WRMS), with our adaptation from the circular pipe geometry to the long thin slit geometry, to derive analytical formulae for the eight types of fluid where these derived formulae are used for comparison and validation of the variational formulae and numerical solutions. Although some examples may be of little value, the optimization principle which the variational method is based upon has a significant theoretical value as it reveals the tendency of the flow system to assume a configuration that minimizes the total stress. Our proposal also offers a new methodology to tackle common problems in fluid dynamics and rheology.
Fitting power-laws in empirical data with estimators that work for all exponents
Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan
2017-01-01
Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes. PMID:28245249
Fitting power-laws in empirical data with estimators that work for all exponents.
Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan
2017-01-01
Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes.
Power-law modeling based on least-squares minimization criteria.
Hernández-Bermejo, B; Fairén, V; Sorribas, A
1999-10-01
The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system.
A Generalized Fluid Formulation for Turbomachinery Computations
NASA Technical Reports Server (NTRS)
Merkle, Charles L.; Sankaran, Venkateswaran; Dorney, Daniel J.; Sondak, Douglas L.
2003-01-01
A generalized formulation of the equations of motion of an arbitrary fluid are developed for the purpose of defining a common iterative algorithm for computational procedures. The method makes use of the equations of motion in conservation form with separate pseudo-time derivatives used for defining the numerical flux for a Riemann solver and the convergence algorithm. The partial differential equations are complemented by an thermodynamic and caloric equations of state of a complexity necessary for describing the fluid. Representative solutions with a new code based on this general equation formulation are provided for three turbomachinery problems. The first uses air as a working fluid while the second uses gaseous oxygen in a regime in which real gas effects are of little importance. These nearly perfect gas computations provide a basis for comparing with existing perfect gas code computations. The third case is for the flow of liquid oxygen through a turbine where real gas effects are significant. Vortex shedding predictions with the LOX formulations reduce the discrepancy between perfect gas computations and experiment by approximately an order of magnitude, thereby verifying the real gas formulation as well as providing an effective case where its capabilities are necessary.
NASA Technical Reports Server (NTRS)
Majumdar, Alok; Leclair, Andre; Moore, Ric; Schallhorn, Paul
2011-01-01
GFSSP stands for Generalized Fluid System Simulation Program. It is a general-purpose computer program to compute pressure, temperature and flow distribution in a flow network. GFSSP calculates pressure, temperature, and concentrations at nodes and calculates flow rates through branches. It was primarily developed to analyze Internal Flow Analysis of a Turbopump Transient Flow Analysis of a Propulsion System. GFSSP development started in 1994 with an objective to provide a generalized and easy to use flow analysis tool for thermo-fluid systems.
Generalized Langevin Theory for Inhomogeneous Fluids.
NASA Astrophysics Data System (ADS)
Grant, Martin Garth
This thesis presents a molecular theory of the dynamics of inhomogeneous fluids. Dynamical correlations in a nonuniform system are studied through the generalized Langevin approach. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamic-like quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We apply this formalism to several problems. We study the correlation of currents orthogonal to a diffuse planar, liquid-vapour, interface, introducing new nonlocal elastic moduli and new nonlocal, frequency dependent, viscosities. Novel symmetry breaking contributions are obtained, which are related to the Young-Laplace equation for pressure balance. The normal modes, associated with the symmetry breaking interface in the liquid-vapour system, are analyzed, taking into account the nonlocal nature of the diffuse planar interface. We obtain the classical dispersion relation for capillary waves, observed in light scattering experiments, from an adiabatic (molecular) approach. We consider the 'capillary wave model' (CWM) of the equilibrium liquid-vapour interface. CWM is reformulated to be consistent with capillary waves; corrections to the standard CWM results, due to self-consistent long range coupling, are obtained for finite surface area and nonzero gravitational acceleration. Finally, we obtain the Landau-Lifshitz theory of fluctuating hydrodynamics from the
Spectra that behave like power-laws are not necessarily power-laws
NASA Astrophysics Data System (ADS)
Podesta, John J.
2016-02-01
It is shown that measured power spectral densities (spectra) that closely resemble power-law spectra may, in fact, have mathematical forms that are not power laws in the mathematical sense. If power spectral estimates show a good fit to a straight line on a log-log plot over a finite frequency range, that is not sufficient evidence to conclude that the mathematical form of the spectrum is, in fact, a power-law over that range. It is also pointed out that to accurately fit a power-law function to experimental data using linear least squares techniques in log-log space, as is often done in practice, it is essential that the data is uniformly distributed along the abscissa in log-space (in the stochastic sense) or, otherwise, the data must be linearly interpolated onto a uniform grid to ensure that the data employed in the fitting procedure is equally weighted along the abscissa. These two important points are not widely appreciated by researchers in the field and the pitfalls associated with commonly used fitting techniques are often overlooked in the analysis of solar wind data.
Power laws and fragility in flow networks☆
Shore, Jesse; Chu, Catherine J.; Bianchi, Matt T.
2015-01-01
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence. PMID:26082568
Implitcation of a Power-Law Climate Response Function
NASA Astrophysics Data System (ADS)
Hébert, R.
2015-12-01
A study of global mean temperature is presented assuming that the climate response function to anthropogenic forcing is a power law. This general form allows for long-range dependancies with only 3 parameter while remaining within the linear forcing paradigm. This establish a one-to-one relation between the scaling exponent H and the ratio of the Transient Climate Response, TCR, and the Equilibrium Climate Sensitivity, ECS. The scaling exponent of the power law is estimated by a regression of temperature as a function of forcing and by a spectral analysis of the temperature and the forcing. We consider for the analysis 5 different datasets of historical global mean temperature and 100 CMIP5 RCP runs distributed among the 4 scenarios. We find that the error function for the estimate on historical temperature is very wide and thus, many scaling exponent can be used without meaningful changes in the fit residuals of historical temperatures; their response in the year 2100 on the other hand, is very broad. CMIP5 runs allow a narrower estimate of H which can then be used to estimate the ECS by dividing the TCR estimated from the historical data.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Stochastic dynamics and a power law for measles variability.
Keeling, M; Grenfell, B
1999-01-01
Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size. PMID:10365402
The invariances of power law size distributions.
Frank, Steven A
2016-01-01
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.
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.
Power law exponents characterizing human DNA
NASA Astrophysics Data System (ADS)
Provata, A.; Oikonomou, Th.
2007-05-01
The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc(S) of size S present long tails Pnc(S)˜S-1-μnc , with exponents μnc ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments Pc(S) in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.
The invariances of power law size distributions
Frank, Steven A.
2016-01-01
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. PMID:27928497
Power law models of stock indices
NASA Astrophysics Data System (ADS)
Tse, Man Kit
Viewing the stock market as a self-organized system, Sornette and Johansen introduced physics-based models to study the dynamics of stock market crashes from the perspective of complex systems. This involved modeling stock market Indices using a mathematical power law exhibiting log-periodicity as the system approaches a market crash, which acts like a critical point in a thermodynamic system. In this dissertation, I aim to investigate stock indices to determine whether or not they exhibit log-periodic oscillations, according to the models proposed by Sornette, as they approach a crash. In addition to analyzing stock market crashes in the frequency domain using the discrete Fourier transform and the Lomb-Scargle periodogram, I perform a detailed analysis of the stock market crash models through parameter estimation and model testing. I find that the probability landscapes have a complex topography and that there is very little evidence that these phase transition-based models accurately describe stock market crashes.
Rate-Controlling Mechanisms in Five-Power-Law Creep
Michael E. Kassner
2004-04-20
OAK-B135 Rate-Controlling Mechanisms in Five-Power-Law Creep. The initial grant emphasized the rate-controlling processes for five power-law creep. The effort has six aspects: (1) Theory of Taylor hardening from the Frank dislocation network in five power law substructures. (2) The dual dynamical and hardening nature of dislocations in five power law substructures. (3) Determination of the existence of long-range internal stress in five-power law creep dislocation substructures. (4) Dynamic recovery mechanisms associated with dislocation heterogeneities during five power law creep. (5) Versatility of five power law creep concept to other (hcp) crystal structures. (6) Writing of a book on ''Fundamental of Creep in Metals and Alloys'' by M.E. Kassner and Maria-Teresa Perez-Frado (postdoctoral scholar, funded by this project) Elsevier Press, 2004, in press. These areas are consistent with the original goals of this project as delineated in the original proposal to Basic Energy Sciences. The progress in each of these areas will be discussed separately and there will be an attempt to tie each aspect together so as to allow a summary regarding the conclusions with respect to the rate-controlling mechanisms of five power-law creep.
Discovery of power-laws in chemical space.
Benz, Ryan W; Swamidass, S Joshua; Baldi, Pierre
2008-06-01
Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank/ frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80/20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Phase diagram of power law and Lennard-Jones systems: crystal phases.
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Pascal (Yang Hui) triangles and power laws in the logistic map
NASA Astrophysics Data System (ADS)
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.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
NASA Astrophysics Data System (ADS)
Travesset, Alex
2014-10-01
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Time-dependent Kramers escape rate in overdamped system with power-law distribution
NASA Astrophysics Data System (ADS)
Zhou, Yanjun; Yin, Cangtao
2016-05-01
The probability distribution of Brownian particles moving in an overdamped complex system follows the generalized Smoluchowski equation, which can be rigorously proven that the exact time-dependent solution for this equation follows Tsallis form. Time-dependent escape rate in overdamped system with power-law distributions is then established based on the flux over population theory. The stationary state escape rate in overdamped system with power-law distribution which has been obtained before based on mean first passage time theory is recovered from time-dependent escape rate as time toward infinity.
Resurrecting power law inflation in the light of Planck results
Unnikrishnan, Sanil; Sahni, Varun E-mail: varun@iucaa.ernet.in
2013-10-01
It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter f{sub N{sub L}{sup equil}} are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our model is structurally similar to that of a canonical scalar field and has a power law form for the kinetic term. A simple extension of our model resolves the graceful exit problem which usually afflicts models of power law inflation.
Power 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.
NASA Astrophysics Data System (ADS)
Langlois, Dominic; Cousineau, Denis; Thivierge, J. P.
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Langlois, Dominic; Cousineau, Denis; Thivierge, J P
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Statistical analyses support power law distributions found in neuronal avalanches.
Klaus, Andreas; Yu, Shan; Plenz, Dietmar
2011-01-01
The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Taking Fluid Mechanics to the General Public
NASA Astrophysics Data System (ADS)
Guyon, Etienne; Guyon, Marie Yvonne
2014-01-01
Fluid flow phenomena are omnipresent; they can be observed and described in many locations and circumstances. However, in most cases, their presence does not stimulate an interest in science. We consider successively domains of activities in which the presence of fluid flow phenomena can be used: natural sites, industrial ones, sporting events, artistic creations and presentations, the production of images and books, science museums, cultural centers, and also popular mass media. The last section is devoted to outreach activities that can be practiced within the educational system.
Simple power law for transport ratio with bimodal distributions of coarse sediments under waves
NASA Astrophysics Data System (ADS)
Calantoni, Joseph; Thaxton, Christopher S.
2008-03-01
Morphodynamic models of coastal evolution require relatively simple parameterizations of sediment transport for application over larger scales. Here we present a transport parameterization for bimodal distributions of coarse quartz grains using simulations from a discrete particle model for sheet flow and near sheet flow conditions. The discrete particle model simulates the simplest one-dimensional fluid using a turbulent eddy viscosity determined from a mixing length coupled to particle motions. The motions of individual sand grains are simulated using spherical elements. Newton's second law in translational and rotational forms is solved for every particle in the domain as determined by both grain-grain and grain-fluid interactions. The forcing from idealized monochromatic waves is accomplished by specifying a spatially constant, time varying horizontal pressure gradient acting on the simulation domain. Consequently, the time series of the free-stream fluid acceleration and velocity are also fixed. Simulations cover a range of wave forcing, diameter ratios for the large and small grains in the bimodal size distribution, and mass ratios of large to small grains in the simulation domain, for a total of 243 unique simulation conditions. The simulation results are successfully parameterized with a simple power law that allows for the prediction of the transport rates of each size fraction in the bimodal distribution. The simple power law determined from simulations provides favorable predictions of transport rates for each size fraction when applied to available laboratory data for sheet flow with bimodal size distributions. It is important to note that rapid vertical kinematic sorting of grains by size is explicitly simulated with the model and thus implicitly captured by the power law. Discussion focuses on practical application of the power law.
Fractal ladder models and power law wave equations
Kelly, James F.; McGough, Robert J.
2009-01-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816
Fractal ladder models and power law wave equations.
Kelly, James F; McGough, Robert J
2009-10-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers-Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters.
Singularity problems of the power law for modeling creep compliance
NASA Technical Reports Server (NTRS)
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
Hidden power law patterns in the top European football leagues
NASA Astrophysics Data System (ADS)
Da Silva, Sergio; Matsushita, Raul; Silveira, Eliza
2013-11-01
Because sports are stylized combat, sports may follow power laws similar to those found for wars, individual clashes, and acts of terrorism. We show this fact for football (soccer) by adjusting power laws that show a close relationship between rank and points won by the clubs participating in the latest seasons of the top fifteen European football leagues. In addition, we use Shannon entropy for gauging league competitive balance. As a result, we are able to rank the leagues according to competitiveness.
THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.
Jiang, H; Liu, F; Meerschaert, M M; McGough, R J
2013-01-01
Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.
NASA Astrophysics Data System (ADS)
Carrano, Charles S.; Rino, Charles L.
2016-06-01
We extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two-component inverse power law spectrum. The two-component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two-dimensional field-aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self-similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large- and small-scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.
THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN
Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.
2013-01-01
Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian. PMID:26425384
Phase diagram of softly repulsive systems: the Gaussian and inverse-power-law potentials.
Prestipino, Santi; Saija, Franz; Giaquinta, Paolo V
2005-10-08
We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.
Generalized dark energy interactions with multiple fluids
NASA Astrophysics Data System (ADS)
van de Bruck, Carsten; Mifsud, Jurgen; Mimoso, José P.; Nunes, Nelson J.
2016-11-01
In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the disformal coupling from Big-Bang Nucleosynthesis and given current limits on the variation of the fine-structure constant.
Distortion of power law blinking with binning and thresholding
Amecke, Nicole; Heber, André; Cichos, Frank
2014-03-21
Fluorescence intermittency is a random switching between emitting (on) and non-emitting (off) periods found for many single chromophores such as semiconductor quantum dots and organic molecules. The statistics of the duration of on- and off-periods are commonly determined by thresholding the emission time trace of a single chromophore and appear to be power law distributed. Here we test with the help of simulations if the experimentally determined power law distributions can actually reflect the underlying statistics. We find that with the experimentally limited time resolution real power law statistics with exponents α{sub on/off} ≳ 1.6, especially if α{sub on} ≠ α{sub off} would not be observed as such in the experimental data after binning and thresholding. Instead, a power law appearance could simply be obtained from the continuous distribution of intermediate intensity levels. This challenges much of the obtained data and the models describing the so-called power law blinking.
NASA Astrophysics Data System (ADS)
Brook, Martin; Hebblewhite, Bruce; Mitra, Rudrajit
2016-04-01
The size-scaling of rock fractures is a well-studied problem in geology, especially for permeability quantification. The intensity of fractures may control the economic exploitation of fractured reservoirs because fracture intensity describes the abundance of fractures potentially available for fluid flow. Moreover, in geotechnical engineering, fractures are important for parameterisation of stress models and excavation design. As fracture data is often collected from widely-spaced boreholes where core recovery is often incomplete, accurate interpretation and representation of fracture aperture-frequency relationships from sparse datasets is important. Fracture intensity is the number of fractures encountered per unit length along a sample scanline oriented perpendicular to the fractures in a set. Cumulative frequency of fractures (F) is commonly related to fracture aperture (A) in the form of a power-law (F = aA-b), with variations in the size of the a coefficient between sites interpreted to equate to fracture frequency for a given aperture (A). However, a common flaw in this approach is that even a small change in b can have a large effect on the response of the fracture frequency (F) parameter. We compare fracture data from the Late Permian Rangal Coal Measures from Australia's Bowen Basin, with fracture data from Jurassic carbonates from the Sierra Madre Oriental, northeastern Mexico. Both power-law coefficient a and exponent b control the fracture aperture-frequency relationship in conjunction with each other; that is, power-laws with relatively low a coefficients have relatively high b exponents and vice versa. Hence, any comparison of different power-laws must take both a and b into consideration. The corollary is that different sedimentary beds in the Sierra Madre carbonates do not show ˜8× the fracture frequency for a given fracture aperture, as based solely on the comparison of coefficient a. Rather, power-law "sensitivity factors" developed from both
A power law approach to orifice flow rate calibration.
Rhinehart, R Russell; Gebreyohannes, Solomon; Sridhar, Upasana Manimegalai; Patrachari, Anirudh; Rahaman, M S
2011-04-01
Although standards for orifice flow meter design, installation, and calibration are supported herein, noncompliant devices exist in many pilot-, lab-scale, and on-board applications. For these, a common calibration practice is to preserve the ideal square root relation and determine a device specific discharge coefficient value. This work provides theoretical and empirical analyses to support relaxing the square root relation between orifice pressure drop and flow rate for noncompliant devices. The resulting power law relation is shown to improve accuracy, precision, and rangeability. Whether a device specific square root or power law model is used, it requires off-line or in-line calibration data. As such, a power law calibration model may only be useful for on-board and small-scale applications.
Between disorder and order: A case study of power law
NASA Astrophysics Data System (ADS)
Cao, Yong; Zhao, Youjie; Yue, Xiaoguang; Xiong, Fei; Sun, Yongke; He, Xin; Wang, Lichao
2016-08-01
Power law is an important feature of phenomena in long memory behaviors. Zipf ever found power law in the distribution of the word frequencies. In physics, the terms order and disorder are Thermodynamic or statistical physics concepts originally and a lot of research work has focused on self-organization of the disorder ingredients of simple physical systems. It is interesting what make disorder-order transition. We devise an experiment-based method about random symbolic sequences to research regular pattern between disorder and order. The experiment results reveal power law is indeed an important regularity in transition from disorder to order. About these results the preliminary study and analysis has been done to explain the reasons.
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.
Edge effect on the power law distribution of granular avalanches.
Lorincz, Kinga A; Wijngaarden, Rinke J
2007-10-01
Many punctuated phenomena in nature are claimed [e.g., by the theory of self-organized criticality (SOC)] to be power-law distributed. In our experiments on a three-dimensional pile of long-grained rice, we find that by only changing the boundary condition of the system, we switch from such power-law-distributed avalanche sizes to quasiperiodic system-spanning avalanches. Conversely, by removing ledges the incidence of system-spanning avalanches is significantly reduced. This may offer a perspective on new avalanche prevention schemes. In addition, our findings may help to explain why the archetype of SOC, the sandpile, was found to have power-law-distributed avalanches in some experiments, while in other experiments quasiperiodic system-spanning avalanches were found.
Robust Statistical Detection of Power-Law Cross-Correlation
NASA Astrophysics Data System (ADS)
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-06-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram.
Soliton solutions with power-law nonlinearity in inhomogeneous media
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Yu, Fang-Bo
2013-04-01
We construct the relation between the variable coefficient nonlinear Schrödinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schrödinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.
Power Laws, Flicker Noise, and the Barkhausen Effect
1993-10-01
AD-A274 702 AD TECHNICAL REPORT ARCCB-TR-93038 POWER LAWS, FLICKER NOISE, AND THE BARKHAUSEN EFFECT DTIC ELECTE JA~N 211994 3 L.V. MEISEL S D P.J...CATES C&MORD October 1993 Fuel 4. TITLE AND SUBTITU S. FUNDING NUMBERS POWER LAWS. FUCKER NOISE. AND THE BARKHAUSEN EFFECT AMCMS: 611L02.H61L1 6. AUTHOR... Barkhausen effect was studied in three ferromagnetic metals: an amorphous alloy, iron. and alumel. The data exhibit all the characteristics of self
Power-law statistics for avalanches in a martensitic transformation.
Ahluwalia, R; Ananthakrishna, G
2001-04-30
We devise a two-dimensional model that mimics the recently observed power-law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [Vives et al., Phys. Rev. Lett. 72, 1694 (1994)]. We include a threshold mechanism, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis and, more importantly, it shows that the energy is released in the form of avalanches with power-law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.
Particle capture in axial magnetic filters with power law flow model
NASA Astrophysics Data System (ADS)
Abbasov, T.; Herdem, S.; Köksal, M.
1999-05-01
A theory of capture of magnetic particle carried by laminar flow of viscous non-Newtonian (power law) fluid in axially ordered filters is presented. The velocity profile of the fluid flow is determined by the Kuwabara-Happel cell model. For the trajectory of the particle, the capture area and the filter performance simple analytical expressions are obtained. These expressions are valid for particle capture processes from both Newtonian and non-Newtonian fluids. For this reason the obtained theoretical results make it possible to widen the application of high-gradient magnetic filtration (HGMF) to other industrial areas. For Newtonian fluids the theoretical results are shown to be in good agreement with the experimental ones reported in the literature.
Intraoperative Fluids and Fluid Management for Ambulatory Dental Sedation and General Anesthesia
Saraghi, Mana
2015-01-01
Intravenous fluids are administered in virtually every parenteral sedation and general anesthetic. The purpose of this article is to review the physiology of body-water distribution and fluid dynamics at the vascular endothelium, evaluation of fluid status, calculation of fluid requirements, and the clinical rationale for the use of various crystalloid and colloid solutions. In the setting of elective dental outpatient procedures with minor blood loss, isotonic balanced crystalloid solutions are the fluids of choice. Colloids, on the other hand, have no use in outpatient sedation or general anesthesia for dental or minor oral surgery procedures but may have several desirable properties in long and invasive maxillofacial surgical procedures where advanced hemodynamic monitoring may assess the adequacy of intravascular volume. PMID:26650497
Generalized Fluid System Simulation Program, Version 6.0
NASA Technical Reports Server (NTRS)
Majumdar, A. K.; LeClair, A. C.; Moore, A.; Schallhorn, P. A.
2013-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependant flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 25 demonstrated example problems.
Generalized Fluid System Simulation Program (GFSSP) - Version 6
NASA Technical Reports Server (NTRS)
Majumdar, Alok; LeClair, Andre; Moore, Ric; Schallhorn, Paul
2015-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, flow control valves and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. Users can introduce new physics, non-linear and time-dependent boundary conditions through user-subroutine.
Power-Law Entanglement Spectrum in Many-Body Localized Phases
NASA Astrophysics Data System (ADS)
Serbyn, Maksym; Michailidis, Alexios A.; Abanin, Dmitry A.; Papić, Z.
2016-10-01
The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
Power-Law Entanglement Spectrum in Many-Body Localized Phases.
Serbyn, Maksym; Michailidis, Alexios A; Abanin, Dmitry A; Papić, Z
2016-10-14
The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
Holm, Sverre; Näsholm, Sven Peter
2014-04-01
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
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.
Medical practices display power law behaviors similar to spoken languages
2013-01-01
Background 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. Methods 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. Results 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. Conclusions 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. PMID:24007376
The power laws of nanoscale forces under ambient conditions.
Lai, Chia-Yun; Olukan, Tuza; Santos, Sergio; Al Ghaferi, Amal; Chiesa, Matteo
2015-12-25
We report a power law derived from experimental atomic force microscopy (AFM) data suggesting a nano to mesoscale transition in force-distance dependencies. Our results are in relative agreement with the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only.
Constraints on cosmological parameters in power-law cosmology
NASA Astrophysics Data System (ADS)
Rani, Sarita; Altaibayeva, A.; Shahalam, M.; Singh, J. K.; Myrzakulov, R.
2015-03-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H0 (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. H0 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.
Constraints on cosmological parameters in power-law cosmology
Rani, Sarita; Singh, J.K.; Altaibayeva, A.; Myrzakulov, R.; Shahalam, M. E-mail: aziza.bibol@mail.ru E-mail: jainendrrakumar@rediffmail.com
2015-03-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H{sub 0} (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H{sub 0} average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → −1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.
General-relativistic rotation laws in rotating fluid bodies
NASA Astrophysics Data System (ADS)
Mach, Patryk; Malec, Edward
2015-06-01
We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to rederive, in the first post-Newtonian approximation, the well-known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic antidragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids self-gravity. One can use the rotation laws to study the uniqueness and the convergence of the post-Newtonian approximations as well as the existence of the post-Newtonian limits.
Generalized Fluid System Simulation Program, Version 5.0-Educational
NASA Technical Reports Server (NTRS)
Majumdar, A. K.
2011-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the point, drag and click method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids and 21 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 12 demonstrated example problems.
Mimicking static anisotropic fluid spheres in general relativity
NASA Astrophysics Data System (ADS)
Boonserm, Petarpa; Ngampitipan, Tritos; Visser, Matt
2016-11-01
We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear combinations of theoretically attractive and quite simple classical matter: a classical (charged) isotropic perfect fluid, a classical electromagnetic field and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore, we show how this decomposition relates to the distribution of both electric charge density and scalar charge density throughout the model. The generalized TOV equation implies that the perfect fluid component in this model is automatically in internal equilibrium, with pressure forces, electric forces, and scalar forces balancing the gravitational pseudo-force. Consequently, we can build theoretically attractive matter models that can be used to mimic almost any static spherically symmetric spacetime.
On the thermodynamics of some generalized second-grade fluids
Man CS, Massoudi M
2010-01-01
The generalized second-grade fluids, which have been used for modeling the creep of ice and the flow of coal-water and coal-oil slurries, are among the simplest non-Newtonian fluid models that can describe shear-thinning/thickening and exhibit normal stress effects. In this article, we conduct thermodynamic analysis on a class of generalized second-grade fluids, one distinguishing feature of which is the existence of a constitutive function that describes frictional heating. We work within the framework of Serrin’s original formulation of neoclassical thermodynamics, where internal energy and entropy functions, if they exist for a continuous body at all, are to be derived from the classical First Law and (quantitatively reformulated) Second Law of thermodynamics for cycles. For the class of generalized second-grade fluids in question, we show from the First Law that an internal energy density u exists, and we derive the equation of energy balance; from the Second Law, we demonstrate the existence of an entropy density s and derive the Clausius–Duhem inequality that it satisfies.We obtain explicit expressions for u, s and the frictional heating , and derive thermodynamic restrictions on thematerial functions of temperature μ, α1, and α2 that appear in the constitutive relation for the Cauchy stress. For the special case of second-grade fluids, our expressions for u and s agree with those which Dunn and Fosdick [6] derived under the theoretical framework of the rational thermodynamics of Coleman and Noll.
High-index asymptotics of spherical Bessel products averaged with modulated Gaussian power laws
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
2014-12-01
Bessel integrals of type are investigated, where the kernel g( k) is a modulated Gaussian power-law distribution , and the jl ( m) are multiple derivatives of spherical Bessel functions. These integrals define the multipole moments of Gaussian random fields on the unit sphere, arising in multipole fits of temperature and polarization power spectra of the cosmic microwave background. Two methods allowing efficient numerical calculation of these integrals are presented, covering Bessel indices l in the currently accessible multipole range 0 ≤ l ≤ 104 and beyond. The first method is based on a representation of spherical Bessel functions by Lommel polynomials. Gaussian power-law averages can then be calculated in closed form as finite Hankel series of parabolic cylinder functions, which allow high-precision evaluation. The second method is asymptotic, covering the high- l regime, and is applicable to general distribution functions g( k) in the integrand; it is based on the uniform Nicholson approximation of the Bessel derivatives in conjunction with an integral representation of squared Airy functions. A numerical comparison of these two methods is performed, employing Gaussian power laws and Kummer distributions to average the Bessel products.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws
Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.
2011-01-01
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.
Power-law scaling in daily rainfall patterns and consequences in urban stream discharges
NASA Astrophysics Data System (ADS)
Park, Jeryang; Krueger, Elisabeth H.; Kim, Dongkyun; Rao, Suresh C.
2016-04-01
Poissonian rainfall has been frequently used for modelling stream discharge in a catchment at the daily scale. Generally, it is assumed that the daily rainfall depth is described by memoryless exponential distribution which is transformed to stream discharge, resulting in an analytical pdf for discharge [Gamma distribution]. While it is true that catchment hydrological filtering processes (censored by constant rate ET losses, and first-order recession) increases "memory", reflected in 1/f noise in discharge time series. Here, we show that for urban watersheds in South Korea: (1) the observation of daily rainfall depths follow power-law pdfs, and spectral slopes range between 0.2 ~ 0.4; and (2) the stream discharge pdfs have power-law tails. These observation results suggest that multiple hydro-climatic factors (e.g., non-stationarity of rainfall patterns) and hydrologic filtering (increasing impervious area; more complex urban drainage networks) influence the catchment hydrologic responses. We test the role of such factors using a parsimonious model, using different types of daily rainfall patterns (e.g., power-law distributed rainfall depth with Poisson distribution in its frequency) and urban settings to reproduce patterns similar to those observed in empirical records. Our results indicate that fractality in temporally up-scaled rainfall, and the consequences of large extreme events are preserved as high discharge events in urbanizing catchments. Implications of these results to modeling urban hydrologic responses and impacts on receiving waters are discussed.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.
Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L
2011-10-01
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.
Huo, Yunlong; Choy, Jenny Susana; Wischgoll, Thomas; Luo, Tong; Teague, Shawn D.; Bhatt, Deepak L.; Kassab, Ghassan S.
2013-01-01
Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length–volume scaling power law ( where Lc and Vc are crown length and volume) were found for both the high-fat and control groups (R2 = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, KLV, decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow–length scaling power law, however, was nearly unaffected by the positive remodelling. The length–volume and flow–length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. KLV < 18 in the length–volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans. PMID:23365197
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W., Jr.
2003-01-01
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
Spinning fluids in general relativity. II - Self-consistent formulation
NASA Technical Reports Server (NTRS)
Ray, John R.; Smalley, Larry, L.; Krisch, Jean P.
1987-01-01
Methods used earlier to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory are specialized to the case of general relativity. The main idea is to include the spin as a thermodynamic variable in the theory.
Deviation from Power Law Behavior in Landslide Phenomenon
NASA Astrophysics Data System (ADS)
Li, L.; Lan, H.; Wu, Y.
2013-12-01
Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law
The origin of power-law rheology in foams
NASA Astrophysics Data System (ADS)
Hwang, Hyun Joo; Riggleman, Robert; Crocker, John
Soft glassy matter (SGM) such as foams, emulsions, and colloids, exhibit interesting rheological properties that have long defied explanation. In particular, the shear modulus of these materials displays weak power law frequency dependence. To understand the origin of this property in more depth, we have built a three-dimensional, modified Bubble Dynamics model. The bubbles interact with a purely repulsive harmonic potential and ripen according to diffusion-based governing equations. Notably, the bubble motion has a Levy flight character, in addition to being spatially correlated in the form of avalanches. Microrheology studies reveal that the power-law shear modulus is the result of constraint release driven by the bubbles' super-diffusive motion combined with simple yield of the resulting stress. The super-diffusive motion of the bubbles, in turn, is the result of the system taking a fractal path in configuration space. We shall discuss the origins of this fractal scaling.
Power-law distribution in Japanese racetrack betting
NASA Astrophysics Data System (ADS)
Ichinomiya, Takashi
2006-08-01
Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)∝1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.
Power law behavior of the zigzag transition in Yukawa clusters
Sheridan, T. E.; Magyar, Andrew L.
2010-11-15
We provide direct experimental evidence that the width of a Yukawa cluster exhibits power law behavior during the one-dimensional (1D) to two-dimensional (2D) zigzag transition. Configurations of small dusty (complex) plasma clusters confined in a biharmonic potential well are characterized as the well anisotropy is varied. When the anisotropy is large the particles are in a 1D straight-line configuration. As the anisotropy is decreased the cluster undergoes a zigzag transition to a 2D configuration. The measured dependence of cluster width on anisotropy follows a power law. A second transition from the zigzag to an elliptical configuration is also observed. The results are in very good agreement with a model of identical particles interacting through a Yukawa potential.
Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---
NASA Astrophysics Data System (ADS)
Kaizoji, T.
In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, P (S > x) ˜ x^{-α}, with an exponent that moves in the range of 1.09 < α < 1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.
Probability distributions and confidence intervals for simulated power law noise.
Ashby, Neil
2015-01-01
A method for simulating power law noise in clocks and oscillators is presented based on modification of the spectrum of white phase noise, then Fourier transforming to the time domain. Symmetric real matrices are introduced whose traces-the sums of their eigenvalues-are equal to the Allan variances, in overlapping or non-overlapping forms, as well as for the corresponding forms of the modified Allan variance. We show that the standard expressions for spectral densities, and their relations to Allan variance, are obtained with this method. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval τ, and hence for estimating confidence in the measurements. Examples are presented for the common power-law noises. Extension to other variances such as the Hadamard variance, and variances with dead time, are discussed.
Lévy flights with power-law absorption.
Cattivelli, Luca; Agliari, Elena; Sartori, Fabio; Cassi, Davide
2015-10-01
We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ+1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x)∼x(-α) and we find that, as long as μ<α, there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
Generalized Langevin theory for inhomogeneous fluids: The equations of motion
NASA Astrophysics Data System (ADS)
Grant, Martin; Desai, Rashmi C.
1982-05-01
We use the generalized Langevin approach to study the dynamical correlations in an inhomogeneous system. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor, and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamiclike quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low-density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We also indicate how the resulting general set of equations would simplify for systems in which the inhomogeneity is unidirectional, e.g., a liquid-vapor interface.
Power law distribution of dividends in horse races
NASA Astrophysics Data System (ADS)
Park, K.; Domany, E.
2001-02-01
We discovered that the distribution of dividends in Korean horse races follows a power law. A simple model of betting is proposed, which reproduces the observed distribution. The model provides a mechanism to arrive at the true underlying winning probabilities, which are initially unknown, in a self-organized collective fashion, through the dynamic process of betting. Numerical simulations yield excellent agreement with the empirical data.
Power law relationships for rain attenuation and reflectivity
NASA Technical Reports Server (NTRS)
Devasirvatham, D. M. J.; Hodge, D. B.
1978-01-01
The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.
Power-law cosmology, SN Ia, and BAO
Dolgov, Aleksander; Halenka, Vitali; Tkachev, Igor E-mail: vithal@umich.edu
2014-10-01
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime a(t) ∼ t{sup β} with β close to 3/2 in a spatially flat universe is a good fit to these data.
Power law cosmology model comparison with CMB scale information
NASA Astrophysics Data System (ADS)
Tutusaus, Isaac; Lamine, Brahim; Blanchard, Alain; Dupays, Arnaud; Zolnierowski, Yves; Cohen-Tanugi, Johann; Ealet, Anne; Escoffier, Stéphanie; Le Fèvre, Olivier; Ilić, Stéphane; Pisani, Alice; Plaszczynski, Stéphane; Sakr, Ziad; Salvatelli, Valentina; Schücker, Thomas; Tilquin, André; Virey, Jean-Marc
2016-11-01
Despite the ability of the cosmological concordance model (Λ CDM ) to describe the cosmological observations exceedingly well, power law expansion of the Universe scale radius, R (t )∝tn, has been proposed as an alternative framework. We examine here these models, analyzing their ability to fit cosmological data using robust model comparison criteria. Type Ia supernovae (SNIa), baryonic acoustic oscillations (BAO) and acoustic scale information from the cosmic microwave background (CMB) have been used. We find that SNIa data either alone or combined with BAO can be well reproduced by both Λ CDM and power law expansion models with n ˜1.5 , while the constant expansion rate model (n =1 ) is clearly disfavored. Allowing for some redshift evolution in the SNIa luminosity essentially removes any clear preference for a specific model. The CMB data are well known to provide the most stringent constraints on standard cosmological models, in particular, through the position of the first peak of the temperature angular power spectrum, corresponding to the sound horizon at recombination, a scale physically related to the BAO scale. Models with n ≥1 lead to a divergence of the sound horizon and do not naturally provide the relevant scales for the BAO and the CMB. We retain an empirical footing to overcome this issue: we let the data choose the preferred values for these scales, while we recompute the ionization history in power law models, to obtain the distance to the CMB. In doing so, we find that the scale coming from the BAO data is not consistent with the observed position of the first peak of the CMB temperature angular power spectrum for any power law cosmology. Therefore, we conclude that when the three standard probes (SNIa, BAO, and CMB) are combined, the Λ CDM model is very strongly favored over any of these alternative models, which are then essentially ruled out.
Robust Statistical Detection of Power-Law Cross-Correlation
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-01-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630
Generalized Fluid System Simulation Program, Version 6.0
NASA Technical Reports Server (NTRS)
Majumdar, A. K.; LeClair, A. C.; Moore, R.; Schallhorn, P. A.
2016-01-01
The Generalized Fluid System Simulation Program (GFSSP) is a general purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. Two thermodynamic property programs (GASP/WASP and GASPAK) provide required thermodynamic and thermophysical properties for 36 fluids: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutene, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride, ammonia, hydrogen peroxide, and air. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. The users can also supply property tables for fluids that are not in the library. Twenty-four different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include pipe flow, flow through a restriction, noncircular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct
Mass transport in a thin layer of power-law mud under surface waves
NASA Astrophysics Data System (ADS)
Liu, Jie; Bai, Yuchuan; Xu, Dong
2017-02-01
The mass transport velocity in a two-layer system is studied theoretically. The wave motion is driven by a periodic pressure load on the free water surface, and mud in the lower layer is described by a power-law rheological model. Perturbation analysis is performed to the second order to find the mean Eulerian velocity. A numerical iteration method is employed to solve the non-linear governing equation at the leading order. The influence of rheological properties on fluid motion characteristics including the flow field, the surface displacement, the mass transport velocity, and the net discharge rates are investigated based on theoretical results. Theoretical analysis shows that under the action of interfacial shearing, a recirculation structure may appear near the interface in the upper water layer. A higher mass transport velocity at the interface does not necessarily mean a higher discharge rate for a pseudo-plastic fluid mud.
Anomalous wave function statistics on a one-dimensional lattice with power-law disorder.
Titov, M; Schomerus, H
2003-10-24
Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.
Counterflow diffusion flames of general fluids: Oxygen/hydrogen mixtures
Ribert, Guillaume; Zong, Nan; Yang, Vigor; Pons, Laetitia; Darabiha, Nasser; Candel, Sebastien
2008-08-15
A comprehensive framework has been established for studying laminar counterflow diffusion flames for general fluids over the entire regime of thermodynamic states. The model incorporates a unified treatment of fundamental thermodynamic and transport theories into an existing flow solver DMCF to treat detailed chemical kinetic mechanisms and multispecies transport. The resultant scheme can thus be applied to fluids in any state. Both subcritical and supercritical conditions are considered. As a specific example, diluted and undiluted H{sub 2}/O{sub 2} flames are investigated at pressures of 1-25 MPa and oxygen inlet temperatures of 100 and 300 K. The effects of pressure p and strain rate {epsilon}{sub s} on the heat release rate q{sub s}-dot, extinction limit, and flame structure are examined. In addition, the impact of cross-diffusion terms, such as the Soret and Dufour effects, on the flame behavior is assessed. Results indicate that the flame thickness {delta}{sub f} and heat release rate correlate well with the square root of the pressure multiplied by the strain rate. The strain rate at the extinction limit exhibits a quasi-linear dependence on p. Significant real-fluid effects take place in the transcritical regimes, as evidenced by the steep property variations in the local flowfield. However, their net influence on the flame properties appears to be limited due to the ideal-gas behavior of fluids in the high-temperature zone. (author)
Event-scale power law recession analysis: quantifying methodological uncertainty
NASA Astrophysics Data System (ADS)
Dralle, David N.; Karst, Nathaniel J.; Charalampous, Kyriakos; Veenstra, Andrew; Thompson, Sally E.
2017-01-01
The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship
Power-law time distribution of large earthquakes.
Mega, Mirko S; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea; Vinciguerra, Sergio
2003-05-09
We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.
Elastohydrodynamic analysis using a power law pressure-viscosity relation
NASA Technical Reports Server (NTRS)
Loewenthal, S. H.; Zaretsky, E. V.
1973-01-01
An isothermal elastohydrodynamic (EHD) inlet analysis of the Grubin type which considers a power law pressure-viscosity relation and a finite pressure at the inlet edge of the Hertzian contact zone was performed. Comparisons made with published X-ray EHD film thickness data for a synthetic paraffinic oil and when conventional EHD theory showed that the present theory exhibits a slightly stronger film thickness load dependence than do previous isothermal EHD theories but far less than that exhibited by the measured data.
Power laws, discontinuities and regional city size distributions
Garmestani, A.S.; Allen, C.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. ?? 2008.
Analytical Limit Distributions from Random Power-Law Interactions
NASA Astrophysics Data System (ADS)
Zaid, Irwin; Mizuno, Daisuke
2016-07-01
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
Theory and applications of drilling fluid hydraulics
Whittaker, A.
1985-01-01
A reference on drilling fluid hydraulics, this text provides information, nomenclature and equations. Chapter 1 introduces the basic principles of fluid properties. Chapter 2 discusses the general principles, models and measurements related to fluid flow. Newtonian, Bingham, Power Law, Casson, Robertson-Stiff and Herschel-Bulkley models are all discussed. Chapters 3 through 10 analyze hydraulic problems specific to drilling fluids and the drilling process including: viscometric measurements, pressure losses, swab and surge pressures, cuttings transport, and hydraulics optimization. Each chapter concludes with a bibliography. For consistency, nomenclature remains constant and SI units are used throughout the text. All key equations using oilfield units are listed in the appendices.
A general framework for robust control in fluid mechanics
NASA Astrophysics Data System (ADS)
Bewley, Thomas R.; Temam, Roger; Ziane, Mohammed
2000-04-01
The application of optimal control theory to complex problems in fluid mechanics has proven to be quite effective when complete state information from high-resolution numerical simulations is available [P. Moin, T.R. Bewley, Appl. Mech. Rev., Part 2 47 (6) (1994) S3-S13; T.R. Bewley, P. Moin, R. Temam, J. Fluid Mech. (1999), submitted for publication]. In this approach, an iterative optimization algorithm based on the repeated computation of an adjoint field is used to optimize the controls for finite-horizon nonlinear flow problems [F. Abergel, R. Temam, Theoret. Comput. Fluid Dyn. 1 (1990) 303-325]. In order to extend this infinite-dimensional optimization approach to control externally disturbed flows in which the controls must be determined based on limited noisy flow measurements alone, it is necessary that the controls computed be insensitive to both state disturbances and measurement noise. For this reason, robust control theory, a generalization of optimal control theory, has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite-dimensional linear and nonlinear problems in fluid mechanics. An aim of the present paper is to put such algorithms into a rigorous mathematical framework, for it cannot be assumed at the outset that a solution to the infinite-dimensional robust control problem even exists. In this paper, conditions on the initial data, the parameters in the cost functional, and the regularity of the problem are established such that existence and uniqueness of the solution to the robust control problem can be proven. Both linear and nonlinear problems are treated, and the 2D and 3D nonlinear cases are treated separately in order to get the best possible estimates. Several generalizations are discussed and an appropriate numerical method is proposed.
Pettersen, Klas H; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T
2014-11-01
Power laws, that is, power spectral densities (PSDs) exhibiting 1/f(α) behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency 1/f(α) power laws with power-law exponents analytically identified as α∞(I) = 1/2 for the soma membrane current, α∞(p) = 3/2 for the current-dipole moment, and α∞(V) = 2 for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink (1/f) noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how 1/f(α) power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.
Pettersen, Klas H.; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T.
2014-01-01
Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation. PMID:25393030
Influence of DBT reconstruction algorithm on power law spectrum coefficient
NASA Astrophysics Data System (ADS)
Vancamberg, Laurence; Carton, Ann-Katherine; Abderrahmane, Ilyes H.; Palma, Giovanni; Milioni de Carvalho, Pablo; Iordache, Rǎzvan; Muller, Serge
2015-03-01
In breast X-ray images, texture has been characterized by a noise power spectrum (NPS) that has an inverse power-law shape described by its slope β in the log-log domain. It has been suggested that the magnitude of the power-law spectrum coefficient β is related to mass lesion detection performance. We assessed β in reconstructed digital breast tomosynthesis (DBT) images to evaluate its sensitivity to different typical reconstruction algorithms including simple back projection (SBP), filtered back projection (FBP) and a simultaneous iterative reconstruction algorithm (SIRT 30 iterations). Results were further compared to the β coefficient estimated from 2D central DBT projections. The calculations were performed on 31 unilateral clinical DBT data sets and simulated DBT images from 31 anthropomorphic software breast phantoms. Our results show that β highly depends on the reconstruction algorithm; the highest β values were found for SBP, followed by reconstruction with FBP, while the lowest β values were found for SIRT. In contrast to previous studies, we found that β is not always lower in reconstructed DBT slices, compared to 2D projections and this depends on the reconstruction algorithm. All β values estimated in DBT slices reconstructed with SBP were larger than β values from 2D central projections. Our study also shows that the reconstruction algorithm affects the symmetry of the breast texture NPS; the NPS of clinical cases reconstructed with SBP exhibit the highest symmetry, while the NPS of cases reconstructed with SIRT exhibit the highest asymmetry.
Power Laws in Real Estate Prices during Bubble Periods
NASA Astrophysics Data System (ADS)
Ohnishi, Takaaki; Mizuno, Takayuki; Shimizu, Chihiro; Watanabe, Tsutomu
How can we detect real estate bubbles? In this paper, we propose making use of information on the cross-sectional dispersion of real estate prices. During bubble periods, prices tend to go up considerably for some properties, but less so for others, so that price inequality across properties increases. In other words, a key characteristic of real estate bubbles is not the rapid price hike itself but a rise in price dispersion. Given this, the purpose of this paper is to examine whether developments in the dispersion in real estate prices can be used to detect bubbles in property markets as they arise, using data from Japan and the U.S. First, we show that the land price distribution in Tokyo had a power-law tail during the bubble period in the late 1980s, while it was very close to a lognormal before and after the bubble period. Second, in the U.S. data we find that the tail of the house price distribution tends to be heavier in those states which experienced a housing bubble. We also provide evidence suggesting that the power-law tail observed during bubble periods arises due to the lack of price arbitrage across regions.
Power-law distributions from additive preferential redistributions
NASA Astrophysics Data System (ADS)
Ree, Suhan
2006-02-01
We introduce a nongrowth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed N -particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.
Beyond the power law: Uncovering stylized facts in interbank networks
NASA Astrophysics Data System (ADS)
Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen
2015-06-01
We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.
An Evaluation of Power Law Breakdown in Metals, Alloys, Dispersion Hardened Materials and Compounds
Lesuer, D.R.; Syn, C.K.; Sherby, O.D.
1999-10-20
Creep at high stresses often produces strain rates that exceed those that would be predicted by a power law relationship. In this paper, we examine available high stress creep data for pure metals, solid solution alloys, dispersion strengthened powder metallurgy materials and compounds for power law breakdown (PLB). The results show that, if PLB is observed, then the onset of PLB is generally observed at about {epsilon}/D{sub eff} = 10{sup 13} m{sup -2}, where D{sub eff} is the effective diffusion coefficient incorporating lattice and dislocation pipe diffusion. The common origins of PLB for the various systems studied can be found in the production of excess vacancies by plastic deformation. Anomalous behavior in two pure metals (nickel and tungsten) and a solid solution alloy (Fe-25Cr and Fe-26Cr-1Mo) has been analyzed and provides insight into this excess vacancy mechanism. In metal systems, the onset of PLB is related to a change in the nature of the subgrain structure developed. In the PLB region, subgrains become imperfect containing dislocation tangles adjacent to the sub-boundary, and dislocation cells are evident. The dislocation tangles and cells are the source of excess vacancies and increase the creep rate above that predicted from power law creep. If subgrains do not form then PLB is not observed. In solid solution alloys, in which the dominant deformation resistance results from the interaction of solute atoms with moving dislocations, excess vacancies influence the diffusion of these solute atoms. PLB is not observed in many systems. This is attributed either to the presence of a high equilibrium vacancy concentration (because of a low activation energy for vacancy formation) or to the inability to form subgrains.
A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks
NASA Technical Reports Server (NTRS)
Majumdar, Alok; Bailey, John W.; Schallhorn, Paul; Steadman, Todd
1998-01-01
This paper describes a general purpose computer program for analyzing steady state and transient flow in a complex network. The program is capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program's preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches. The program contains subroutines for computing "real fluid" thermodynamic and thermophysical properties for 33 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride and ammonia. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. Seventeen different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thompson device. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This paper also illustrates the application and verification of the code by comparison with Hardy Cross method for steady state flow and analytical solution for unsteady flow.
Power-Law Type Solutions of Fourth-Order Gravity for Multidimensional Bianchi i Universes
NASA Astrophysics Data System (ADS)
Caprasse, H.; Demaret, J.; Gatermann, K.; Melenk, H.
This paper is devoted to the application of computer algebra to the study of solutions of the field equations derived from a non-linear Lagrangian, as suggested by recently proposed unified theories. More precisely, we restrict ourselves to the most general quadratic Lagrangian, i.e. containing quadratic contributions in the different curvature tensors exclusively. The corresponding field equations are then fourth-order in the metric tensor components. The cosmological models studied are the simplest ones in the class of spatially homogeneous but anisotropic models, i.e. Bianchi I models. For these models, we consider only power-law type solutions of the field equations. All the solutions of the associated system of algebraic equations are found, using computer algebra, from a search of its Groebner bases. While, in space dimension d=3, the Einsteinian-Kasner metric is still the most general power-law type solution, for d>3, no solution, other than the Minkowski space-time, is common to the three systems of equations corresponding to the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution to the Lagrangian (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the d-dimensional space into a (d-3)-dimensional internal space and a physical 3-dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when d=9).
“Slimming” of power-law tails by increasing market returns
NASA Astrophysics Data System (ADS)
Sornette, D.
2002-06-01
We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r> rδ corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power-law exponent and thus the thinner is the tail of the distribution of price returns.
Generalized approach to global renormalization-group theory for fluids
NASA Astrophysics Data System (ADS)
Ramana, A. Sai Venkata; Menon, S. V. G.
2012-04-01
The global renormalization-group theory (GRGT) for fluids is derived starting with the square-gradient approximation for the Helmholtz free energy functional such that any mean-field free energy density and direct correlation function can be employed. The new derivation uses Wilson's functions for representing density fluctuations, thereby relaxing the assumption of cosine variation of density fluctuations used in earlier approaches. The generality of the present approach is shown by deriving the relationships to the earlier developments. A qualitative way to infer the free parameters in the present form of GRGT is also suggested. The new theory is applied to square-well fluids of ranges 1.5 and 3.0 (in units of hard-sphere diameter) and Lennard-Jones fluids. It is shown that the present theory produces a flat isotherm in the two-phase region. Thus the theory accounts for fluctuations at all length scales and avoids the use of Maxwell's construction. An analysis of the liquid-vapor phase diagrams and the critical constants obtained for different potentials shows that, with a mean-field free energy density that is accurate away from the critical region and an appropriate coarse graining length for the mean-field theory, GRGT can provide results in good agreement with the simulation and experimental results.
Mathematical modeling of genome evolution: Where do the power laws come from
NASA Astrophysics Data System (ADS)
Koonin, Eugene
2003-03-01
Power law distributions appear in numerous biological, physical, social 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 interaction partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium were derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models were found and their appearance depending on model parameters was investigated. It was proved that the power law asymptotics appears if, and only if, the model is balanced, i.e., domain duplication (birth) and deletion (death) rates are asymptotically equal up to the second order. It was further proved that any power asymptotic with the degree not equal to -1 can appear only if the assumption of independence of the birth/death rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, were
Chevalier, Thibaud; Talon, Laurent
2015-02-01
In this paper, we numerically investigate the statistical properties of the nonflowing areas of Bingham fluid in two-dimensional porous media. First, we demonstrate that the size probability distribution of the unyielded clusters follows a power-law decay with a large size cutoff. This cutoff is shown to diverge following a power law as the imposed pressure drop tends to a critical value. In addition, we observe that the exponents are almost identical for two different types of porous media. Finally, those scaling properties allow us to account for the quadratic relationship between the pressure gradient and velocity.
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W.
2002-01-01
A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from
Expanding perfect fluid generalizations of the C metric
Wylleman, Lode; Beke, David
2010-05-15
Petrov type D gravitational fields, generated by a perfect fluid with spatially homogeneous energy density and with flow lines which form a nonshearing and nonrotating timelike congruence, are reexamined. It turns out that the anisotropic such spacetimes, which comprise the vacuum C metric as a limit case, can have nonzero expansion, contrary to the conclusion in the original investigation by Barnes [A. Barnes, Gen. Relativ. Gravit. 4, 105 (1973).]. Apart from the static members, this class consists of cosmological models with precisely one symmetry. The general line element is constructed and some important properties are discussed. It is also shown that purely electric Petrov type D vacuum spacetimes admit shear-free normal timelike congruences everywhere, even in the nonstatic regions. This result incited to deduce intrinsic, easily testable criteria regarding shear-free normality and staticity of Petrov type D spacetimes in general, which are added in an appendix.
Deviation from power law of the global seismic moment distribution
NASA Astrophysics Data System (ADS)
Serra, Isabel; Corral, Álvaro
2017-01-01
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to the global CMT earthquake catalog. Although the Tap distribution does not introduce any significant improvement of fit respect the PL, the truncated gamma does. Simulated samples of this distribution, with parameters β = 0.68 and mc = 9.15 and reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, are able to explain the temporal heterogeneity of global seismicity both before and after the great Sumatra-Andaman earthquake of 2004.
Optimized dynamical decoupling for power-law noise spectra
Pasini, S.; Uhrig, G. S.
2010-01-15
We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal pi pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder.
Power-law creep and residual stresses in carbopol microgels
NASA Astrophysics Data System (ADS)
Lidon, Pierre; Manneville, Sebastien
We report on the interplay between creep and residual stresses in carbopol microgels. When a constant shear stress σ is applied below the yield stress σc, the strain is shown to increase as a power law of time, γ (t) =γ0 +(t / τ) α , with and exponent α ~= 0 . 38 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some characteristic value of about σc / 10 , the microgels experience a more complex creep behavior that we link to the existence of residual stresses and to weak aging of the system after preshear. The influence of the preshear protocol, of boundary conditions and of microgel concentration on residual stresses is investigated. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.
Power-law weighted networks from local attachments
NASA Astrophysics Data System (ADS)
Moriano, P.; Finke, J.
2012-07-01
This letter introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on extended power-law weighted networks with both a desired scaling exponent and a fixed clustering coefficient. The analytical results show that the connectivity distribution converges to the scaling behavior often found in social and engineering systems. To illustrate the approach of the proposed framework we generate network substrates that resemble steady state properties of the empirical citation distributions of i) publications indexed by the Institute for Scientific Information from 1981 to 1997; ii) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and iii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.
Deviation from power law of the global seismic moment distribution
Serra, Isabel; Corral, Álvaro
2017-01-01
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to the global CMT earthquake catalog. Although the Tap distribution does not introduce any significant improvement of fit respect the PL, the truncated gamma does. Simulated samples of this distribution, with parameters β = 0.68 and mc = 9.15 and reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, are able to explain the temporal heterogeneity of global seismicity both before and after the great Sumatra-Andaman earthquake of 2004. PMID:28053311
Power-law rheology controls aftershock triggering and decay
Zhang, Xiaoming; Shcherbakov, Robert
2016-01-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established. PMID:27819355
Power-law rheology controls aftershock triggering and decay
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Shcherbakov, Robert
2016-11-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.
Power-law resistivity, magnetic relaxation and ac susceptibility
Gilchrist, J.; van der Beek, C.J.
1994-07-01
The nonlinear diffusion of magnetic flux into a superconducting sample can be studied by measuring the relaxation of the magnetisation after application of a step field or by measuring the ac susceptibility, {chi}{sub 1} and its third harmonic, {chi}{sub 3}, or preferably both methods covering different time scales. Each has been analysed recently for a field-cooled sample of a material whose creep activation energy depends logarithmically on current density, J corresponding to a power-law relation between electric field, E and J. Here, results are compared, using a universal scaling depth. Maximum {chi}{sub 1}{double_prime} {vert_bar}{chi}{sub 3}{vert_bar} and values occur, and also the magnetisation has relaxed to half its initial value when the scaling depth is comparable to the sample half-thickness.
Deviations from uniform power law scaling in nonstationary time series
NASA Technical Reports Server (NTRS)
Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.
1997-01-01
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
Rethinking hospital general ward ventilation design using computational fluid dynamics.
Yam, R; Yuen, P L; Yung, R; Choy, T
2011-01-01
Indoor ventilation with good air quality control minimises the spread of airborne respiratory and other infections in hospitals. This article considers the role of ventilation in preventing and controlling infection in hospital general wards and identifies a simple and cost-effective ventilation design capable of reducing the chances of cross-infection. Computational fluid dynamic (CFD) analysis is used to simulate and compare the removal of microbes using a number of different ventilation systems. Instead of the conventional corridor air return arrangement used in most general wards, air return is rearranged so that ventilation is controlled from inside the ward cubicle. In addition to boosting the air ventilation rate, the CFD results reveal that ventilation performance and the removal of microbes can be significantly improved. These improvements are capable of matching the standards maintained in a properly constructed isolation room, though at much lower cost. It is recommended that the newly identified ventilation parameters be widely adopted in the design of new hospital general wards to minimise cross-infection. The proposed ventilation system can also be retrofitted in existing hospital general wards with far less disruption and cost than a full-scale refurbishment.
Thermodynamics of (2 +1 )-dimensional charged black holes with power-law Maxwell field
NASA Astrophysics Data System (ADS)
Dehghani, M.
2016-11-01
In this work, the three-dimensional nonlinearly charged black holes have been considered with a power-law modified electromagnetic theory. The black hole solutions to Einstein's three-dimensional field equations with a negative cosmological constant have been constructed in the presence of power-law nonlinear electrodynamics. Through the physical and mathematical interpretation of the solutions, a new class of asymptotically anti-de Sitter (AdS) black hole solutions has been introduced. The area law, surface gravity, and Gauss's law are utilized to obtain the entropy, temperature, and electric charge of the new AdS black holes, respectively. The quasilocal mass of the solutions has been calculated based on the counterterm method. A Smarr-type formula for the mass as a function of entropy and charge has been obtained. It has been shown that the thermodynamical quantities satisfy the first law of thermodynamics for the new AdS black holes. Also, it has been found that in order for the Smarr mass formula to be compatible with the first law of black hole thermodynamics, the cosmological parameter Λ should be treated as a thermodynamical variable and the generalized first law of thermodynamics has been introduced. Through the canonical ensemble method, the black hole remnant or phase transitions have been investigated regarding the black hole heat capacity. It has been found that the AdS black hole solutions we just obtained are thermodynamically stable.
NASA Technical Reports Server (NTRS)
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.
Validity of a power law approach to model tablet strength as a function of compaction pressure.
Kloefer, Bastian; Henschel, Pascal; Kuentz, Martin
2010-03-01
Designing quality into dosage forms should not be only based on qualitative or purely heuristic relations. A knowledge space must be generated, in which at least some mechanistic understanding is included. This is of particular interest for critical dosage form parameters like the strength of tablets. In line with this consideration, the scope of the work is to explore the validity range of a theoretically derived power law for the tensile strength of tablets. Different grades of microcrystalline cellulose and lactose, as well as mixtures thereof, were used to compress model tablets. The power law was found to hold true in a low pressure range, which agreed with theoretical expectation. This low pressure range depended on the individual material characteristics, but as a rule of thumb, the tablets having a porosity of more than about 30% or being compressed below 100 MPa were generally well explained by the tensile strength relationship. Tablets at higher densities were less adequately described by the theory that is based on large-scale heterogeneity of the relevant contact points in the compact. Tablets close to the unity density therefore require other theoretical approaches. More research is needed to understand tablet strength in a wider range of compaction pressures.
Brain Network Dynamics Adhere to a Power Law
Tomasi, Dardo G.; Shokri-Kojori, Ehsan; Volkow, Nora D.
2017-01-01
The temporal dynamics of complex networks such as the Internet are characterized by a power scaling between the temporal mean and dispersion of signals at each network node. Here we tested the hypothesis that the temporal dynamics of the brain networks are characterized by a similar power law. This realization could be useful to assess the effects of randomness and external modulators on the brain network dynamics. Simulated data using a well-stablished random diffusion model allowed us to predict that the temporal dispersion of the amplitude of low frequency fluctuations (ALFF) and that of the local functional connectivity density (lFCD) scale with their temporal means. We tested this hypothesis in open-access resting-state functional magnetic resonance imaging datasets from 66 healthy subjects. A robust power law emerged from the temporal dynamics of ALFF and lFCD metrics, which was insensitive to the methods used for the computation of the metrics. The scaling exponents (ALFF: 0.8 ± 0.1; lFCD: 1.1 ± 0.1; mean ± SD) decreased with age and varied significantly across brain regions; multimodal cortical areas exhibited lower scaling exponents, consistent with a stronger influence of external inputs, than limbic and subcortical regions, which exhibited higher scaling exponents, consistent with a stronger influence of internal randomness. Findings are consistent with the notion that external inputs govern neuronal communication in the brain and that their relative influence differs between brain regions. Further studies will assess the potential of this metric as biomarker to characterize neuropathology. PMID:28261049
Khamzin, A A; Popov, I I; Nigmatullin, R R
2014-03-01
Based on the supposition related to fractal nature of transport processes in ion-conducting materials, an expression for the low-frequency ac conductivity dependence was derived. This expression for the ac conductivity generalizes the power-law dependence and gives a possibility to take into account the influence of the electrode polarization effect. The ac conductivity expression obtained is in excellent agreement with experimental data for a wide frequency range.
Generalized Newtonian fluid flow through fibrous porous media
NASA Astrophysics Data System (ADS)
Mierzwiczak, Magdalena; Kołodziej, Jan Adam; Grabski, Jakub Krzysztof
2016-06-01
The numerical calculations of the velocity field and the component of transverse permeability in the filtration equation for steady, incompressible flow of the generalized Newtonian fluid through the assemblages of cylindrical fibers are presented in this paper. The fibers are arranged regularly in arrays. Flow is transverse with respect to the fibers. The non-linear governing equation in the repeated element of the array is solved using iteration method. At each iteration step the method of fundamental solutions and the method of particular solutions are used. The bundle of fibers is treated as a porous media and on the base of velocity field the permeability coefficients are calculated as a function of porosity.
Viscous generalized Chaplygin gas as a unified dark fluid
NASA Astrophysics Data System (ADS)
Li, Wei; Xu, Lixin
2013-06-01
In this paper, we revisit viscous generalized Chaplygin gas (VGCG) as a unified dark fluid, which modifies the pressure only by redefining the effective pressure p eff, according to p_{eff}=p-√{3}ζ0ρ, where ζ 0 is the newly added model parameter which characterizes the viscous property and can be determined by the cosmic observations. By using the currently available cosmic observational data from WMAP, BAO, and SN Ia, the model parameter space is obtained via a Markov Chain Monte Carlo method: ζ0=0.000708_{- 0.00155- 0.00311- 0.00503}^{+ 0.00151+ 0.00275+ 0.00425} in 1, 2, 3 σ regions. The results show that the viscous effect is very small due the value ζ 0≈0 and the VGCG model can match observational data points as well as ΛCDM model.
The time-domain behavior of power-law noises. [of many geophysical phenomena
NASA Technical Reports Server (NTRS)
Agnew, Duncan C.
1992-01-01
The power spectra of many geophysical phenomena are well approximated by a power-law dependence on frequency or wavenumber. A simple expression for the root-mean-square variability of a process with such a spectrum over an interval of time or space is derived. The resulting expression yields the powerlaw time dependence characteristic of fractal processes, but can be generalized to give the temporal variability for more general spectral behaviors. The method is applied to spectra of crustal strain (to show what size of strain events can be detected over periods of months to seconds) and of sea level (to show the difficulty of extracting long-term rates from short records).
Hirose, H
1997-01-01
This paper proposes a new treatment for electrical insulation degradation. Some types of insulation which have been used under various circumstances are considered to degrade at various rates in accordance with their stress circumstances. The cross-linked polyethylene (XLPE) insulated cables inspected by major Japanese electric companies clearly indicate such phenomena. By assuming that the inspected specimen is sampled from one of the clustered groups, a mixed degradation model can be constructed. Since the degradation of the insulation under common circumstances is considered to follow a Weibull distribution, a mixture model and a Weibull power law can be combined. This is called The mixture Weibull power law model. By using the maximum likelihood estimation for the newly proposed model to Japanese 22 and 33 kV insulation class cables, they are clustered into a certain number of groups by using the AIC and the generalized likelihood ratio test method. The reliability of the cables at specified years are assessed.
Theoretical studies of non-Newtonian and Newtonian fluid flow through porous media
Wu, Yu-Shu.
1990-02-01
A comprehensive theoretical study has been carried out on the flow behavior of both single and multiple phase non-Newtonian fluids in porous media. This work is divided into three parts: development of numerical and analytical solutions; theoretical studies of transient flow of non-Newtonian fluids in porous media; and applications of well test analysis and displacement efficiency evaluation to field problems. A fully implicit, integral finite difference model has been developed for simulation of non-Newtonian and Newtonian fluid flow through porous media. Several commonly-used rheological models of power-law and Bingham plastic non-Newtonian fluids have been incorporated in the simulator. A Buckley-Leverett type analytical solution for one-dimensional, immiscible displacement involving non-Newtonian fluids in porous media has been developed. An integral method is also presented for the study of transient flow of Bingham fluids in porous media. In addition, two well test analysis methods have been developed for analyzing pressure transient tests of power-law and Bingham fluids, respectively. Applications are included to demonstrate this new technology. The physical mechanisms involved in immiscible displacement with non-Newtonian fluids in porous media have been studied using the Buckley-Leverett type analytical solution. In another study, an idealized fracture model has been used to obtain some insights into the flow of a power-law fluid in a double-porosity medium. Transient flow of a general pseudoplastic fluid has been studied numerically. 125 refs., 91 figs., 12 tabs.
Power-law cross-correlations estimation under heavy tails
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2016-11-01
We examine the performance of six estimators of the power-law cross-correlations-the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator-under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the α-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.
Power law distributions and dynamic behaviour of stock markets
NASA Astrophysics Data System (ADS)
Richmond, P.
2001-04-01
A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t' = 2Dδ t-t' and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψ ϕ - ln G(ϕ)} where Ψ ϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ2 - cϕ3 and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ>>ɛ, a distribution function with power law tails, viz: P ϕ = exp{ 2bϕ-cϕ2 /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D | J|.
The speed–curvature power law in Drosophila larval locomotion
2016-01-01
We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species. PMID:28120807
Evaluation of detection model performance in power-law noise
NASA Astrophysics Data System (ADS)
Burgess, Arthur E.
2001-06-01
Two alternative forced-choice (2AFC) nodule detection performances of a number of model observers were evaluated for detection of simulated nodules in filtered power-law (1/f3) noise. The models included the ideal observer, the channelized Fisher-Hotelling (FH) model with two different basis function sets, the non-prewhitening matched filter with an eye filter (NPWE), and the Rose model with no DC response (RoseNDC). Detectability of the designer nodule signal was investigated. It has equation s((rho) )equalsA*Rect((rho) /2)(1-(rho) 2)v, where (rho) is a normalized distance (r/R), R is the nodule radius and A is signal amplitude. The nodule profile can be changed (designed) by changing the value of v. For example, the result is a sharp-edged, flat-topped disc for v equal to zero and the projection of a sphere for v equal to 0.5. Human observer experiments were done with nodules based on v equal to 0, 0.5 and 1.5. For the v equal to 1.5 case, human results could be well fitted using a variety of models. The human CD diagram slopes were -0.12, +0.27 and +0.44 for v equal to 0, 0.5 and 1.5 respectively.
There is More than a Power Law in Zipf
Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano
2012-01-01
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law. PMID:23139862
Reciprocity and the Emergence of Power Laws in Social Networks
NASA Astrophysics Data System (ADS)
Schnegg, Michael
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.
NASA Astrophysics Data System (ADS)
Bianucci, M.
2016-01-01
This letter has two main goals. The first one is to give a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the El Ninõ-Southern Oscillation (ENSO) phenomenon. The second one is to obtain, from the theory, an analytical expression for the equilibrium density function of the anomaly sea surface temperature, an expression that fits the data from observations well, reproducing the asymmetry and the power law tail of the histograms of the NIÑO3 index. We succeed in these tasks exploiting some recent theoretical results of the author in the field of the dynamical origin of the stochastic processes. More precisely, we apply this approach to the celebrated recharge oscillator model (ROM), weakly interacting by a multiplicative term, with a general deterministic complex forcing (Madden-Julian Oscillations, westerly wind burst, etc.), and we obtain a Fokker-Planck equation that describes the statistical behavior of the ROM.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The maximum likelihood procedure is developed for estimating the three spectral parameters of an assumed broken power law energy spectrum from simulated detector responses and their statistical properties investigated. The estimation procedure is then generalized for application to real cosmic-ray data. To illustrate the procedure and its utility, analytical methods were developed in conjunction with a Monte Carlo simulation to explore the combination of the expected cosmic-ray environment with a generic space-based detector and its planned life cycle, allowing us to explore various detector features and their subsequent influence on estimating the spectral parameters. This study permits instrument developers to 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.
Collision-dependent power law scalings in two dimensional gyrokinetic turbulence
Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.
2014-08-15
Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.
NASA Astrophysics Data System (ADS)
Saichev, A.; Helmstetter, A.; Sornette, D.
2005-06-01
We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (“fertility”), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities μ is characterized by a power law ~1/μ1+γ. For earthquakes we expect such a power-distribution of fertilities with γ=b/α based on the Gutenberg-Richter magnitude distribution ~ 10-bm and on the increase ~ 10-αm of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions pr(r) and pg(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime γ < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values α=0.8 1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother
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.
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2015-03-01
The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).
Numerical tools for obtaining power-law representations of heavy-tailed datasets
NASA Astrophysics Data System (ADS)
Mansfield, Marc L.
2016-01-01
Many empirical datasets have highly skewed, non-Gaussian, heavy-tailed distributions, dominated by a relatively small number of data points at the high end of the distribution. Consistent with their role as stable distributions, power laws have frequently been proposed to model such datasets. However there are physical situations that require distributions with finite means. Such situations may call for power laws with high-end cutoffs. Here, I present a maximum-likelihood technique for determining an optimal cut-off power law to represent a given dataset. I also develop a new statistical test of the quality of fit. Results are demonstrated for a number of benchmark datasets. Non-power-law datasets can frequently be represented by power laws, but this is a trivial result unless the dataset spans a broad domain. Nevertheless, I demonstrate that there are non-power-law distributions, including broad log-normal distributions, whose tails can be fit to power laws over many orders of magnitude. Therefore, caution is called for whenever power laws are invoked to represent empirical data. Supplementary material in the form of one pdf file available from the Journal web page at: http://dx.doi.org/10.1140/epjb/e2015-60452-3
Shalashilin, Dmitrii V; Beddard, Godfrey S; Paci, Emanuele; Glowacki, David R
2012-10-28
Molecular dynamics (MD) methods are increasingly widespread, but simulation of rare events in complex molecular systems remains a challenge. We recently introduced the boxed molecular dynamics (BXD) method, which accelerates rare events, and simultaneously provides both kinetic and thermodynamic information. We illustrate how the BXD method may be used to obtain high-resolution kinetic data from explicit MD simulations, spanning picoseconds to microseconds. The method is applied to investigate the loop formation dynamics and kinetics of cyclisation for a range of polypeptides, and recovers a power law dependence of the instantaneous rate coefficient over six orders of magnitude in time, in good agreement with experimental observations. Analysis of our BXD results shows that this power law behaviour arises when there is a broad and nearly uniform spectrum of reaction rate coefficients. For the systems investigated in this work, where the free energy surfaces have relatively small barriers, the kinetics is very sensitive to the initial conditions: strongly non-equilibrium conditions give rise to power law kinetics, while equilibrium initial conditions result in a rate coefficient with only a weak dependence on time. These results suggest that BXD may offer us a powerful and general algorithm for describing kinetics and thermodynamics in chemical and biochemical systems.
NASA Astrophysics Data System (ADS)
Mehedi Faruk, Mir; Muktadir Rahman, Md.; Debnath, Dwaipayan; 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.
Power law distribution in high frequency financial data? An econometric analysis
NASA Astrophysics Data System (ADS)
Todorova, Lora; Vogt, Bodo
2011-11-01
Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov-Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.
Do wealth distributions follow power laws? Evidence from ‘rich lists’
NASA Astrophysics Data System (ADS)
Brzezinski, Michal
2014-07-01
We use data on the wealth of the richest persons taken from the 'rich lists' provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012, and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.
NASA Astrophysics Data System (ADS)
Echeverria, J. C.; Rodriguez, E.; Aguilar-Cornejo, M.; Alvarez-Ramirez, J.
2016-10-01
In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA.
POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Das, Sudeep; Hincks, Adam D.; Page, Lyman A.; Staggs, Suzanne T.; Viero, Marco; Bond, J. Richard; Devlin, Mark J.; Reese, Erik D.; Halpern, Mark; Scott, Douglas; Hlozek, Renee; Marriage, Tobias A.; Spergel, David N.; Moodley, Kavilan; Wollack, Edward
2012-06-20
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 {approx}< l {approx}< 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 {mu}m; 1000 {approx}< l {approx}< 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C{sup clust}{sub l}{proportional_to}l{sup -n} with n = 1.25 {+-} 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, {nu}{sup {beta}} B({nu}, T{sub eff}), with a single emissivity index {beta} = 2.20 {+-} 0.07 and effective temperature T{sub eff} = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be {alpha}{sub 150-220} = 3.68 {+-} 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Power law olivine crystal size distributions in lithospheric mantle xenoliths
NASA Astrophysics Data System (ADS)
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.
Exponential and power-law mass distributions in brittle fragmentation
NASA Astrophysics Data System (ADS)
Åström, J. A.; Linna, R. P.; Timonen, J.; Møller, Peder Friis; Oddershede, Lene
2004-08-01
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size s scales as s-(2D-1)/Df1(-(2/λ)Ds)+f2(-s0-1(λ+s1/D)D) , where D is the Euclidean dimension of the space, λ is the penetration depth, and f1 and f2 can be approximated by exponential functions. Simulation results and experiments can both be described by this theoretical fragment-size distribution. The typical largest fragment size s0 was found to diverge at the minimum strain required for fragmentation as it is inversely related to the density of initially formed cracks. Our results also indicate that scaling of s0 close to this divergence depends on, e.g., loading conditions, and thus is not universal. At the same time, the density of fragment surface vanishes as L-1 , L being the linear dimension of the brittle solid. The results obtained provide an explanation as to why the fragment-size distributions found in nature can have two components, an exponential as well as a power-law component, with varying relative weights.
Power-Law Template for IR Point Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglass; Spergel, David N.; Staggs,Suzanne T.; Wollack, Edward
2011-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Power-Law Template for Infrared Point-Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark J.; Halpern, Mark; Hincks, Adam D; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglas; Spergel, David N.; Staggs, Suzanne T.; Wollack, Edward
2012-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ?(sup Beta)B(?, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Beets, I A M; Rösler, F; Fiehler, K
2010-09-01
Few studies have reported direct effects of motor learning on visual perception, especially when using novel movements for the motor system. Atypical motor behaviors that violate movement constraints provide an excellent opportunity to study action-to-perception transfer. In our study, we passively trained blindfolded participants on movements violating the 2/3 power law. Before and after motor training, participants performed a visual discrimination task in which they decided whether two consecutive movements were same or different. For motor training, we randomly assigned the participants to two motor training groups or a control group. The motor training group experienced either a weak or a strong elliptic velocity profile on a circular trajectory that matched one of the visual test stimuli. The control group was presented with linear trajectories unrelated to the viewed movements. After each training session, participants actively reproduced the movement to assess motor learning. The group trained on the strong elliptic velocity profile reproduced movements with increasing elliptic velocity profiles while circular geometry remained constant. Furthermore, both training groups improved in visual discrimination ability for the learned movement as well as for highly similar movements. Participants in the control group, however, did not show any improvements in the visual discrimination task nor did participants who did not acquire the trained movement. The present results provide evidence for a transfer from action to perception which generalizes to highly related movements and depends on the success of motor learning. Moreover, under specific conditions, it seems to be possible to acquire movements deviating from the 2/3 power law.
Caduff, Marloes; Huijbregts, Mark A J; Althaus, Hans-Joerg; Hendriks, A Jan
2011-01-15
To perform life-cycle assessment studies, data on the production and use of the products is required. However, often only few data or measurements are available. Estimation of properties can be performed by applying scaling relationships. In many disciplines, they are used to either predict data or to search for underlying patterns, but they have not been considered in the context of product assessments hitherto. The goal of this study was to explore size scaling for commonly used energy conversion equipment, that is, boilers, engines, and generators. The variables mass M, fuel consumption Q, and costs C were related to power P. The established power-law relationships were M = 10(0.73.. 1.89)P(0.64.. 1.23) (R(2) ≥ 0.94), Q = 10(0.06.. 0.68)P(0.82.. 1.02) (R(2) ≥ 0.98) and C = 10(2.46.. 2.86)P(0.83.. 0.85) (R(2) ≥ 0.83). Mass versus power and costs versus power showed that none of the equipment types scaled isometrically, that is, with a slope of 1. Fuel consumption versus power scaled approximately isometrically for steam boilers, the other equipments scaled significantly lower than 1. This nonlinear scaling behavior induces a significant size effect. The power laws we established can be applied to scale the mass, fuel consumption and costs of energy conversion equipments up or down. Our findings suggest that empirical scaling laws can be used to estimate properties, particularly relevant in studies focusing on early product development for which generally only little information is available.
Relativistic model of anisotropic charged fluid sphere in general relativity
NASA Astrophysics Data System (ADS)
Pant, Neeraj; Pradhan, N.; Bansal, Rajeev K.
2016-01-01
In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters. In the absence of pressure anisotropy and charge present model reduces to the isotropic model Pant et al. (Astrophys. Space Sci. 330:353-359, 2010). Our solution is well behaved in all respects for all values of X lying in the range 0< X ≤ 0.18, α lying in the range 0 ≤ α ≤6.6, K lying in the range 0< K ≤ 6.6 and Schwarzschild compactness parameter "u" lying in the range 0< u ≤ 0.38. Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X=0.088, α=0.6 and K=4.3 for which u=0.2054 and by assuming surface density ρb = 4.6888 × 10^{14} g/cm3 the mass and radius are found to be 1.51 M_{\\varTheta} and 10.90 km respectively. Assuming surface density ρb = 2 × 10^{14} g/cm3 the mass and radius for a neutron star candidate are found to be 2.313 M_{\\varTheta} and 16.690 km respectively. Hence we obtain masses and radii that fall in the range of what is generally expected for quark stars and neutron stars.
AEGIS: A MULTIWAVELENGTH STUDY OF SPITZER POWER-LAW GALAXIES
Park, S. Q.; Barmby, P.; Willner, S. P.; Ashby, M. L. N.; Fazio, G. G.; Georgakakis, A.; Ivison, R. J.; Konidaris, N. P.; Rosario, D. J.; Nandra, K.
2010-07-10
This paper analyzes a sample of 489 Spitzer/Infrared Array Camera (IRAC) sources in the Extended Groth Strip (EGS), whose spectral energy distributions fit a red power law (PL) from 3.6 to 8.0 {mu}m. The median redshift for sources with known redshifts is (z) = 1.6. Though all or nearly all of the sample galaxies are likely to be active galactic nuclei (AGNs), only 33% were detected in the EGS X-ray survey (AEGIS-X) using 200 ks Chandra observations. The detected sources are X-ray luminous with L {sub X}>10{sup 43} erg s{sup -1} and moderately to heavily obscured with N {sub H}>10{sup 22} cm{sup -2}. Stacking the X-ray-undetected sample members yields a statistically significant X-ray signal, suggesting that they are on average more distant or more obscured than sources with X-ray detections. The ratio of X-ray to mid-infrared fluxes suggests that a substantial fraction of the sources undetected in X-rays are obscured at the Compton-thick level, in contrast to the X-ray-detected sources, all of which appear to be Compton thin. For the X-ray-detected PL sources with redshifts, an X-ray luminosity L {sub X} {approx} 10{sup 44} erg s{sup -1} marks a transition between low-luminosity, blue sources dominated by the host galaxy to high-luminosity, red PL sources dominated by nuclear activity. X-ray-to-optical ratios, infrared variability, and 24 {mu}m properties of the sample are consistent with the identification of infrared PL sources as active nuclei, but a rough estimate is that only 22% of AGNs are selected by the PL criteria. Comparison of the PL selection technique and various IRAC color criteria for identifying AGNs confirms that high-redshift samples selected via simple IRAC colors may be heavily contaminated by starlight-dominated objects.
Scale Invariance in Landscape Evolution Models Using Stream Power Laws
NASA Astrophysics Data System (ADS)
Kwang, J. S.; Parker, G.
2014-12-01
Landscape evolution models (LEM) commonly utilize stream power laws to simulate river incision with formulations such as E = KAmSn, where E is a vertical incision rate [L/T], K is an erodibility constant [L1-2m/T], A is an upstream drainage area [L2], S is a local channel gradient [-], and m and n are positive exponents that describe the basin hydrology. In our reduced complexity model, the landscape approached equilibrium by balancing an incision rate with a constant, uniform, vertical rock uplift rate at every location in the landscape. From our simulations, for a combination of m and n, the landscape exhibited scale invariance. That is, regardless of the size and scale of the basin, the relief and vertical structure of the landscape remained constant. Therefore, the relief and elevation profile of the landscape at equilibrium were only dependent on the coefficients for erodibility and uplift and an equation that described how upstream area, A, increased as the length of a stream increased. In our analytical 1D models, we utilized two equations that described upslope area, (a) A = Bl, where B is the profile width [L], and l is the stream length from the ridge [L] and (b) A = Clh, Hack's Law, where C is a constant [L2-h] and h is a positive exponent. With these equations, (a) m = n and (b) hm = n resulted in scale invariance. In our numerical 2D models, the relationship between A and l was inherent in the actual structure of the drainage network. From our numerical 2D results, scale invariance occurred when 2m = n. Additionally, using reasonable values from the literature for exponents, n, m and h, resulted in singularities at the ridges in the landscape, which caused truncation error. In consequence, the elevation of the ridge increased as the number of grid cells in the domain increased in the numerical model, and the model was unable to converge. These singularities at the ridges appeared when (a) m ≥ n and (b) hm ≥ n in the analytical model and 2m ≥ n in
Simple inflationary quintessential model. II. Power law potentials
NASA Astrophysics Data System (ADS)
de Haro, Jaume; Amorós, Jaume; Pan, Supriya
2016-09-01
The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive
The Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid
NASA Astrophysics Data System (ADS)
Fetecau, Corina; Jamil, Muhammad; Fetecau, Constantin; Vieru, Dumitru
2009-09-01
The velocity field corresponding to the Rayleigh-Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.
Blinking in quantum dots: The origin of the grey state and power law statistics
NASA Astrophysics Data System (ADS)
Ye, Mao; Searson, Peter C.
2011-09-01
Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State
NASA Astrophysics Data System (ADS)
Stoop, Ruedi; Gomez, Florian
2016-07-01
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
On the origin of power-law X-ray spectra of active galactic nuclei
NASA Technical Reports Server (NTRS)
Schlosman, I.; Shaham, J.; Shaviv, G.
1984-01-01
In the present analytical model for a power law X-ray continuum production in active galactic nuclei, the dissipation of turbulent energy flux above the accretion disk forms an optically thin transition layer with an inverted temperature gradient. The emitted thermal radiation has a power law spectrum in the 0.1-100 keV range, with a photon energy spectral index gamma of about 0.4-1.0. Thermal X-ray contribution from the layer is 5-10 percent of the total disk luminosity. The gamma value of 0.75 is suggested as a 'natural' power law index for Seyfert galaxies and QSOs.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State.
Stoop, Ruedi; Gomez, Florian
2016-07-15
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
The double power law in human collaboration behavior: The case of Wikipedia
NASA Astrophysics Data System (ADS)
Kwon, Okyu; Son, Woo-Sik; Jung, Woo-Sung
2016-11-01
We study human behavior in terms of the inter-event time distribution of revision behavior on Wikipedia, an online collaborative encyclopedia. We observe a double power law distribution for the inter-editing behavior at the population level and a single power law distribution at the individual level. Although interactions between users are indirect or moderate on Wikipedia, we determine that the synchronized editing behavior among users plays a key role in determining the slope of the tail of the double power law distribution.
The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer
NASA Astrophysics Data System (ADS)
Castillo, Luciano; Hussain, Fazle
2017-02-01
Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ' + and the Reynolds shear stress, u'v'¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50 ≤y+≤170 ). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u' 2 ¯+ and v'θ'¯+ change little with the strength of acceleration, while v'+, w'+, and u'v'¯+ continue to decay in the flow direction. Furthermore, θ'+ and u'θ'¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for "transient growth" generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, "Coherent structure generation near-wall turbulence," J. Fluid Mech. 453, 57-108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.
Richardson, Magnus J E; Flash, Tamar
2002-09-15
The movements of the human arm have been extensively studied for a variety of goal-directed experimental tasks. Analyses of the trajectory and velocity of the arm have led to many hypotheses for the planning strategies that the CNS might use. One family of control hypotheses, including minimum jerk, snap and their generalizations to higher orders, comprises those that favor smooth movements through the optimization of an integral cost function. The predictions of each order of this family are examined for two standard experimental tasks: point-to-point movements and the periodic tracing of figural forms, and compared both with experiment and the two-thirds power law. The aim of the analyses is to generalize previous numerical observations as well as to examine movement segmentation. It is first shown that contrary to recent statements in the literature, the only members of this family of control theories that match reaching movement experiments well are minimum jerk and snap. Then, for the case of periodic drawing, both the ellipse and cloverleaf are examined and the experimentally observed power law is derived from a first-principles approach. The results for the ellipse are particularly general, representing a unification of the two-thirds power law and smoothness hypotheses for ellipses of all reasonable eccentricities. For complex shapes it is shown that velocity profiles derived from the cost-function approach exhibit the same experimental features that were interpreted as segmented control by the CNS. Because the cost function contains no explicit segmented control, this result casts doubt on such an interpretation of the experimental data.
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1991-07-01
Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
SALE2D. General Transient Fluid Flow Algorithm
Amsden, A.A.; Ruppel, H.M.; Hirt, C.W.
1981-06-01
SALE2D calculates two-dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a two-dimensional network of quadrilateral cells for either cylindrical or Cartesian coordinates, and a variety of user-selectable boundary conditions are provided in the program.
Charged Noncommutative Wormhole Solutions via Power-Law f(T) Models
NASA Astrophysics Data System (ADS)
Rani, Shamaila; Jawad, Abdul; Bilal Amin, M.
2016-10-01
In this paper, we explore static spherically symmetric charged wormhole solutions in extended teleparallel gravity taking power-law f(T) models. We consider noncommutative geometry under Lorentzian distribution. In order to obtain matter components, we develop field equations using effective energy-momentum tensor for non-diagonal tetrad. We explore solutions by considering various viable power-law f(T) models, which also include teleparallel gravity case. The violation of energy conditions obtain by exotic matter to form wormhole solutions in teleparallel case while, physical acceptable wormhole solutions exist for charged noncommutative wormhole solutions for some cases of power-law models. The effective energy-momentum tensor and charge are responsible for the violation of the energy conditions. Also, we check the equilibrium condition for these solutions. The equilibrium condition meets for the teleparallel case and some power-law solutions while remaining solutions are either in less equilibrium or in disequilibrium situation.
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.
Convex and concave successions of power-law decays in small-angle scattering
NASA Astrophysics Data System (ADS)
Anitas, E. M.
2016-08-01
The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with fractal iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: convex/concave - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power- law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.
Sato, Aki-Hiro
2004-04-01
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
NASA Astrophysics Data System (ADS)
Sato, Aki-Hiro
2004-04-01
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
Exploring the effect of power law social popularity on language evolution.
Gong, Tao; Shuai, Lan
2014-01-01
We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
Oliveira, Gilson F. de Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de
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.
Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems
NASA Astrophysics Data System (ADS)
Rodin, Aleksandr; Fogler, Michael
2011-03-01
Observation of power-law dependence of conductance on temperature and voltage has been reported for a wide variety of low-dimensional systems(nano-wires, nano-tubes, and conducting polymers). This behavior has been attributed to the Luttinger liquid effects expected in a pure one-dimensional wire. However, the systems studied were neither one-dimensional nor defect-free. Using numerical simulations we show that the power-law behavior can arise from variable-range hopping in an ensemble of non-interacting disordered wires connected in parallel. This power-law behavior holds in restricted ranges of voltage and temperature, typical of experimental situations. Physically, it comes from rare, but highly conducting hopping paths that appear by chance in some members of the ensemble. The power-law exponents and their dependence on system parameters are consistent with the great majority of available empirical data. Supported by Grant NSF DMR-0706654.
An Analytical Model of Wave-Induced Longshore Current Based on Power Law Wave Height Decay.
1988-01-01
34I ANALYtTICAL MODEL OF NAVE-INDUCED LON6SHORE CURRENT BASED ON PONE* LAW.. (U) COASTAL ENG INEERING RESEAKNH CENTER VICKSBURG NS J N SMITH ET AL...j . - .L .V . : ; * AN ANALYTICAL MODEL OF WAVE-INDUCED ~ z * LONGSHORE CURRENT BASED ON POWER LAW * - WAVE HEIGHT DECAY by Jane McKee...I_ I IF 31592 11. TITLE (Include Security Classfication) • An Analytical Model of Wave-Induced Longshore Current Based on Power Law . Wave
Analytical study of solitons in the fiber waveguide with power law nonlinearity
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah
2017-01-01
This work deals with the existence of exact soliton solutions in fiber waveguide with power law nonlinearity. The propagation equation that is the resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity is studied by three analytical methods. The integration tools are the extended trial equation method, exp(-Φ(ξ)) -expansion method and extended G‧ / G - expansion method. The presented results show that analytical optical solitons can exist in this setting.
Conductivity scaling in supercritical percolation of nanoparticles--not a power law.
Li, Jiantong; Östling, Mikael
2015-02-28
The power-law behavior widely observed in supercritical percolation systems of conductive nanoparticles may merely be a phenomenological approximation to the true scaling law not yet discovered. In this work, we derive a comprehensive yet simple scaling law and verify its extensive applicability to various experimental and numerical systems. In contrast to the power law which lacks theoretical backing, the new scaling law is explanatory and predictive, and thereby helpful to gain more new insights into percolation systems of conductive nanoparticles.
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model
Teka, Wondimu; Stockton, David; Santamaria, Fidel
2016-01-01
We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron. PMID:26937967
Fluid spheres of uniform density in general relativity
Ponce de Leon, J.
1986-01-01
A number of exact solutions for spherically symmetric nonstatic fluids of uniform density, surrounded by empty space, are derived and investigated. Solutions that represent expanding and contracting spheres, which tend asymptotically to static configurations described by the Schwarzschild interior solution ( rho = const), are obtained In some cases the motion of contraction or expansion is reversed, while in other cases there is no bouncing at all. Oscillating solutions are presented.
Electro-osmotic mobility of non-Newtonian fluids
Zhao, Cunlu; Yang, Chun
2011-01-01
Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy–Chapman solution to the Poisson–Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases. PMID:21503161
Electro-osmotic mobility of non-Newtonian fluids.
Zhao, Cunlu; Yang, Chun
2011-03-23
Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy-Chapman solution to the Poisson-Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases.
Age Differences in Fluid Intelligence: Contributions of General Slowing and Frontal Decline
ERIC Educational Resources Information Center
Bugg, Julie M.; Zook, Nancy A.; DeLosh, Edward L.; Davalos, Deana B.; Davis, Hasker P.
2006-01-01
The current study examined the contributions of general slowing and frontal decline to age differences in fluid intelligence. Participants aged 20-89 years completed Block Design, Matrix Reasoning, simple reaction time, choice reaction time, Wisconsin Card Sorting, and Tower of London tasks. Age-related declines in fluid intelligence, speed of…
30 CFR 250.455 - What are the general requirements for a drilling fluid program?
Code of Federal Regulations, 2010 CFR
2010-07-01
... drilling fluid program? 250.455 Section 250.455 Mineral Resources MINERALS MANAGEMENT SERVICE, DEPARTMENT OF THE INTERIOR OFFSHORE OIL AND GAS AND SULPHUR OPERATIONS IN THE OUTER CONTINENTAL SHELF Oil and Gas Drilling Operations Drilling Fluid Requirements § 250.455 What are the general requirements for...
Stochastic modeling of the migration of Cs-137 in the soil considering a power law tailing in space
NASA Astrophysics Data System (ADS)
Oka, Hiroki; Hatano, Yuko
2016-04-01
We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. In our past study, we derived the analytic solution under the generalized Robin boundary condition (Oka-Yamamoto solution). This is a generalization of the He-Walling solution (1996). We compared our solution with the Fukushima soil data of for 3 years after the accident and found that the concentration of Cs-137 has a discrepancy from our solution, specifically in a deep part because the depth profiles have a power law tailing. Therefore, we improved our model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x,t|D) in terms of the diffusion coefficient D and calculate C(x,t)=∫_(0~∞) C(x,t|D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.
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.
Wave-speed dispersion associated with an attenuation obeying a frequency power law.
Buckingham, Michael J
2015-11-01
An attenuation scaling as a power of frequency, |ω|(β), over an infinite bandwidth is neither analytic nor square-integrable, thus calling into question the application of the Kramers-Krönig dispersion relations for determining the frequency dependence of the associated phase speed. In this paper, three different approaches are developed, all of which return the dispersion formula for the wavenumber, K(ω). The first analysis relies on the properties of generalized functions and the causality requirement that the impulse response, k(t), the inverse Fourier transform of -iK(ω), must vanish for t < 0. Second, a wave equation is introduced that yields the phase-speed dispersion associated with a frequency-power-law attenuation. Finally, it is shown that, with minor modification, the Kramers-Krönig dispersion relations with no subtractions (the Plemelj formulas) do in fact hold for an attenuation scaling as |ω|(β), yielding the same dispersion formula as the other two derivations. From this dispersion formula, admissible values of the exponent β are established. Physically, the inadmissible values of β, which include all the integers, correspond to attenuation-dispersion pairs whose Fourier components cannot combine in such a way as to make the impulse response, k(t), vanish for t < 0. There is no upper or lower limit on the value that β may take.
A Recommended Procedure for Estimating the Cosmic Ray Spectral Parameter of a Simple Power Law
NASA Technical Reports Server (NTRS)
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.
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.
Wright, Christopher K
2010-07-01
Although habitat networks show promise for conservation planning at regional scales, their spatiotemporal dynamics have not been well studied, especially in climate-sensitive landscapes. Here I use satellite remote sensing to compile wetland habitat networks from the Prairie Pothole Region (PPR) of North America. An ensemble of networks assembled across a hydrologic gradient from deluge to drought and a range of representative dispersal distances exhibits power-law scaling of important topological parameters. Prairie wetland networks are "meso-worlds" with mean topological distance increasing faster with network size than small-world networks, but slower than a regular lattice (or "large world"). This scaling implies rapid dispersal through wetland networks without some of the risks associated with "small worlds" (e.g., extremely rapid propagation of disease or disturbance). Retrospective analysis of wetland networks establishes a climatic envelope for landscape connectivity in the PPR, where I show that a changing climate might severely impact metapopulation viability and restrict long-distance dispersal and range shifts. More generally, this study demonstrates an efficient approach to conservation planning at a level of abstraction addressing key drivers of the global biodiversity crisis: habitat fragmentation and climatic change.
NASA Astrophysics Data System (ADS)
Eadie, Chris; Favis-Mortlock, David
2010-05-01
distribution is fitted, but a much longer recurrence interval — on the order of 1000 years — using the USA's standard LP3 method. In addition Pandey et al. (1998) found that fitting a power-law distribution, compared with fitting a Generalized Extreme Value distribution, can lead to a large decrease in the predicted return period for a given flood event. Both these findings have obvious implications for river management design. Power-law distributions have been fitted to fluvial discharge data by many authors (most notably by Malamud et al., 1996 and Pandey et al., 1998), who then use these fitted distributions to estimate flow probabilities. These authors found that the power-law performed as well or better than many of the distributions currently used around the world, despite utilising fewer parameters. The power-law has not, however, been officially adopted by any country for fitting to fluvial discharge data. This paper demonstrates a statistically robust method, based on Maximum Likelihood Estimation, for fitting a power-law distribution to mean daily streamflows. The fitted distribution is then used to calculate return periods, which are compared to the return periods obtained by other, more commonly used, distributions. The implications for river management, extremes of flow in particular, are then explored.
Kong, Feng; Chen, Zhencai; Xue, Song; Wang, Xu; Liu, Jia
2015-11-01
Lower parental education impairs cognitive abilities of their offspring such as general fluid intelligence dependent on the prefrontal cortex (PFC), but the independent contribution of mother's and father's education is unknown. We used an individual difference approach to test whether mother's and father's education independently affected general fluid intelligence in emerging adulthood at both the behavioral and neural level. Behaviorally, mother's but not father's education accounted for unique variance in general fluid intelligence in emerging adulthood (assessed by the Raven's advanced progressive matrices). Neurally, the whole-brain correlation analysis revealed that the regional gray matter volume (rGMV) in the medial PFC was related to both mother's education and general fluid intelligence but not father's education. Furthermore, after controlling for mother's education, the association between general fluid intelligence and the rGMV in medial PFC was no longer significant, indicating that mother's education plays an important role in influencing the structure of the medial PFC associated with general fluid intelligence. Taken together, our study provides the first behavioral and neural evidence that mother's education is a more important determinant of general cognitive ability in emerging adulthood than father's education.
Conformal collineations and anisotropic fluids in general relativity
NASA Astrophysics Data System (ADS)
Duggal, K. L.; Sharma, R.
1986-10-01
Recently, Herrera et al. [L. Herrera, J. Jimenez, L. Leal, J. Ponce de Leon, M. Esculpi, and V. Galino, J. Math. Phys. 25, 3274 (1984)] studied the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter. They concluded that for special conformal motions, the stiff equation of state (p=μ) is singled out in a unique way, provided the generating conformal vector field is orthogonal to the four-velocity. In this paper, the same problem is studied by using conformal collineations (which include conformal motions as subgroups). It is shown that, for a special conformal collineation, the stiff equation of state is not singled out. Non-Einstein Ricci-recurrent spaces are considered as physical models for the fluid matter.
Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid
NASA Astrophysics Data System (ADS)
Karra, Satish; Rajagopal, K. R.
2012-02-01
The mechanical response and load bearing capacity of high performance polymer composites changes due to degradation or healing associated with diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation/healing mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid—which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context—creeps and stress relaxes due to degradation/healing when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a degrading/healing generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection-diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions
NASA Astrophysics Data System (ADS)
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy γr-α . Such systems are useful in modeling melting transitions. The limit α→∞ corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (α>3) and repulsive (γ>0) interactions. The geometric theory solutions for given α>3 , γ>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b(ρT-3/α) , where ρ is the density; (2) all solutions are equivalent up to a single scaling constant for ρT-3/α , related to γ via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3<α<3.7913 , the solution goes from the low to the expected high density limit smoothly; (6) for α>3.7913 a phase transition is required to go between these regimes; (7) for any α>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if α→∞ , the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.
NASA Astrophysics Data System (ADS)
Boyko, Evgeniy; Bercovici, Moran; Gat, Amir
2016-11-01
We analyze flow of a non-Newtonian fluid in a Hele-Shaw cell, subjected to spatially non-uniform electroosmotic flow. We specifically focus on power-law fluids with wall depletion properties and derive a p-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behavior. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one and two dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behavior. The asymptotic model thus enables prediction of the flow and pressure fields for non-Newtonian fluids, and may be particularly useful for the analysis and design of microfluidic systems involving electro-kinetic transport of such fluids.
Direct simulation Monte Carlo of rarefied hypersonic flow on power law shaped leading edges
NASA Astrophysics Data System (ADS)
Santos, Wilson Fernando Nogueira Dos
A numerical study of several parameters that influence the flowfield structure, aerodynamic surface quantities and shock wave structure at rarefied hypersonic flow conditions is conducted on power law shaped leading edges. The calculations are performed with a detailed computer code that properly accounts for nonequilibrium effects and that has been demonstrated to yield excellent comparisons with flight- and ground-test data. The flowfield structure, aerodynamic surface quantities and shock wave structure of power law shaped leading edges are examined in order to provide information on how well these shapes could stand as possible candidates for blunting geometries of hypersonic leading edges. Newtonian flow analysis has shown that these shapes exhibit both blunt and sharp aerodynamic properties. Moreover, computational investigation of minimum-drag bodies at supersonic and moderate hypersonic speeds has indicated that power law shapes for certain exponents yield the lowest wave drag. These qualities make power law shapes strong candidates for leading edge design. A very detailed description of the impact on the flow properties, such as velocity, density, temperature and pressure, has been presented separately in the vicinity of the nose of the leading edges due to changes in their shapes. Numerical solutions show that the shape of the leading edge disturbed the flowfield far upstream, where the domain of influence decreased as the leading edge became aerodynamically sharp. A detailed procedure is presented to predict the pressure gradient along the body surface in a rarefied environment. Numerical solutions show that the pressure gradient behavior follows that predicted by Newtonian theory. It is found that the pressure gradient along the body surface goes to zero at the nose of the leading edge for power law exponents less than 2/3, a characteristic of a blunt body. It is finite for power law exponent of 2/3 and goes to minus infinite for power law exponents
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
Gutiérrez, Ricardo; Garrahan, Juan P; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity.
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions
NASA Astrophysics Data System (ADS)
Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.
Constraints on the tensor-to-scalar ratio for non-power-law models
NASA Astrophysics Data System (ADS)
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M. P.
2013-08-01
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 & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: rLD = 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.
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.
Double Power Laws in the Event-integrated Solar Energetic Particle Spectrum
NASA Astrophysics Data System (ADS)
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K.
2016-04-01
A double power law or a power law with exponential rollover at a few to tens of MeV nucleon-1 of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochastic approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon-1 is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.
The JKR-type adhesive contact problems for power-law shaped axisymmetric punches
NASA Astrophysics Data System (ADS)
Borodich, Feodor M.; Galanov, Boris A.; Suarez-Alvarez, Maria M.
2014-08-01
The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres, and between a flat-ended axisymmetric punch and an elastic half-space respectively. However, the shapes of contacting solids may be more general than spherical or flat ones. In addition, the derivation of the main formulae of these models is based on the assumption that the material points within the contact region can move along the punch surface without any friction. However, it is more natural to assume that a material point that came to contact with the punch sticks to its surface, i.e. to assume that the non-slipping boundary conditions are valid. It is shown that the frictionless JKR model may be generalized to arbitrary convex, blunt axisymmetric body, in particular to the case of the punch shape being described by monomial (power-law) punches of an arbitrary degree d≥1. The JKR and Boussinesq-Kendall models are particular cases of the problems for monomial punches, when the degree of the punch d is equal to two or it goes to infinity respectively. The generalized problems for monomial punches are studied under both frictionless and non-slipping (or no-slip) boundary conditions. It is shown that regardless of the boundary conditions, the solution to the problems is reduced to the same dimensionless relations among the actual force, displacements and contact radius. The explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. Connections of the results obtained for problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape and the shape function can be approximated by a monomial function of radius, are discussed.
ERIC Educational Resources Information Center
Binous, Housam
2007-01-01
We study four non-Newtonian fluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…
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.
Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays
NASA Astrophysics Data System (ADS)
Sibatov, R. T.
2011-08-01
A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.
Taylor's power law of fluctuation scaling and the growth-rate theorem.
Cohen, Joel E
2013-09-01
Taylor's law (TL), a widely verified empirical relationship in ecology, states that the variance of population density is approximately a power-law function of mean density. The growth-rate theorem (GR) states that, in a subdivided population, the rate of change of the overall growth rate is proportional to the variance of the subpopulations' growth rates. We show that continuous-time exponential change implies GR at every time and, asymptotically for large time, TL with power-law exponent 2. We also show why diverse population-dynamic models predict TL in the limit of large time by identifying simple features these models share: If the mean population density and the variance of population density are (exactly or asymptotically) non-constant exponential functions of a parameter (e.g., time), then the variance of density is (exactly or asymptotically) a power-law function of mean density.
Power-law X-ray and gamma-ray emission from relativistic thermal plasmas
NASA Technical Reports Server (NTRS)
Zdziarski, A. A.
1985-01-01
A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.
NASA Astrophysics Data System (ADS)
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.
The fractal nature of nature: power laws, ecological complexity and biodiversity.
Brown, James H; Gupta, Vijay K; Li, Bai-Lian; Milne, Bruce T; Restrepo, Carla; West, Geoffrey B
2002-01-01
Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science. PMID:12079523
The fractal nature of nature: power laws, ecological complexity and biodiversity.
Brown, James H; Gupta, Vijay K; Li, Bai-Lian; Milne, Bruce T; Restrepo, Carla; West, Geoffrey B
2002-05-29
Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science.
Power laws from individual differences in learning and forgetting: mathematical analyses.
Murre, Jaap M J; Chessa, Antonio G
2011-06-01
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 functions, if the distribution of learning rates follows a gamma distribution, a uniform distribution, or a half-normal function. Through a number of simulations, we further investigate to what extent these findings may affect empirical results in practice.
NASA Astrophysics Data System (ADS)
Tippett, Michael K.; Cohen, Joel E.
2016-02-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from `outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
Eliazar, Iddo
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.
Tippett, Michael K; Cohen, Joel E
2016-02-29
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.
Spherical collapse model and cluster number counts in power-law f(T) gravity
NASA Astrophysics Data System (ADS)
Malekjani, M.; Basilakos, S.; Heidari, N.
2017-04-01
We study the spherical collapse model in the framework of spatially flat power law f(T) ∝ (- T)b gravity model. We find that the linear and non-linear growth of spherical overdensities of this particular f(T) model are affected by the power-law parameter b. Finally, we compute the predicted number counts of virialized haloes in order to distinguish the current f(T) model from the expectations of the concordance Λ cosmology. Specifically, the present analysis suggests that the f(T) gravity model with positive (negative) b predicts more (less) virialized objects with respect to those of Λ cold dark matter.
Power-law behavior of power spectra in low Prandtl number Rayleigh-Bénard convection.
Paul, M R; Cross, M C; Fischer, P F; Greenside, H S
2001-10-08
The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; Nalewajko, K.; Begelman, M. C.
2015-12-30
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron–positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power law ${\\gamma }^{-\\alpha }$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.
One-dimensional quantum liquids with power-law interactions: the Luttinger staircase.
Dalmonte, M; Pupillo, G; Zoller, P
2010-10-01
We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|(β), with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a "Luttinger staircase." Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.
Transport coefficients in Lorentz plasmas with the power-law kappa-distribution
Jiulin, Du
2013-09-15
Transport coefficients in Lorentz plasma with the power-law κ-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient, and thermal conductivity for the power-law κ-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the κ-parameter, and in the limit of the parameter κ→∞ they are reduced to the standard forms for a Maxwellian distribution.
Numerical Simulations of Power Law Heating Functions for Quiescent Loops: Stability and Observables
NASA Astrophysics Data System (ADS)
Martens, P. C.; Winter, H. D.; Munetsi-Mugomba, K.
2007-12-01
We present the numerical simulations of quiescent coronal loops with heating functions that are power law functions of pressure and temperature. These simulations are made using a time-dependent, 1D hydrodynamics code with heating functions that are treated as dynamic variables which are constantly re- evaluated during the loops' lifetimes. These numerical simulations provide a stability test for the analytical solutions formulated by Martens (2007, submitted) for the same heating functions. TRACE and XRT datasets are simulated to determine if present observables can provide adequate information to discriminate between power law heating functions.
Power-law electrokinetic behavior as a direct probe of effective surface viscosity
NASA Astrophysics Data System (ADS)
Uematsu, Yuki; Netz, Roland R.; Bonthuis, Douwe Jan
2017-02-01
An exact solution to the Poisson-Boltzmann and Stokes equations is derived to describe the electric double layer with inhomogeneous dielectric and viscosity profiles in a lateral electric field. In the limit of strongly charged surfaces and low salinity, the electrokinetic flow magnitude follows a power law as a function of the surface charge density. Remarkably, the power-law exponent is determined by the interfacial dielectric constant and viscosity, the latter of which has eluded experimental determination. Our approach provides a novel method to extract the effective interfacial viscosity from standard electrokinetic experiments. We find good agreement between our theory and experimental data.
Evidence for power-law dominated noise in vacuum deposited CaF2.
Luhman, D R; Hallock, R B
2004-06-25
We have studied the surface roughness of CaF2 vacuum deposited on glass using atomic force microscopy for film coverages spanning an order of magnitude. We find the roughness exponent alpha=0.88+/-0.03, the growth exponent beta=0.75+/-0.03, and the dynamic exponent z=alpha/beta=1.17+/-0.06. Multifractality is also present, along with power-law behavior in the nearest neighbor height difference probability distribution. The results indicate noise dominated by a power-law distribution with exponent micro+1 approximately 4.6.
Effect of Body Perturbations on Hypersonic Flow Over Slender Power Law Bodies
NASA Technical Reports Server (NTRS)
Mirels, Harold; Thornton, Philip R.
1959-01-01
Hypersonic-slender-body theory, in the limit as the free-stream Mach number becomes infinite, is used to find the effect of slightly perturbing the surface of slender two-dimensional and axisymmetric power law bodies, The body perturbations are assumed to have a power law variation (with streamwise distance downstream of the nose of the body). Numerical results are presented for (1) the effect of boundary-layer development on two dimensional and axisymmetric bodies, (2) the effect of very small angles of attack (on tow[dimensional bodies), and (3) the effect of blunting the nose of very slender wedges and cones.
Modified power law equations for vertical wind profiles. [in investigation of windpower plant siting
NASA Technical Reports Server (NTRS)
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.
NASA Astrophysics Data System (ADS)
Lillo, F.
2007-02-01
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons.
Reed, William J; Hughes, Barry D
2002-12-01
We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes of incomes, cities, internet files, biological taxa, and in gene family and protein family frequencies.
The interrupted power law and the size of shadow banking.
Fiaschi, Davide; Kondor, Imre; Marsili, Matteo; Volpati, Valerio
2014-01-01
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is "interrupted" by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a large body of empirical literature which finds a Pareto distribution for firm sizes both across countries and over time. Pareto distributions are generally traced back to a mechanism of proportional random growth, based on a regime of constant returns to scale. This makes our findings of an "interrupted" Pareto distribution all the more puzzling, because we provide evidence that financial firms in our sample should operate in such a regime. We claim that the missing mass from the upper tail of the asset size distribution is a consequence of shadow banking activity and that it provides an (upper) estimate of the size of the shadow banking system. This estimate-which we propose as a shadow banking index-compares well with estimates of the Financial Stability Board until 2009, but it shows a sharper rise in shadow banking activity after 2010. Finally, we propose a proportional random growth model that reproduces the observed distribution, thereby providing a quantitative estimate of the intensity of shadow banking activity.
Stochastic Mixing Model with Power Law Decay of Variance
NASA Technical Reports Server (NTRS)
Fedotov, S.; Ihme, M.; Pitsch, H.
2003-01-01
Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.
The Interrupted Power Law and the Size of Shadow Banking
Fiaschi, Davide; Kondor, Imre; Marsili, Matteo; Volpati, Valerio
2014-01-01
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is “interrupted” by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a large body of empirical literature which finds a Pareto distribution for firm sizes both across countries and over time. Pareto distributions are generally traced back to a mechanism of proportional random growth, based on a regime of constant returns to scale. This makes our findings of an “interrupted” Pareto distribution all the more puzzling, because we provide evidence that financial firms in our sample should operate in such a regime. We claim that the missing mass from the upper tail of the asset size distribution is a consequence of shadow banking activity and that it provides an (upper) estimate of the size of the shadow banking system. This estimate–which we propose as a shadow banking index–compares well with estimates of the Financial Stability Board until 2009, but it shows a sharper rise in shadow banking activity after 2010. Finally, we propose a proportional random growth model that reproduces the observed distribution, thereby providing a quantitative estimate of the intensity of shadow banking activity. PMID:24728096
On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy
NASA Astrophysics Data System (ADS)
Ahnen, Max L.
2017-02-01
The high-energy non-thermal universe is dominated by power-law-like spectra. Therefore, results in high-energy astronomy are often reported as parameters of power-law fits, or, in the case of a non-detection, as an upper limit assuming the underlying unseen spectrum behaves as a power law. In this paper, I demonstrate a simple and powerful one-to-one relation of the integral upper limit in the two-dimensional power-law parameter space into the spectrum parameter space and use this method to unravel the so-far convoluted question of the sensitivity of astroparticle telescopes.
Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.
Sardar, Tridip; Saha, Bapi
2017-03-06
In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R0). It is shown that if R0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic.
Why credit risk markets are predestined for exhibiting log-periodic power law structures
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Leker, Jens
2014-01-01
Recent research has established the existence of log-periodic power law (LPPL) patterns in financial institutions’ credit default swap (CDS) spreads. The main purpose of this paper is to clarify why credit risk markets are predestined for exhibiting LPPL structures. To this end, the credit risk prediction of two variants of logistic regression, i.e. polynomial logistic regression (PLR) and kernel logistic regression (KLR), are firstly compared to the standard logistic regression (SLR). In doing so, the question whether the performances of rating systems based on balance sheet ratios can be improved by nonlinear transformations of the explanatory variables is resolved. Building on the result that nonlinear balance sheet ratio transformations hardly improve the SLR’s predictive power in our case, we secondly compare the classification performance of a multivariate SLR to the discriminative powers of probabilities of default derived from three different capital market data, namely bonds, CDSs, and stocks. Benefiting from the prompt inclusion of relevant information, the capital market data in general and CDSs in particular increasingly outperform the SLR while approaching the time of the credit event. Due to the higher classification performances, it seems plausible for creditors to align their investment decisions with capital market-based default indicators, i.e., to imitate the aggregate opinion of the market participants. Since imitation is considered to be the source of LPPL structures in financial time series, it is highly plausible to scan CDS spread developments for LPPL patterns. By establishing LPPL patterns in governmental CDS spread trajectories of some European crisis countries, the LPPL’s application to credit risk markets is extended. This novel piece of evidence further strengthens the claim that credit risk markets are adequate breeding grounds for LPPL patterns.
Branching random walk with step size coming from a power law
NASA Astrophysics Data System (ADS)
Bhattacharya, Ayan; Subhra Hazra, Rajat; Roy, Parthanil
2015-09-01
In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.
Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?
ERIC Educational Resources Information Center
Bauer, Ben
2009-01-01
Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less…
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
ERIC Educational Resources Information Center
Thelwall, Mike; Wilkinson, David
2003-01-01
Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)
Realization of power law inflation & variants via variation of the strong coupling constant
AlHallak, M.; Chamoun, N.
2016-09-05
We present a model of power law inflation generated by variation of the strong coupling constant. We then extend the model to two varying coupling constants which leads to a potential consisting of a linear combination of exponential terms. Some variants of the latter may be self-consistent and can accommodate the experimental data of the Planck 2015 and other recent experiments.
Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method
NASA Astrophysics Data System (ADS)
Abbasi Souraki, B.; Tondro, H.; Ghavami, M.
2014-10-01
In this study, unsteady one-dimensional mass transfer during osmotic dehydration of apple was modeled using an approximate mathematical model. The mathematical model has been developed based on a power law profile approximation for moisture and solute concentrations in the spatial direction. The proposed model was validated by the experimental water loss and solute gain data, obtained from osmotic dehydration of infinite slab and cylindrical shape samples of apple in sucrose solutions (30, 40 and 50 % w/w), at different temperatures (30, 40 and 50 °C). The proposed model's predictions were also compared with the exact analytical and also a parabolic approximation model's predictions. The values of mean relative errors respect to the experimental data were estimated between 4.5 and 8.1 %, 6.5 and 10.2 %, and 15.0 and 19.1 %, for exact analytical, power law and parabolic approximation methods, respectively. Although the parabolic approximation leads to simpler relations, the power law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time. Considering both simplicity and precision of the mathematical models, the power law model for short dehydration times and the simplified exact analytical model for long dehydration times could be used for explanation of the variations of the average water loss and solute gain in the whole domain of dimensionless times.
Exponential and power-law contact distributions represent different atmospheric conditions.
Reynolds, A M
2011-12-01
It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions.
The effect of a power-law mantle viscosity on trench retreat rate
NASA Astrophysics Data System (ADS)
Holt, Adam F.; Becker, Thorsten W.
2017-01-01
The subduction of lithospheric plates is partitioned between subducting plate motion and lateral slab migration (i.e. trench retreat and advance). We use 3-D, dynamic models of subduction to address the role of a power-law mantle viscosity on subduction dynamics and, in particular, rates of trench retreat. For all numerical models tested, we find that a power-law rheology results in reduced rates of trench retreat, and elevated slab dip angles, relative to the equivalent isoviscous mantle model. We analyse the asthenospheric pressure distribution and the style of mantle flow, which exhibits only limited variability as a function of mantle rheology, in order to compute estimates of the mantle forces associated with subduction. The inclusion of a power-law rheology reduces the mantle shear force (which resists subducting plate motion) to a greater degree than it reduces the dynamic pressure gradient across the slab (which resists trench retreat). Therefore, the inclusion of a power-law mantle rheology favours a shift towards a subduction mode with a reduced trench retreat component, typically a relative reduction of order 25 per cent in our 3-D models. We suggest that this mechanism may be of importance for reducing the high trench retreat rates observed in many previous models to levels more in line with the average subduction partitioning observed on Earth at present (i.e. trench velocity ≤ plate velocity), for most absolute plate motion reference frames.
Apparent power-law behavior of conductance in disordered quasi-one-dimensional systems.
Rodin, A S; Fogler, M M
2010-09-03
The dependence of hopping conductance on temperature and voltage for an ensemble of modestly long one-dimensional wires is studied numerically using the shortest-path algorithm. In a wide range of parameters this dependence can be approximated by a power law rather than the usual stretched-exponential form. The relation to recent experiments and prior analytical theory is discussed.
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Channel geometry and hydraulic characteristics of a given river network, i.e., spatio-temporal variability of width, depth, and velocity, can be described as power functional relationships of flow discharge, named 'hydraulic geometry' (Leopold and Maddock, 1953). Many studies have focused on the implication of this power-law itself, i.e., self-similarity, and accordingly its exponents. Coefficients of the power functional relationships, on the contrary, have received little attention. They are often regarded as empirical constants, determined by 'best fitting' to the power-law without significant scientific implications. Here, we investigate and claim that power-law coefficients of hydraulic geometry relationships carry vital information of a given river system. We approach the given problem on the basis of 'basin hydraulic geometry' formulation (Stall and Fok, 1968) which decomposes power-law coefficients into more elementary constants. The linkage between classical power-law relationship (Leopold and Maddock, 1953) and the basin hydraulic geometry is provided by Paik and Kumar (2004). On the basis of this earlier study, it can be shown that coefficients and exponents of power-law hydraulic geometry are interrelated. In this sense, we argue that more elementary constants that constitute both exponents and coefficients carry important messages. In this presentation, we will demonstrate how these elementary constants vary over a wide range of catchments provided from Stall and Fok (1968) and Stall and Yang (1970). Findings of this study can provide new insights on fundamental understanding about hydraulic geometry relationships. Further, we expect that this understanding can help interpretation of hydraulic geometry relationship in the context of flood propagation through a river system as well. Keywords: Hydraulic geometry; Power-law; River network References Leopold, L. B., & Maddock, T. J. (1953). The hydraulic geometry of stream channels and some physiographic
Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain
NASA Astrophysics Data System (ADS)
Khan, Masood; Farooq, Asma; Khan, Waqar Azeem; Hussain, Mazhar
The present paper reports a theoretical study of the dynamics of an electroosmotic flow (EOF) in cylindrical domain. The Cauchy momentum equation is first simplified by incorporating the electrostatic body force in the electric double layer and the generalized Burgers fluid constitutive model. The electric potential distribution is given by the linearized Poisson-Boltzmann equation. After solving the linearized Poisson-Boltzmann equation, the Cauchy momentum equation with electrostatic body force is solved analytically by using the temporal Fourier and finite Hankel transforms. The effects of important involved parameters are examined and presented graphically. The results obtained reveal that the magnitude of velocity increases with increase of the Debye-Huckel and electrokinetic parameters. Further, it is shown that the results presented for generalized Burgers fluid are quite general so that results for the Burgers, Oldroyd-B, Maxwell and Newtonian fluids can be obtained as limiting cases.
PLNoise: a package for exact numerical simulation of power-law noises
NASA Astrophysics Data System (ADS)
Milotti, Edoardo
2006-08-01
Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1<β⩽1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v1_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B
Power-law ansatz in complex systems: Excessive loss of information
NASA Astrophysics Data System (ADS)
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.
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.
Li, Gen; Lee, Martin A.
2015-09-01
The effects of scatter-dominated interplanetary transport on the spectral properties of the differential fluence of large gradual solar energetic particle (SEP) events are investigated analytically. The model assumes for simplicity radial constant solar wind and radial magnetic field. The radial diffusion coefficient is calculated with quasilinear theory by assuming a spectrum of Alfvén waves propagating parallel to the magnetic field. Cross-field transport is neglected. The model takes into consideration several essential features of gradual event transport: nearly isotropic ion distributions, adiabatic deceleration in a divergent solar wind, and particle radial scattering mean free paths increasing with energy. Assuming an impulsive and spherically symmetric injection of SEPs with a power-law spectrum near the Sun, the predicted differential fluence spectrum exhibits at 1 AU three distinctive power laws for different energy domains. The model naturally reproduces the spectral features of the double power-law proton differential fluence spectra that tend to be observed in extremely large SEP events. We select nine western ground-level events (GLEs) out of the 16 GLEs during Solar Cycle 23 and fit the observed double power-law spectra to the analytical predictions. The compression ratio of the accelerating shock wave, the power-law index of the ambient wave intensity, and the proton radial scattering mean free path are determined for the nine GLEs. The derived parameters are generally in agreement with the characteristic values expected for large gradual SEP events.
NASA Astrophysics Data System (ADS)
Pfister, Herbert
2011-04-01
In comparison to previous existence proofs for static and spherically symmetric perfect fluid stars in general relativity the new proof applies to a more general class of equations of state. In the star's interior we allow for piecewise Lipschitz continuous functions, including in this way the physically important case of phase transitions. Near the star's surface we allow for even more general functions, thereby including a large class of polytropic equations of state. Furthermore, the proof technique proceeds along standard techniques of functional analysis (Banach's fixed point theorem), and therefore applies in a similar manner to static stars in Newtonian gravity, and perhaps to rotating Newtonian and Einsteinian stars. In detail, the Einstein field equations for static perfect fluid stars are transformed to a system of coupled nonlinear integral equations being valid equally in the matter region and in the vacuum exterior. These integral equations are interpreted as a mapping in a Banach space. With the standard iteration technique, beginning with appropriate start functions, it is proven that the mapping has a unique fixed point, and that the solutions have appropriate regularity properties determined by the properties of the equation of state. The introduction gives an overview of earlier work on such systems, on the question of sphericity of static fluid stars, and on possible extensions of the above methods to rotating Newtonian and Einsteinian stars. An outlook addresses the question whether our proof method may be extensible to piecewise Hölder continuous equations of state.
Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations.
Thieulot, Cedric; Janssen, L P B M; Español, Pep
2005-07-01
We present a thermodynamically consistent discrete fluid particle model for the simulation of a recently proposed set of hydrodynamic equations for a phase separating van der Waals fluid mixture [P. Español and C.A.P. Thieulot, J. Chem. Phys. 118, 9109 (2003)]. The discrete model is formulated by following a discretization procedure given by the smoothed particle hydrodynamics (SPH) method within the thermodynamically consistent general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework. Each fluid particle carries information on the mass, momentum, energy, and the mass fraction of the different components. The discrete model allows one to simulate nonisothermal dynamic evolution of phase separating fluids with surface tension effects while respecting the first and second laws of thermodynamics exactly.
Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations
NASA Astrophysics Data System (ADS)
Thieulot, Cedric; Janssen, L. P. B. M.; Español, Pep
2005-07-01
We present a thermodynamically consistent discrete fluid particle model for the simulation of a recently proposed set of hydrodynamic equations for a phase separating van der Waals fluid mixture [P. Español and C.A.P. Thieulot, J. Chem. Phys. 118, 9109 (2003)]. The discrete model is formulated by following a discretization procedure given by the smoothed particle hydrodynamics (SPH) method within the thermodynamically consistent general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework. Each fluid particle carries information on the mass, momentum, energy, and the mass fraction of the different components. The discrete model allows one to simulate nonisothermal dynamic evolution of phase separating fluids with surface tension effects while respecting the first and second laws of thermodynamics exactly.
A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme
NASA Astrophysics Data System (ADS)
Meng, Hua; Yang, Vigor
2003-07-01
A unified treatment of general fluid thermodynamics is developed to handle fluid flows over their entire thermodynamic states. The analysis is based on the concepts of partial-mass and partial-density properties, and accommodates thermodynamic non-idealities and transport anomalies in the transcritical regime. The resultant routine is incorporated into a preconditioning scheme. All the thermophysical properties and numerical Jacobian matrices are derived directly from fundamental thermodynamic theories, rendering a robust algorithm valid for fluid flows at all speeds and at all thermodynamic states. As a specific example, a modified Soave-Redlich-Kwong equation of state is employed to obtain the fluid p- V- T properties. Several test cases concerning supercritical droplet vaporization in both quiescent and convective environments are presented to demonstrate the effectiveness of the present algorithm.
Power laws and self-organized criticality in theory and nature
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Zhang, Xiao-Fei; Fan, Yan; Chen, Liang
2017-02-01
We investigate the generalized (n+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials, and derive two families of analytical sech-type and Gaussian-type localized modes (soliton solutions). Based on these analytical solutions, the powers, power-flow densities and the phase jumps are analyzed. The linear stability analysis and the direct numerical simulation for these exact solutions indicate that sech-type and Gaussian-type solutions are both stable below some thresholds for the imaginary part of PT-symmetric potentials (except for the extended Rosen-Morse potential) in the focusing power-law nonlinear medium, while they are always unstable in the defocusing power-law nonlinear medium. The gain (loss) related to the values of the imaginary part of the potential (Wn) should be enough small compared with the fixed value of the real part of the potential (V0) in order to ensure the stability of exact solutions.
Dehydration, hemodynamics and fluid volume optimization after induction of general anesthesia
Li, Yuhong; He, Rui; Ying, Xiaojiang; Hahn, Robert G
2014-01-01
OBJECTIVES: Fluid volume optimization guided by stroke volume measurements reduces complications of colorectal and high-risk surgeries. We studied whether dehydration or a strong hemodynamic response to general anesthesia increases the probability of fluid responsiveness before surgery begins. METHODS: Cardiac output, stroke volume, central venous pressure and arterial pressures were measured in 111 patients before general anesthesia (baseline), after induction and stepwise after three bolus infusions of 3 ml/kg of 6% hydroxyethyl starch 130/0.4 (n = 86) or Ringer's lactate (n = 25). A subgroup of 30 patients who received starch were preloaded with 500 ml of Ringer's lactate. Blood volume changes were estimated from the hemoglobin concentration and dehydration was estimated from evidence of renal water conservation in urine samples. RESULTS: Induction of anesthesia decreased the stroke volume to 62% of baseline (mean); administration of fluids restored this value to 84% (starch) and 68% (Ringer's). The optimized stroke volume index was clustered around 35-40 ml/m2/beat. Additional fluid boluses increased the stroke volume by ≥10% (a sign of fluid responsiveness) in patients with dehydration, as suggested by a low cardiac index and central venous pressure at baseline and by high urinary osmolality, creatinine concentration and specific gravity. Preloading and the hemodynamic response to induction did not correlate with fluid responsiveness. The blood volume expanded 2.3 (starch) and 1.8 (Ringer's) times over the infused volume. CONCLUSIONS: Fluid volume optimization did not induce a hyperkinetic state but ameliorated the decrease in stroke volume caused by anesthesia. Dehydration, but not the hemodynamic response to the induction, was correlated with fluid responsiveness. PMID:25627992
Interfacing a General Purpose Fluid Network Flow Program with the SINDA/G Thermal Analysis Program
NASA Technical Reports Server (NTRS)
Schallhorn, Paul; Popok, Daniel
1999-01-01
A general purpose, one dimensional fluid flow code is currently being interfaced with the thermal analysis program Systems Improved Numerical Differencing Analyzer/Gaski (SINDA/G). The flow code, Generalized Fluid System Simulation Program (GFSSP), is capable of analyzing steady state and transient flow in a complex network. The flow code is capable of modeling several physical phenomena including compressibility effects, phase changes, body forces (such as gravity and centrifugal) and mixture thermodynamics for multiple species. The addition of GFSSP to SINDA/G provides a significant improvement in convective heat transfer modeling for SINDA/G. The interface development is conducted in multiple phases. This paper describes the first phase of the interface which allows for steady and quasi-steady (unsteady solid, steady fluid) conjugate heat transfer modeling.
General proof of the entropy principle for self-gravitating fluid in f ( R) gravity
NASA Astrophysics Data System (ADS)
Fang, Xiongjun; Guo, Minyong; Jing, Jiliang
2016-08-01
The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in f ( R) gravity, which is an important theory could explain the accelerated expansion of the universe. We first show that the Tolman-Oppenheimer-Volkoff equation of f ( R) theories can be obtained by thermodynamical method in spherical symmetric spacetime. Then we prove that the maximum entropy principle is also valid for f ( R) gravity in general static spacetimes beyond spherical symmetry. The result shows that if the constraint equation is satisfied and the temperature of fluid obeys Tolmans law, the extrema of total entropy implies other components of gravitational equations. Conversely, if f ( R) gravitational equation hold, the total entropy of the fluid should be extremum. Our work suggests a general and solid connection between f ( R) gravity and thermodynamics.
NASA Astrophysics Data System (ADS)
Liang, Li-Fu; Liu, Zong-Min; Guo, Qing-Yong
2009-03-01
The fluid-solid coupling theory, an interdisciplinary science between hydrodynamics and solid mechanics, is an important tool for response analysis and direct design of structures in naval architecture and ocean engineering. By applying the corresponding relations between generalized forces and generalized displacements, convolutions were performed between the basic equations of elasto-dynamics in the primary space and corresponding virtual quantities. The results were integrated and then added algebraically. In light of the fact that body forces and surface forces are both follower forces, the generalized quasi-complementary energy principle with two kinds of variables for an initial value problem is established in non-conservative systems. Using the generalized quasi-complementary energy principle to deal with the fluid-solid coupling problem and to analyze the dynamic response of structures, a method for using two kinds of variables simultaneously for calculation of force and displacement was derived.
Inhomogeneous generalizations of Bianchi Type VIh universes with stiff perfect fluid and radiation
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1995-03-01
Families of inhomogeneous models filled with a stiff perfect fluid and radiation have been derived in which there is no flow of total momentum. The models are generalizations of those of Bianchi Type VIh and are discussed for some particular forms of the arbitrary functions appearing in them.
2011-01-01
Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520
The energy-momentum tensor for a dissipative fluid in general relativity
NASA Astrophysics Data System (ADS)
Pimentel, Oscar M.; Lora-Clavijo, F. D.; González, Guillermo A.
2016-10-01
Considering the growing interest of the astrophysicist community in the study of dissipative fluids with the aim of getting a more realistic description of the universe, we present in this paper a physical analysis of the energy-momentum tensor of a viscous fluid with heat flux. We introduce the general form of this tensor and, using the approximation of small velocity gradients, we relate the stresses of the fluid with the viscosity coefficients, the shear tensor and the expansion factor. Exploiting these relations, we can write the stresses in terms of the extrinsic curvature of the normal surface to the 4-velocity vector of the fluid, and we can also establish a connection between the perfect fluid and the symmetries of the spacetime. On the other hand, we calculate the energy conditions for a dissipative fluid through contractions of the energy-momentum tensor with the 4-velocity vector of an arbitrary observer. This method is interesting because it allows us to compute the conditions in a reasonably easy way and without considering any approximation or restriction on the energy-momentum tensor.
Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources
NASA Technical Reports Server (NTRS)
Fiorito, Ralph; Titarchuk, Lev
2004-01-01
Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.
Power-law statistics and universal scaling in the absence of criticality.
Touboul, Jonathan; Destexhe, Alain
2017-01-01
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
Linking multiple relaxation, power-law attenuation, and fractional wave equations.
Näsholm, Sven Peter; Holm, Sverre
2011-11-01
The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.
AC losses in superconductors with a power-law constitutive relation
NASA Astrophysics Data System (ADS)
Agassi, Y. D.
2015-10-01
The observed constitutive relation between the electrical field and current density in cuprates high temperature superconductors is a power-law of the current. This functional dependence is presumably related to the giant flux-creep domain. It is shown that this constitutive relation reflects the statistical spread of the pinning potential associated with creep motion of vortex bundles. The AC losses emanating from a power-law constitutive relation are calculated in an approach focused on the superconductor's electric field. For a slab geometry in the presence of a parallel AC magnetic field or transport current, the calculated AC-loss scaling laws are consistent with BSCCO data and the critical state model. Extensions of the approach are briefly discussed.
Segmentation of genomic DNA through entropic divergence: Power laws and scaling
NASA Astrophysics Data System (ADS)
Azad, Rajeev K.; Bernaola-Galván, Pedro; Ramaswamy, Ramakrishna; Rao, J. Subba
2002-05-01
Genomic DNA is fragmented into segments using the Jensen-Shannon divergence. Use of this criterion results in the fragments being entropically homogeneous to within a predefined level of statistical significance. Application of this procedure is made to complete genomes of organisms from archaebacteria, eubacteria, and eukaryotes. The distribution of fragment lengths in bacterial and primitive eukaryotic DNAs shows two distinct regimes of power-law scaling. The characteristic length separating these two regimes appears to be an intrinsic property of the sequence rather than a finite-size artifact, and is independent of the significance level used in segmenting a given genome. Fragment length distributions obtained in the segmentation of the genomes of more highly evolved eukaryotes do not have such distinct regimes of power-law behavior.
Power-law statistics and universal scaling in the absence of criticality
NASA Astrophysics Data System (ADS)
Touboul, Jonathan; Destexhe, Alain
2017-01-01
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
NASA Technical Reports Server (NTRS)
Raj, S. V.; Pharr, G. M.
1989-01-01
Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.
Deviations from uniform power-law scaling due to exposure to high altitude
NASA Astrophysics Data System (ADS)
Posiewnik, A.
2002-12-01
A major challenge in biological physics is the analysis of time series that are typically highly nonstationary. Viswanathan et al. (Phys. Rev. E 55 (1) (1997) 845-899) using techniques based on the Fano factor and the Allan factor functions, as well as on detrended fluctuation analysis showed that the scaling properties of the dynamics of healthy physiological systems in normal conditions are more stable than those of pathological systems-there is underlying loss of uniform power-law scaling in disease. Here we test, using the same techniques as Viswanathan et al. (1997), the hypothesis that deviations from uniform power-law scaling, similar to those seen in heart failure and deep apnea syndrome occur also for healthy subjects under pathological conditions (hypoxaemic stress during exposure to high altitude, over 6000 m).
Finite sample properties of power-law cross-correlations estimators
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2015-02-01
We study finite sample properties of estimators of power-law cross-correlations-detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA)-with a special focus on short-term memory bias as well as power-law coherency. We present a broad Monte Carlo simulation study that focuses on different time series lengths, specific methods' parameter setting, and memory strength. We find that each method is best suited for different time series dynamics so that there is no clear winner between the three. The method selection should be then made based on observed dynamic properties of the analyzed series.
Speed-invariant encoding of looming object distance requires power law spike rate adaptation.
Clarke, Stephen E; Naud, Richard; Longtin, André; Maler, Leonard
2013-08-13
Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.
Market reaction to a bid-ask spread change: A power-law relaxation dynamics
NASA Astrophysics Data System (ADS)
Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N.
2009-07-01
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.
Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions
NASA Astrophysics Data System (ADS)
Kuo, Huan-Yu; Wu, Kuo-An
2015-12-01
We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α ≤1 is identical to that of the all-to-all coupling case. For α >1 , oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations.
Treeby, Bradley E; Cox, B T
2010-05-01
The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.
Market reaction to a bid-ask spread change: a power-law relaxation dynamics.
Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N
2009-07-01
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.
Urinary Analysis of Fluid Retention in the General Population: A Cross-Sectional Study
Grankvist, Nina; Krizhanovskii, Camilla
2016-01-01
Objective Renal conservation (retention) of fluid might affect the outcome of hospital care and can be indicated by increased urinary concentrations of metabolic waste products. We obtained a reference material for further studies by exploring the prevalence of fluid retention in a healthy population. Methods Spot urine sampling was performed in 300 healthy hospital workers. A previously validated algorithm summarized the urine-specific gravity, osmolality, creatinine, and color to a fluid retention index (FRI), where 4.0 is the cut-off for fluid retention consistent with dehydration. In 50 of the volunteers, we also studied the relationships between FRI, plasma osmolality, and water-retaining hormones. Results The cut-off for fluid retention (FRI ≥ 4.0) was reached by 38% of the population. No correlation was found between the FRI and the time of the day of urine sample collection, and the FRI was only marginally correlated with the time period spent without fluid intake. Volunteers with fluid retention were younger, generally men, and more often had albuminuria (88% vs. 34%, P < 0.001). Plasma osmolality and plasma sodium were somewhat higher in those with a high FRI (mean 294.8 vs. 293.4 mosmol/kg and 140.3 vs. 139.9 mmol/l). Plasma vasopressin was consistently below the limit of detection, and the plasma cortisol, aldosterone, and renin concentrations were similar in subjects with a high or low FRI. The very highest FRI values (≥ 5.0, N = 61) were always accompanied by albuminuria. Conclusion Fluid retention consistent with moderate dehydration is common in healthy staff working in a Swedish hospital. PMID:27764121
A General Nonlinear Fluid Model for Reacting Plasma-Neutral Mixtures
Meier, E T; Shumlak, U
2012-04-06
A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed.
Soloway, Alexander G; Dahl, Peter H; Odom, Robert I
2015-10-01
Experimental measurements of Scholte waves from underwater explosions collected off the coast of Virginia Beach, VA in shallow water are presented. It is shown here that the dispersion of these explosion-generated Scholte waves traveling in the sandy seabed can be modeled using a power-law dependent shear wave speed profile and an empirical source model that determines the pressure time-series at 1 m from the source as a function of TNT-equivalent charge weight.
Fertility heterogeneity as a mechanism for power law distributions of recurrence times
NASA Astrophysics Data System (ADS)
Saichev, A.; Sornette, D.
2013-02-01
We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future events. Specifically, we analyze the impact of the power law distribution of fertilities with exponent α, where the fertility of an event is the number of triggered events of first generation, on the probability distribution function (PDF) f(τ) of the recurrence times τ between successive events. The other input of the model is an exponential law quantifying the PDF of waiting times between an event and its first generation triggered events, whose characteristic time scale is taken as our time unit. At short-time scales, we discover two intermediate power law asymptotics, f(τ)˜τ-(2-α) for τ≪τc and f(τ)˜τ-α for τc≪τ≪1, where τc is associated with the self-excited cascades of triggered events. For 1≪τ≪1/ν, we find a constant plateau f(τ)≃const, while at long times, 1/ν≲τ, f(τ)≃e-ντ has an exponential tail controlled by the arrival rate ν of exogenous events. These results demonstrate a novel mechanism for the generation of power laws in the distribution of recurrence times, which results from a power law distribution of fertilities in the presence of self-excitation and cascades of triggering.
Epitrochoid Power-Law Nozzle Rapid Prototype Build/Test Project (Briefing Charts)
2015-02-01
Production Approved for public release; distribution is unlimited. PA clearance # 15122. 4 Epitrochoid Power-Law Nozzle Build/Test Build on SpaceX ...Multiengine Approach SpaceX ) Approved for public release; distribution is unlimited. PA clearance # 15122. Engines: Merlin 1D on Falcon 9 v1.1 (Photo 5...to utilize features of high performance engines advances and the economies of scale of the multi-engine approach of SpaceX Falcon 9 – Rapid Prototype
DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K.
2016-04-10
A double power law or a power law with exponential rollover at a few to tens of MeV nucleon{sup −1} of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochastic approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon{sup −1} is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.
A power-law distribution for tenure lengths of sports managers
NASA Astrophysics Data System (ADS)
Aidt, Toke S.; Leong, Bernard; Saslaw, William C.; Sgroi, Daniel
2006-10-01
We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.
Improved power-law estimates from multiple samples provided by millennium climate simulations
NASA Astrophysics Data System (ADS)
Henriksson, S. V.; Räisänen, P.; Silen, J.; Järvinen, H.; Laaksonen, A.
2015-02-01
Using the long annual mean temperature time series provided by millennium Earth System Model simulations and a method of discrete Fourier transform with varying starting point and length of time window together with averaging, we get good fits to power laws between two characteristic oscillatory timescales of the model climate: multidecadal (50-80 years) and El Nino (3-6 years) timescales. For global mean temperature, we fit β ˜ 0.35 in a relation S( f) ˜ f - β in a simulation without external climate forcing and β over 0.7 in a simulation with external forcing included. The power law is found both with and without external forcing despite the forcings, e.g. the volcanic forcing, not showing similar behaviour, indicating a nonlinear temperature response to time-varying forcing. We also fit a power law with β ˜ 8 to the narrow frequency range between El Nino frequencies (up to 1/(3.2 years)) and the Nyquist frequency (1/(2 years)). Also, monthly mean temperature time series are considered and a decent power-law fit for frequencies above 1/year is obtained. Regional variability in best-fit β is explored, and the impact of choosing the frequency range on the result is illustrated. When all resolved frequencies are used, land areas seem to have lower βs than ocean areas on average, but when fits are restricted to frequencies below 1/(6 years), this difference disappears, while regional differences still remain. Results compare well with measurements both for global mean temperature and for the central England temperature record.
Multiple short time power laws in the orientational relaxation of nematic liquid crystals.
Jose, Prasanth P; Bagchi, Biman
2006-11-14
Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.
Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
Adler, Miri; Mayo, Avi; Alon, Uri
2014-01-01
Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling. PMID:25121598
Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields
Steffen, J. H.; Baumbaugh, A.; Chou, A. S.; Mazur, P. O.; Tomlin, R.; Wester, W.; Upadhye, A.; Weltman, A.
2010-12-31
We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Global analysis of the stream power law parameters based on worldwide 10Be denudation rates
NASA Astrophysics Data System (ADS)
Harel, M.-A.; Mudd, S. M.; Attal, M.
2016-09-01
The stream power law, expressed as E = KAmSn - where E is erosion rate [LT - 1], K is an erodibility coefficient [T - 1L (1 - 2m)], A is drainage area [L 2], 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 topographic evolution, knickpoint migration, palaeotopography reconstruction, and the determination of rock 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 limits the use and interpretation of the model. In this study, we compile a unique global data set of published basin-averaged erosion rates that use detrital cosmogenic 10Be. These data (N = 1457) enable values for fundamental river properties to be empirically constrained, often for the first time, such as the concavity of the river profile (m/n ratio or concavity index), the link between channel slope and erosion rate (slope exponent n), and substrate erodibility (K). These three parameters are calculated for 59 geographic areas using the integral method of channel profile analysis and allow for a global scale analysis in terms of climatic, tectonic, and environmental settings. In order to compare multiple sites, we also normalize n and K using a reference concavity index m/n = 0.5. A multiple regression analysis demonstrates that intuitive or previously demonstrated local-scale trends, such as the correlation between K and precipitation rates, do not appear at a global scale. Our results suggest that the slope exponent is generally > 1, meaning that the relationship between erosion rate and the channel gradient is nonlinear and thus support the hypothesis that incision is a threshold controlled process. This result questions the validity of many regional interpretations of climate and/or tectonics where
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.
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.
NASA Astrophysics Data System (ADS)
Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.
2014-09-01
We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.
Frequency variations of solar radio zebras and their power-law spectra
NASA Astrophysics Data System (ADS)
Karlický, M.
2014-01-01
Context. During solar flares several types of radio bursts are observed. The fine striped structures of the type IV solar radio bursts are called zebras. Analyzing them provides important information about the plasma parameters of their radio sources. We present a new analysis of zebras. Aims: Power spectra of the frequency variations of zebras are computed to estimate the spectra of the plasma density variations in radio zebra sources. Methods: Frequency variations of zebra lines and the high-frequency boundary of the whole radio burst were determined with and without the frequency fitting. The computed time dependencies of these variations were analyzed with the Fourier method. Results: First, we computed the variation spectrum of the high-frequency boundary of the whole radio burst, which is composed of several zebra patterns. This power spectrum has a power-law form with a power-law index -1.65. Then, we selected three well-defined zebra-lines in three different zebra patterns and computed the spectra of their frequency variations. The power-law indices in these cases are found to be in the interval between -1.61 and -1.75. Finally, assuming that the zebra-line frequency is generated on the upper-hybrid frequency and that the plasma frequency ωpe is much higher than the electron-cyclotron frequency ωce, the Fourier power spectra are interpreted to be those of the electron plasma density in zebra radio sources.
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-03-16
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.
NASA Astrophysics Data System (ADS)
Furey, Peter R.; Gupta, Vijay K.
2007-11-01
Observations from the Goodwin Creek experimental watershed (GCEW), Mississippi show that peak-discharge Q( A) and drainage area A are related, on average, by a power law or scaling relationship, Q( A) = αAθ, during single rainfall-runoff events. Observations also show that α and θ change between events, and, based on a recent analysis of 148 events, observations indicate that α and θ change because of corresponding changes in the depth, duration, and spatial variability of excess-rainfall. To improve our physical understanding of these observations, a 5-step framework for diagnosing observed power laws, or other space-time patterns in a basin, is articulated and applied to GCEW using a combination of analysis and numerical simulations. Diagnostic results indicate how the power laws are connected to physical conditions and processes. Derived expressions for α and θ show that if excess-rainfall depth is fixed then there is a decreasing concave relationship between α and excess-rainfall duration, and an increasing and slightly convex relationship between θ and excess rainfall duration. These trends are consistent with observations only when hillslope velocity vh is given a physically realistic value near 0.1 m/s. If vh ≫ 0.1 m/s, then the predicted trends deviate from observed trends. Results also suggest that trends in α and θ can be impacted by the dependence of vh and link velocity vl on excess-rainfall rate.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Kiflawi, Moshe; Mann, Ofri; Meekan, Mark G
2016-10-21
Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes.
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-01-01
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns. PMID:25779306
Bose-Einstein condensation with a finite number of particles in a power-law trap
NASA Astrophysics Data System (ADS)
Jaouadi, A.; Telmini, M.; Charron, E.
2011-02-01
Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number N of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation temperature Tc in terms of a power series in x0=ɛ0/kBTc, where ɛ0 denotes the zero-point energy of the trapping potential. This expression, which applies in Cartesian, cylindrical, and spherical power-law traps, is given analytically at infinite order. It is also given numerically for specific potential shapes as an expansion in powers of x0 up to the second order. We show that, for a harmonic trap, the well-known first-order shift of the critical temperature ΔTc/Tc∝N-1/3 is inaccurate when N⩽105, the next order (proportional to N-1/2) being significant. We also show that finite-size effects on the condensation temperature cancel out in a cubic trapping potential, e.g., V(r)∝r3. Finally, we show that in a generic power-law potential of higher order, e.g., V(r)∝rα with α>3, the shift of the critical temperature becomes positive. This effect provides a large increase of Tc for relatively small atom numbers. For instance, an increase of about +40% is expected with 104 atoms in a V(r)∝r12 trapping potential.
A stability analysis of the power-law steady state of marine size spectra.
Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J
2011-10-01
This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.
Power law for the duration of recession and prosperity in Latin American countries
NASA Astrophysics Data System (ADS)
Redelico, Francisco O.; Proto, Araceli N.; Ausloos, Marcel
2008-11-01
Ormerod and Mounfield [P. Ormerod, C. Mounfield, Power law distribution of duration and magnitude of recessions in capitalist economies: Breakdown of scaling, Physica A 293 (2001) 573] and Ausloos et al. [M. Ausloos, J. Mikiewicz, M. Sanglier, The durations of recession and prosperity: Does their distribution follow a power or an exponential law? Physica A 339 (2004) 548] have independently analyzed the duration of recessions for developed countries through the evolution of the GDP in different time windows. It was found that there is a power law governing the duration distribution. We have analyzed data collected from 19 Latin American countries in order to observe whether such results are valid or not for developing countries. The case of prosperity years is also discussed. We observe that the power law of recession time intervals, see Ref. [1], is valid for Latin American countries as well. Thus an interesting point is discovered: the same scaling time is found in the case of recessions for the three data sets (ca. 1 year), and this could represent a universal feature. Other time scale parameters differ significantly from each other.
NASA Astrophysics Data System (ADS)
Huang, M.; Wada, R.; Chen, Z.; Keutgen, T.; Kowalski, S.; Hagel, K.; Barbui, M.; Bonasera, A.; Bottosso, C.; Materna, T.; Natowitz, J. B.; Qin, L.; Rodrigues, M. R. D.; Sahu, P. K.; Schmidt, K. J.; Wang, J.
2010-11-01
Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, asym/T, extracted in previous work and that of the pairing term, ap/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I=N-Z value, the corrected yields of isotopes relative to the yield of C12 show a power law distribution Y(N,Z)/Y(12C)~A-τ in the mass range 1⩽A⩽30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted τ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be τprim=2.4±0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.
Comment on ``Time needed to board an airplane: A power law and the structure behind it''
NASA Astrophysics Data System (ADS)
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.011130 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.
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
NASA Astrophysics Data System (ADS)
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-03-01
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.
Dong, S.
2015-02-15
We present a family of physical formulations, and a numerical algorithm, based on a class of general order parameters for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids with given densities, dynamic viscosities, and pairwise surface tensions. The N-phase formulations stem from a phase field model we developed in a recent work based on the conservations of mass/momentum, and the second law of thermodynamics. The introduction of general order parameters leads to an extremely strongly-coupled system of (N−1) phase field equations. On the other hand, the general form enables one to compute the N-phase mixing energy density coefficients in an explicit fashion in terms of the pairwise surface tensions. We show that the increased complexity in the form of the phase field equations associated with general order parameters in actuality does not cause essential computational difficulties. Our numerical algorithm reformulates the (N−1) strongly-coupled phase field equations for general order parameters into 2(N−1) Helmholtz-type equations that are completely de-coupled from one another. This leads to a computational complexity comparable to that for the simplified phase field equations associated with certain special choice of the order parameters. We demonstrate the capabilities of the method developed herein using several test problems involving multiple fluid phases and large contrasts in densities and viscosities among the multitude of fluids. In particular, by comparing simulation results with the Langmuir–de Gennes theory of floating liquid lenses we show that the method using general order parameters produces physically accurate results for multiple fluid phases.
Mirigian, Stephen; Schweizer, Kenneth S
2014-05-21
We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.
NASA Astrophysics Data System (ADS)
Stewart, Michael; Morgenstern, Uwe
2013-04-01
Understanding runoff generation is important for management of freshwater systems. Determining transit time distributions of streamwaters and how they change with discharge gives information on the flowpaths and recharge sources of streams - vital information for determining the responses of streams to stressors such as pollution, landuse change, or climate change. This work takes a first look at unique information on how transit time distributions change with discharge in some New Zealand catchments. Transit time distributions of streamwaters have been determined from tritium measurements on single samples in this work. This allows changes with stream discharge to be observed, in contrast to previous isotope studies which have given averaged transit time distributions based on series of samples. In addition, tritium reveals the wide spectrum of ages present in streams whereas oxygen-18 or chloride variations only show the younger ages (Stewart et al., 2010). It was found that the mean transit time (MTT) data could be reasonably represented by straight lines in log-log plots, indicating power law relationships between MTT and discharge. Similar power law behaviour has been observed for the rock forming elements such as silica in streamwaters (Godsey et al., 2009). Case studies are presented for two New Zealand catchments, both with volcanic ash substrates. Toenepi is a dairy catchment near Hamilton, which shows well-constrained power law relationships between MTT and discharge, and between silica concentration and discharge (Morgenstern et al., 2010). Baseflow MTTs vary from 2.5 to 157 years. Tutaeuaua is a pastoral farming catchment near Taupo. Results for nested catchments along the stream also show power law relationships for both MTT and silica with discharge. Streamwater MTTs vary from 1 to 11 years. The results indicate that (1) relatively old waters dominate many streams, (2) streamwater ages vary with discharge, and (3) age, like silica, varies according to
2015-01-01
Background 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. Objectives 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. Methods 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. Results All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R 2 values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). Conclusions This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns
Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells
NASA Astrophysics Data System (ADS)
Kunte, M. V.; Sarkar, Abhijit; Sonti, Venkata R.
2010-12-01
Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order ( n). The shallow shell theory (which is more accurate at higher frequencies) is used to model the cylinder. Initially, the in vacuo shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high- and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter μ, we find solutions for the limiting cases of small and large μ. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases, Poisson's ratio ν is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory ( in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders ( n).
Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi
2016-01-01
We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria. PMID:27505155
On the interplay between short and long term memory in the power-law cross-correlations setting
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Pandian, Arun; Swisher, Nora C.; Abarzhi, S. I.
2017-01-01
Rayleigh-Taylor (RT) mixing occurs in a variety of natural and man-made phenomena in fluids, plasmas and materials, from celestial event to atoms. In many circumstances, RT flows are driven by variable acceleration, whereas majority of existing studies have considered only sustained acceleration. In this work we perform detailed analytical and numerical study of RT mixing with a power-law time-dependent acceleration. A set of deterministic nonlinear non-homogeneous ordinary differential equations and nonlinear stochastic differential equations with multiplicative noise are derived on the basis of momentum model. For a broad range of parameters, self-similar asymptotic solutions are found analytically, and their statistical properties are studied numerically. We identify two sub-regimes of RT mixing dynamics depending on the acceleration exponent—the acceleration-driven mixing and dissipation-driven mixing. Transition between the sub-regimes is studied, and it is found that each sub-regime has its own characteristic dimensionless invariant quantity.
ERIC Educational Resources Information Center
Conway, Andrew R. A.; Cowan, Nelsin; Bunting, Michael F.; Therriault, David J.; Minkoff, Scott R. B.
2002-01-01
Studied the interrelationships among general fluid intelligence, short-term memory capacity, working memory capacity, and processing speed in 120 young adults and used structural equation modeling to determine the best predictor of general fluid intelligence. Results suggest that working memory capacity, but not short-term memory capacity or…
NASA Astrophysics Data System (ADS)
Zhao, Guangpu; Jian, Yongjun; Chang, Long; Buren, Mandula
2015-08-01
By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented.
NASA Astrophysics Data System (ADS)
Tripathi, Dharmendra; Pandey, S. K.; Das, S.
2011-07-01
The present investigation deals with the peristaltic transport of generalized Burgers' fluid with fractional element model in a channel. The analysis is carried out under long wavelength and low Reynolds number assumptions. An efficient mathematical tool, namely, Adomian decomposition method, is used to obtain the analytical approximate solutions of the fractional differential equation. The channel is governed by the propagation of sinusoidal waves that help the walls contract and relax but not expand beyond the natural boundary. The expressions of axial velocity, volume flow rate and pressure gradient are obtained. The effects of the fractional parameters and the material constants are discussed on pressure difference and the friction force across one wavelength. The comparative studies for various models of viscoelastic fluids such as fractional generalized Burgers' model, generalized Burgers' model, fractional Burgers' model and Burgers' model are performed. It is inferred that the movement of viscoelastic chyme with generalized Burgers' model through the small intestine is favorable in comparison to the movement of viscoelastic chyme with fractional generalized Burgers' model.
NASA Astrophysics Data System (ADS)
Liu, Hsing; Chen, Ying-Hsing; Lih, Jiann-Shing
2015-05-01
Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution.
Froese, M. W.; Blaum, K.; Fellenberger, F.; Grieser, M.; Lange, M.; Laux, F.; Menk, S.; Orlov, D. A.; Repnow, R.; Sieber, T.; Hahn, R. von; Wolf, A.; Toker, Y.
2011-02-15
The decay of excited aluminum-cluster anions (Al{sub n}{sup -}, n=4 and 5) has been investigated in a cryogenic linear ion-beam trap. A power-law is found to accurately reproduce the time dependence of the observed decay rates at early storage times, although the exponents are significantly larger than the typically observed 1/t decay. It is shown that the power-law exponent is, at most, weakly dependent on the cluster electron affinity and heat capacity. A previous power-law exponent model for small clusters is also shown to be in disagreement with both investigated species. The attribution of a drop in the decay rate at later times to radiative cooling as observed in larger molecules also does not appear justified in our case. A strong dependence of the power-law exponent on the ambient temperature was observed.
Ceronio, A D; Haarhoff, J
2005-01-01
In potable water treatment, the use of the power law to describe particle size distributions (PSDs) in particle counting practice is common. The power law is popular because it allows the reduction of numerous data bits to two meaningful parameters that completely describe the size distribution characteristics of a particle suspension. The model is however flawed. This paper presents the further development of an improved model (the variable-beta model) first proposed by Lawler (1997). Both the power law model and variable-beta model are used to describe the PSDs of a large number of potable water treatment samples taken from full-scale plants and the resulting correlations are compared. The findings from the comparison of data reduction methodologies support the argument that the variable-beta model is fundamentally more correct than the power law model and consequently describes the PSDs better.
Power-law Growth and Punctuated Equilibrium Dynamics in Water Resources Systems
NASA Astrophysics Data System (ADS)
Parolari, A.; Katul, G. G.; Porporato, A. M.
2015-12-01
The global rise in population-driven water scarcity and recent appreciation of strong dynamic coupling between human and natural systems has called for new approaches to predict the future sustainability of regional and global water resources systems. The dynamics of coupled human-water systems are driven by a complex set of social, environmental, and technological factors. Present projections of water resources systems range from a finite carrying capacity regulated by accessible freshwater, or `peak renewable water,' to punctuated evolution with new supplied and improved efficiency gained from technological and social innovation. However, these projections have yet to be quantified from observations or in a comprehensive theoretical framework. Using data on global water withdrawals and storage capacity of regional water supply systems, non-trivial dynamics are identified in water resources systems development over time, including power-law growth and punctuated equilibria. Two models are introduced to explain this behavior: (1) a delay differential equation and (2) a power-law with log-periodic oscillations, both of which rely on past conditions (or system memory) to describe the present rate of growth in the system. In addition, extension of the first model demonstrates how system delays and punctuated equilibria can emerge from coupling between human population growth and associated resource demands. Lastly, anecdotal evidence is used to demonstrate the likelihood of power-law growth in global water use from the agricultural revolution 3000 BC to the present. In a practical sense, the presence of these patterns in models with delayed oscillations suggests that current decision-making related to water resources development results from the historical accumulation of resource use decisions, technological and social changes, and their consequences.
Air-chemistry "turbulence": power-law scaling and statistical regularity
NASA Astrophysics Data System (ADS)
Hsu, H.-M.; Lin, C.-Y.; Guenther, A.; Tribbia, J. J.; Liu, S. C.
2011-03-01
With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, and plain/hill locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, intermediate (20 ~ 30 days) and intraseasonal (30 ~ 100 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of -5/3 and -1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, -3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are intriguingly interesting, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.
Air-chemistry "turbulence": power-law scaling and statistical regularity
NASA Astrophysics Data System (ADS)
Hsu, H.-M.; Lin, C.-Y.; Guenther, A.; Tribbia, J. J.; Liu, S. C.
2011-08-01
With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, plain/hill, and industrial/agricultural locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, and intermediate (20 ~ 30 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of -5/3 and -1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. These exponents are mostly independent of the averages and standard deviations of time series measured at various geographic settings, i.e., the spatial inhomogeneities. In other words, they possess dominant universal structures. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, -3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are important structural information, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.
Power-Law Modeling of Cancer Cell Fates Driven by Signaling Data to Reveal Drug Effects
Zhang, Fan; Wu, Min; Kwoh, Chee Keong; Zheng, Jie
2016-01-01
Extracellular signals are captured and transmitted by signaling proteins inside a cell. An important type of cellular responses to the signals is the cell fate decision, e.g., apoptosis. However, the underlying mechanisms of cell fate regulation are still unclear, thus comprehensive and detailed kinetic models are not yet available. Alternatively, data-driven models are promising to bridge signaling data with the phenotypic measurements of cell fates. The traditional linear model for data-driven modeling of signaling pathways has its limitations because it assumes that the a cell fate is proportional to the activities of signaling proteins, which is unlikely in the complex biological systems. Therefore, we propose a power-law model to relate the activities of all the measured signaling proteins to the probabilities of cell fates. In our experiments, we compared our nonlinear power-law model with the linear model on three cancer datasets with phosphoproteomics and cell fate measurements, which demonstrated that the nonlinear model has superior performance on cell fates prediction. By in silico simulation of virtual protein knock-down, the proposed model is able to reveal drug effects which can complement traditional approaches such as binding affinity analysis. Moreover, our model is able to capture cell line specific information to distinguish one cell line from another in cell fate prediction. Our results show that the power-law data-driven model is able to perform better in cell fate prediction and provide more insights into the signaling pathways for cancer cell fates than the linear model. PMID:27764199
Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators
NASA Astrophysics Data System (ADS)
Casteels, W.; Storme, F.; Le Boité, A.; Ciuti, C.
2016-03-01
We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states; in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a nonadiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in the presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.
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 approximately 1/t(alpha) with 0
Effects of diversity and procrastination in priority queuing theory: The different power law regimes
NASA Astrophysics Data System (ADS)
Saichev, A.; Sornette, D.
2010-01-01
Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law ˜1/tα with 0<α≤1 over a time scale of years. We present a simple model for this persistence phenomenon, framed within the standard priority queuing theory, of a target task which has the lowest priority compared to all other tasks that flow on the computer of an individual. We identify a “time deficit” control parameter β and a bifurcation to a regime where there is a nonzero probability for the target task to never be completed. The distribution of waiting time T until the completion of the target task has the power law tail ˜1/t1/2 , resulting from a first-passage solution of an equivalent Wiener process. Taking into account a diversity of time deficit parameters in a population of individuals, the power law tail is changed into 1/tα , with αɛ(0.5,∞) , including the well-known case 1/t . We also study the effect of “procrastination,” defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks. This regime provides an explanation for even slower apparent decay and longer persistence.
NASA Astrophysics Data System (ADS)
Wang, Q.; Yang, M.; Song, X. L.; Jia, J.; Xiang, Z. D.
2016-07-01
The conventional power law creep equation (Norton equation) relating the minimum creep rate to creep stress and temperature cannot be used to predict the long-term creep strengths of creep-resistant steels if its parameters are determined only from short-term measurements. This is because the stress exponent and activation energy of creep determined on the basis of this equation depend on creep temperature and stress and these dependences cannot be predicted using this equation. In this work, it is shown that these problems associated with the conventional power law creep equation can be resolved if the new power law equation is used to rationalize the creep data. The new power law creep equation takes a form similar to the conventional power law creep equation but has a radically different capability not only in rationalizing creep data but also in predicting the long-term creep strengths from short-term test data. These capabilities of the new power law creep equation are demonstrated using the tensile strength and creep test data measured for both pipe and tube grades of the creep-resistant steel 9Cr-1.8W-0.5Mo-V-Nb-B (P92 and T92).
On the power-law distributions of X-ray fluxes from solar flares observed with GOES
NASA Astrophysics Data System (ADS)
Li, You-Ping; Feng, Li; Zhang, Ping; Liu, Si-Ming; Gan, Wei-Qun
2016-10-01
The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality (SOC). In this paper, we first show that, so long as the shape of the normalized light curve is not correlated with the peak flux, the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the power-law frequency distribution of the peak flux, which may partially explain why power-law distributions are ubiquitous in the Universe. We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different: the higher energy channel has a harder distribution than the lower energy channel, which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites. The temperature (T) distribution, on the other hand, approaches a power-law distribution with an index of 2 for high values of T. Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.
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; /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.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; ...
2015-12-30
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron–positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power lawmore » $${\\gamma }^{-\\alpha }$$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.« less
Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids
Maloney, C. E.; Robbins, M. O.
2009-06-05
The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.
On global minimizers of repulsive–attractive power-law interaction energies
Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong
2014-01-01
We consider the minimization of the repulsive–attractive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations. PMID:25288810
Apparent Power Law Scaling of Variable Range Hopping Conduction in Carbonized Polymer Nanofibers
Kim, Kyung Ho; Lara-Avila, Samuel; Kang, Hojin; He, Hans; Eklӧf, Johnas; Hong, Sung Ju; Park, Min; Moth-Poulsen, Kasper; Matsushita, Satoshi; Akagi, Kazuo; Kubatkin, Sergey; Park, Yung Woo
2016-01-01
We induce dramatic changes in the structure of conducting polymer nanofibers by carbonization at 800 °C and compare charge transport properties between carbonized and pristine nanofibers. Despite the profound structural differences, both types of systems display power law dependence of current with voltage and temperature, and all measurements can be scaled into a single universal curve. We analyze our experimental data in the framework of variable range hopping and argue that this mechanism can explain transport properties of pristine polymer nanofibers as well. PMID:27886233
Apparent Power Law Scaling of Variable Range Hopping Conduction in Carbonized Polymer Nanofibers
NASA Astrophysics Data System (ADS)
Kim, Kyung Ho; Lara-Avila, Samuel; Kang, Hojin; He, Hans; Eklӧf, Johnas; Hong, Sung Ju; Park, Min; Moth-Poulsen, Kasper; Matsushita, Satoshi; Akagi, Kazuo; Kubatkin, Sergey; Park, Yung Woo
2016-11-01
We induce dramatic changes in the structure of conducting polymer nanofibers by carbonization at 800 °C and compare charge transport properties between carbonized and pristine nanofibers. Despite the profound structural differences, both types of systems display power law dependence of current with voltage and temperature, and all measurements can be scaled into a single universal curve. We analyze our experimental data in the framework of variable range hopping and argue that this mechanism can explain transport properties of pristine polymer nanofibers as well.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
NASA Astrophysics Data System (ADS)
Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco
2015-06-01
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
Bakalis, Evangelos E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco E-mail: francesco.zerbetto@unibo.it; Venturini, Alessandro
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.
An explanation for the universal 3.5 power-law observed in currency markets
NASA Astrophysics Data System (ADS)
Johnson, Nicholas A.; Johnson, Neil F.
We present a mathematical theory to explain a recent empirical finding in the Physics literature (Zhao et al., 2013) in which the distributions of waiting-times between discrete events were found to exhibit power-law tails with an apparent universal exponent: α ∼ 3.5 . This new theory provides the first ever qualitative and quantitative explanation of Zhao et al.'s surprising finding. It also provides a mechanistic description of the origin of the observed universality, assigning its cause to the emergence of dynamical feedback processes between evolving clusters of like-minded agents.
Power-law tail of the velocity distribution in granular gases
NASA Astrophysics Data System (ADS)
Kang, Wenfeng; Ben-Naim, Eli; Machta, Jon
2007-03-01
We use a two-dimensional event-driven molecular dynamics simulation to study the velocity distribution of a granular gas. We implement the high energy injection mechanism described in Ref. [1]. At a small rate γ we boost randomly chosen particles to a high energy. The resulting driven steady state is found to have a power-law high-energy tail in the velocity distribution, f(v) ˜ v ^- σ. The simulation results for the exponent σ are in good agreement with the theoretical predictions of Ref. [1]. [1] E. Ben-Naim and J. Machta, Phys. Rev. Lett. 94, 138001 (2005).
Additivity property and emergence of power laws in nonequilibrium steady states.
Das, Arghya; Chatterjee, Sayani; Pradhan, Punyabrata; Mohanty, P K
2015-11-01
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.
NASA Technical Reports Server (NTRS)
Farassat, Fereidoun; Myers, Michael K.
2011-01-01
This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.
Generalized multiscale finite element method for non-Newtonian fluid flow in perforated domain
NASA Astrophysics Data System (ADS)
Chung, E. T.; Iliev, O.; Vasilyeva, M. V.
2016-10-01
In this work, we consider a non-Newtonian fluid flow in perforated domains. Fluid flow in perforated domains have a multiscale nature and solution techniques for such problems require high resolution. In particular, the discretization needs to honor the irregular boundaries of perforations. This gives rise to a fine-scale problems with many degrees of freedom which can be very expensive to solve. In this work, we develop a multiscale approach that attempt to solve such problems on a coarse grid by constructing multiscale basis functions. We follow Generalized Multiscale Finite Element Method (GMsFEM) [1, 2] and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems [3, 4]. We show that with a few basis functions in each coarse block, one can accurately approximate the solution, where each coarse block can contain many small inclusions.
A Generalized Multi-Phase Framework for Modeling Cavitation in Cryogenic Fluids
NASA Technical Reports Server (NTRS)
Dorney, Dan (Technical Monitor); Hosangadi, Ashvin; Ahuja, Vineet
2003-01-01
A generalized multi-phase formulation for cavitation in fluids operating at temperatures elevated relative to their critical temperatures is presented. The thermal effects and the accompanying property variations due to phase change are modeled rigorously. Thermal equilibrium is assumed and fluid thermodynamic properties are specified along the saturation line using the NIST-12 databank. Fundamental changes in the physical characteristics of the cavity when thermal effects become pronounced are identified; the cavity becomes more porous, the interface less distinct, and has increased entrainment when temperature variations are present. Quantitative estimates of temperature and pressure depressions in both liquid nitrogen and liquid hydrogen were computed and compared with experimental data of Hord for hydrofoils. Excellent estimates of the leading edge temperature and pressure depression were obtained while the comparisons in the cavity closure region were reasonable. Liquid nitrogen cavities were consistently found to be in thermal equilibrium while liquid hydrogen cavities exhibited small, but distinct, non-equilibrium effects.
Exact relativistic expressions for wave refraction in a generally moving fluid.
Cavalleri, G; Tonni, E; Barbero, F
2013-04-01
The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation.
Generalized coupling parameter expansion: application to square well and Lennard-Jones fluids.
Sai Venkata Ramana, A
2013-07-28
The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function with respect to coupling parameter. We applied seventh order version of the theory to Square-Well (SW) and Lennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, the theory reproduced the radial distribution functions obtained from integral equation theory (IET) and simulations with good accuracy. Also, the method worked inside the liquid-vapor coexistence region where the IETs are known to fail. In the case of SW fluids, the use of Carnahan-Starling expression for Helmholtz free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET with the same bridge function. The derivatives of the bridge function are seen to have significant effect on the liquid part of the LVPD. For extremely narrow SW fluids, we found that the third order theory is more accurate than the higher order versions. However, considering the convergence of the perturbation series, we concluded that the accuracy of the third order version is a spurious result. We also obtained the surface tension for SW fluids of various ranges. Results of present theory and simulations are in good agreement. In the case of LJ fluids, the equation of state obtained from the present method matched with that obtained from IET with negligible deviation. We also obtained LVPD of LJ fluid from virial and energy routes and found that there is slight inconsistency between the two routes. The applications lead to the following conclusions. In cases where reference system properties are known accurately, the present method gives results which are very much improved over those obtained from the IET with the same bridge function. In cases where reference system data is not available, the method serves as an alternative way of solving the Ornstein-Zernike equation with a given closure relation
NASA Astrophysics Data System (ADS)
Kang, Jianhong; Xu, Mingyu
2009-04-01
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
Vortex Lattice Metastability and Power Law Dynamics in MgB2
NASA Astrophysics Data System (ADS)
Rastovski, Catherine; Kuhn, S. J.; Smith, K.; Eskildsen, M. R.; Debeer-Schmitt, L.; Dewhurst, C. D.; Gannon, W. J.; Zhigadlo, N. D.; Karpinski, J.
2014-03-01
Previous small-angle neutron scattering (SANS) studies of the vortex lattice (VL) of MgB2 with H ∥ c found a triangular VL which undergoes a field-driven 30° reorientation transition, forming three distinct ground state phases. A high degree of metastability exists between the VL phases of MgB2 that cannot be attributed to vortex pinning and may be a result of the jamming of VL domains [C. Rastovski et al., Phys. Rev. Lett. 111, 107002 (2013)]. To further investigate the effect of vortex motion on the metastable to ground state VL transition, we applied a small AC magnetic field parallel or perpendicular to the vortices to ``shake'' the lattice. The metastable VL volume fraction decreased with a two-step power law dependence on the number of applied AC cycles. The slow and then fast power law decay of the metastable state may indicate first nucleation and then growth of ground state VL domains. This work was supported by the Department of Energy, Basic Energy Sciences under Award No. DE-FG02-10ER46783.
Power law distribution in statistics of failures in operation of spacecraft onboard equipment
NASA Astrophysics Data System (ADS)
Karimova, L. M.; Kruglun, O. A.; Makarenko, N. G.; Romanova, N. V.
2011-10-01
The possibility of using the statistics of recurrence time for extreme events is studied in this paper having in mind the problems of control and prediction of failures in spacecraft operation. The information about failures onboard satellites of various types presented by the US National Geophysical Data Center was analyzed. It was found that the probability density of recurrence intervals followed a power law of the Pareto type with an index equal to 2.3. The obtained result is consistent both with the theory of normal catastrophes and with the principle of self-organization of criticality for metastable active heterogeneous environment. A practical consequence of the obtained result consists in the fact that predictions of these extreme events should not rely on traditional models with the second-order Pearson statistics. To make predictions, the models are necessary that take into account the power law distribution of recurrence intervals for failures on satellites. The failures should be considered in these models as extreme events connected with manifestation of the space environment factors.
Nonuniversal power law scaling in the probability distribution of scientific citations.
Peterson, George J; Pressé, Steve; Dill, Ken A
2010-09-14
We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ("classics") are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The "tipping point" at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975-1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited.
NASA Astrophysics Data System (ADS)
Cota, Wesley; Ferreira, Silvio C.; Ódor, Géza
2016-03-01
We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space λ1<λ <λ2 , suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at λ2. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at λc=0 . Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.
NASA Astrophysics Data System (ADS)
Hong, S. Lee; Bodfish, James W.; Newell, Karl M.
2006-03-01
We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.
Lifetimes of metastable ion clouds in a Paul trap: Power-law scaling
NASA Astrophysics Data System (ADS)
Weiss, D. K.; Nam, Y. S.; Blümel, R.
2016-04-01
It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime τ¯m of the metastable cloud follows a power law, τ¯m˜(γ-γc) -β , where γc is the value of the damping constant at which the transition occurs. The exponent β depends on the trap control parameter q , but is independent of both the number of particles N stored in the trap and the trap control parameter a , which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given a and q , γc scales approximately like γc=C ln[ln(N ) ] +D as a function of N , where C and D are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.
Ueno, Taro; Masuda, Naoki; Kume, Shoen; Kume, Kazuhiko
2012-01-01
We analyzed the effects of dopamine signaling on the temporal organization of rest and activity in Drosophila melanogaster. Locomotor behaviors were recorded using a video-monitoring system, and the amounts of movements were quantified by using an image processing program. We, first, confirmed that rest bout durations followed long-tailed (i.e., power-law) distributions, whereas activity bout durations did not with a strict method described by Clauset et al. We also studied the effects of circadian rhythm and ambient temperature on rest bouts and activity bouts. The fraction of activity significantly increased during subjective day and at high temperature, but the power-law exponent of the rest bout distribution was not affected. The reduction in rest was realized by reduction in long rest bouts. The distribution of activity bouts did not change drastically under the above mentioned conditions. We then assessed the effects of dopamine. The distribution of rest bouts became less long-tailed and the time spent in activity significantly increased after the augmentation of dopamine signaling. Administration of a dopamine biosynthesis inhibitor yielded the opposite effects. However, the distribution of activity bouts did not contribute to the changes. These results suggest that the modulation of locomotor behavior by dopamine is predominantly controlled by changing the duration of rest bouts, rather than the duration of activity bouts.
Observations of Suprathermal Power Law Tails with ACE, Ulysses, MESSENGER, and Voyager
NASA Astrophysics Data System (ADS)
Gloeckler, G.; Fisk, L. A.
2007-12-01
Observations of ubiquitous, suprathermal power law tails with the unique spectral index of -5 on the velocity distributions of solar wind and pickup ions raise important questions and have far reaching consequences. The question of how these tails are formed during quiet times, when no shocks are present, was previously addressed and is briefly reviewed here. One consequence of the existence of these tails during quiet times is that sufficiently energetic particles are always readily available for further acceleration by shocks. To study the evolution of suprathermal tails over a large range of heliocentric distances, we will use proton spectra measured with ACE, Ulysses and Voyager during quiet times as well as upstream and downstream of quasi-stationary and traveling shocks. To look for the first time at suprathermal tails at distances closer to the Sun than 1 AU, we will present our preliminary results from the FIPS instrument on the Mercury MESSENGER Mission. Applying thermodynamic constraints on non-adiabatic heating of upstream particles by a shock, we obtain the downstream -5 power law spectra that are observed and derive an expression for the tail pressure jump across the shock.
Universal correlations and power-law tails in financial covariance matrices
NASA Astrophysics Data System (ADS)
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.
Keeping the edge: an accurate numerical method to solve the stream power law
NASA Astrophysics Data System (ADS)
Campforts, B.; Govers, G.
2015-12-01
Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.
Podesta, J. J.
2008-12-15
The relativistic plasma dispersion relation is derived for Langmuir waves in a spatially homogeneous unmagnetized plasma in which the electrons have an isotropic power-law distribution in momentum space. The theory is applied to the study of Langmuir waves in the quiescent solar wind near the orbit of the Earth assuming that the electron distribution function can be approximated as a power-law from thermal energies {approx}10 eV to relativistic energies < or approx. 100 keV. Numerical solutions of the dispersion relation show that in the regime of weak Landau damping the phase speeds of the waves match the velocities of the high-energy particles, known in the solar wind literature as the superhalo, which lie in the range 0.09
Nonuniversal power law scaling in the probability distribution of scientific citations
Peterson, George J.; Pressé, Steve; Dill, Ken A.
2010-01-01
We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations (“classics”) are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The “tipping point” at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975–1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited. PMID:20805513
Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales
NASA Technical Reports Server (NTRS)
Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.
2006-01-01
The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.
Bose-Einstein condensation in dark power-law laser traps
Jaouadi, A.; Gaaloul, N.; Viaris de Lesegno, B.; Pruvost, L.; Telmini, M.; Charron, E.
2010-08-15
We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order l allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a 'finger' or of a 'hockey puck' in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.
Bose-Einstein condensation in dark power-law laser traps
NASA Astrophysics Data System (ADS)
Jaouadi, A.; Gaaloul, N.; Viaris de Lesegno, B.; Telmini, M.; Pruvost, L.; Charron, E.
2010-08-01
We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order ℓ allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a “finger” or of a “hockey puck” in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.
Emergence of power-law in a market with mixed models
NASA Astrophysics Data System (ADS)
Ali Saif, M.; Gade, Prashant M.
2007-10-01
We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.
Accurate and unbiased estimation of power-law exponents from single-emitter blinking data.
Hoogenboom, Jacob P; den Otter, Wouter K; Offerhaus, Herman L
2006-11-28
Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching.
Power-law decay exponents: A dynamical criterion for predicting thermalization
NASA Astrophysics Data System (ADS)
Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.
2017-01-01
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.
So You Think the Crab is Described by a Power-Law Spectrum
NASA Technical Reports Server (NTRS)
Weisskopf, Martin C.
2008-01-01
X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.
Underestimating extreme events in power-law behavior due to machine-dependent cutoffs
NASA Astrophysics Data System (ADS)
Radicchi, Filippo
2014-11-01
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subject to severe machine-dependent limitations. As a result, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, which are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies, they also pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.
Transition from Exponential to Power Law Income Distributions in a Chaotic Market
NASA Astrophysics Data System (ADS)
Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.
Moduli of curve families and (quasi-)conformality of power-law entropies
NASA Astrophysics Data System (ADS)
Kalogeropoulos, Nikos
2016-03-01
We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the calculations of the moduli of curve families for a cylinder and for an annulus in ℝn. The underlying motivation for these studies is that the definitions and some properties of the modulus of a curve family resembles those of the Tsallis entropy, when the latter is seen from a micro-canonical viewpoint. We comment on the origin of the conjectured invariance of the Tsallis entropy under Möbius transformations of the non-extensive (entropic) parameter. Needing techniques applicable to both locally Euclidean and fractal classes of spaces, we examine the behavior of the Tsallis functional, via the modulus, under quasi-conformal maps. We comment on properties of such maps and their possible significance for the dynamical foundations of power-law entropies.
NASA Astrophysics Data System (ADS)
Blaes, Omer
Stellar mass black holes in certain types of binary systems accrete matter from their companion stars through rotating, turbulent flows known as accretion disks. These disks are observed by space X-ray missions to have a number of distinct spectral/variability states, the most mysterious one being the very high/steep power law state that generally occurs at very high luminosities. This state is particularly interesting as it exhibits unique quasi-periodic oscillations observed in the X-rays that, if understood, might help us directly measure the properties of the black hole spacetime. Radiation pressure is an important physical process at such high luminosities, and modifies the character of the accretion disk in a number of unique ways. One of the ways that it does this is that it enables turbulent speeds in the disk to exceed thermal speeds of electrons, thereby introducing a completely new radiation process - turbulent Comptonization. This radiation process is promising for explaining the unique spectral characteristics of the very high/steep power law state. We will test this hypothesis by making detailed calculations of the emergent radiation spectrum from numerical simulation data of the turbulence in local patches of the disk at high levels of radiation pressure. These will be the first detailed theoretical calculations of turbulent Comptonization, which should be an important process for modeling NASA data from high luminosity black hole accretion. We hope that this will shed light on the nature of the mysterious very high/steep power law state. The research will form the basis of the PhD thesis of a graduate student, in line with NASA's educational and training objectives.
NASA Technical Reports Server (NTRS)
Majumdar, Alok
2013-01-01
The purpose of the paper is to present the analytical capability developed to model no vent chill and fill of cryogenic tank to support CPST (Cryogenic Propellant Storage and Transfer) program. Generalized Fluid System Simulation Program (GFSSP) was adapted to simulate charge-holdvent method of Tank Chilldown. GFSSP models were developed to simulate chilldown of LH2 tank in K-site Test Facility and numerical predictions were compared with test data. The report also describes the modeling technique of simulating the chilldown of a cryogenic transfer line and GFSSP models were developed to simulate the chilldown of a long transfer line and compared with test data.
Reduced viscosity interpreted for fluid/gas mixtures
NASA Technical Reports Server (NTRS)
Lewis, D. H.
1981-01-01
Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.
NASA Astrophysics Data System (ADS)
Jin, Fan; Guo, Xu; Gao, Huajian
2013-12-01
A cohesive zone model of axisymmetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the double-Hertz model of Greenwood and Johnson (1998). Closed-form solutions are obtained analytically for the surface stress, deformation fields and equilibrium relations among applied load, indentation depth, inner and outer radii of the cohesive zone, which include the corresponding solutions for homogeneous isotropic materials and the Gibson solid as special cases. These solutions provide a continuous transition between JKR and DMT type contact models through a generalized Tabor parameter μ. Our analysis reveals that the magnitude of the pull-off force ranges from (3+k)πRΔγ/2 to 2πRΔγ, where k, R and Δγ denote the gradient exponent of the elastic modulus for the half-space, the radius of the sphere and the work of adhesion, respectively. Interestingly, the pull-off force for the Gibson solid is found to be identically equal to 2πRΔγ, independent of the corresponding Tabor parameter. The obtained analytical solutions are validated with finite element simulations.
NASA Astrophysics Data System (ADS)
Li, Guang-Xing; Burkert, Andreas
2017-02-01
Gravity plays a determining role in the evolution of the molecular ISM. In 2016, we proposed a measure called gravitational energy spectrum to quantify the importance of gravity on multiple physical scales. In this paper, using a wavelet-based decomposition technique, we derive the gravitational energy spectra of the Orion A and the Orion B molecular cloud from observational data. The gravitational energy spectra exhibit power-law-like behaviours. From a few parsec down to ˜0.1 pc scale, the Orion A and Orion B molecular cloud have Ep(k) ˜ k-1.88 and Ep(k) ˜ k-2.09, respectively. These scaling exponents are close to the scaling exponents of the kinetic energy power spectrum of compressible turbulence (where E ˜ k-2), with a near-equipartition of turbulent versus gravitational energy on multiple scales. This provides a clear evidence that gravity is able to counteract effectively against turbulent motion for these length-scales. The results confirm our earlier analytical estimates. For the Orion A molecular cloud, gravity inevitably dominates turbulence inside the cloud. Our results provide a clear observational proof that gravity is playing a determining role in the evolution these molecular clouds from the cloud scale down to ˜ 0.1 pc. However, turbulence is likely to dominate in clouds such as California. The method is general and should be applicable to all the astrophysical problems where gravity plays a role.
Mondal, Sourav; De, Sirshendu
2013-01-01
Mass transport of a neutral solute for a power law fluid in a porous microtube under electro-osmotic flow regime is characterized in this study. Combined electro-osmotic and pressure driven flow is conducted herein. An analytical solution of concentration profile within mass transfer boundary layer is derived from the first principle. The solute transport through the porous wall is also coupled with the electro-osmotic flow to predict the solute concentration in the permeate stream. The effects of non-Newtonian rheology and the operating conditions on the permeation rate and permeate solute concentration are analyzed in detail. Both cases of assisting (electro-osmotic and poiseulle flow are in same direction) and opposing flow (the individual flows are in opposite direction) cases are taken care of. Enhancement of Sherwood due to electro-osmotic flow for a non-porous conduit is also quantified. Effects if non-Newtonian rheology on Sherwood number enhancement are observed. PMID:24404046
Generalized fictitious methods for fluid-structure interactions: Analysis and simulations
NASA Astrophysics Data System (ADS)
Yu, Yue; Baek, Hyoungsu; Karniadakis, George Em
2013-07-01
We present a new fictitious pressure method for fluid-structure interaction (FSI) problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in [1]. The fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver. We analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor (convergence rate index) at the FSI interface [2]. This analysis also demonstrates an apparent similarity of fictitious methods to the FSI approach based on Robin boundary conditions, which have been found to be very effective in FSI problems. We implement all methods, including the semi-implicit Robin based coupling method, in the context of spectral element discretization, which is more sensitive to temporal instabilities than low-order methods. However, the methods we present here are simple and general, and hence applicable to FSI based on any other spatial discretization. In numerical tests, we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex-induced vibrations (VIV) even at zero mass ratio ("for-ever-resonance"). We also develop an empirical a posteriori analysis for complex geometries and apply it to 3D patient-specific flexible brain arteries with aneurysms for very large deformations. We demonstrate that the fictitious pressure method enhances stability and convergence, and is comparable or better in most cases to the Robin approach or the other fictitious methods.
Listing triangles in expected linear time on a class of power law graphs.
Nordman, Daniel J.; Wilson, Alyson G.; Phillips, Cynthia Ann; Berry, Jonathan W.
2010-07-01
Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysis for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is
From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies
NASA Astrophysics Data System (ADS)
Soesoo, Alvar; Bons, Paul D.
2015-07-01
Magma is generated by partial melting from micrometre-scale droplets at the source and may accumulate to form >100 km-scale plutons. Magma accumulation thus spans well over ten orders of magnitude in scale. Here we provide measurements of migmatitic leucosomes and granitic veins in drill cores from the Estonian Proterozoic basement and outcrops at Masku in SW Finland and Montemor-o-Novo, central Portugal. Despite the differences in size and number of measured leucosomes and magmatic veins, differences in host rock types and metamorphic grades, the cumulative width distribution of the studied magmatic leucosomes/veins follows a power law with exponents usually between 0.7 and 1.8. Published maps of the SE Australian Lachlan Fold Belt were used to investigate the distribution of granitoid pluton sizes. The granites occupy ca. 22 % of the 2.6 × 105 km2 area. The cumulative pluton area distributions show good power law distributions with exponents between 0.6 and 0.8 depending on pluton area group. Using the self-affine nature of pluton shapes, it is possible to estimate the total volume of magma that was expelled from the source in the 2.6 × 105 km2 map area, giving an estimated 0.8 km3 of magma per km2. It has been suggested in the literature that magma batches in the source merge to form ever-bigger batches in a self-organized way. This leads to a power law for the cumulative distribution of magma volumes, with an exponent m V between 1 for inefficient melt extraction, and 2/3 for maximum accumulation efficiency as most of the volume resides in the largest batches that can escape from the source. If m V ≥ 1, the mass of the magma is dominated by small batches; in case m = 2/3, about 50 % of all magma in the system is placed in a single largest batch. Our observations support the model that the crust develops a self-organized critical state during magma generation. In this state, magma batches accumulate in a non-continuous, step-wise manner to form ever
Zhao, Xiaofeng; McGough, Robert J
2016-05-01
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.
Wavelet-based analysis and power law classification of C/NOFS high-resolution electron density data
NASA Astrophysics Data System (ADS)
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.
Origins of power-law degree distribution in the heterogeneity of human activity in social networks
Muchnik, Lev; Pei, Sen; Parra, Lucas C.; Reis, Saulo D. S.; Andrade Jr, José S.; Havlin, Shlomo; Makse, Hernán A.
2013-01-01
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a “maximum entropy attachment” model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people. PMID:23648793
Observation of the 1/2 power law in Rayleigh-Bénard convection.
Roche, P E; Castaing, B; Chabaud, B; Hébral, B
2001-04-01
The 1/2 power law is reported in a Rayleigh-Bénard experiment: Nu approximately Ra(1/2), where Ra and Nu are the Rayleigh and Nusselt numbers. This observation is coherent with the predictions of the ultimate convection regime, characterized by fully turbulent heat transfers. Ordered rough boundaries are used to cancel the correction due to the thickness variation of the viscous sublayer, and the observation of the asymptotic regime is therefore possible. This result supports the interpretation of a laminar-turbulent boundary-layer transition to account for the observation of Chavanne et al. of a new regime [X. Chavanne et al., Phys. Rev. Lett. 79, 3648 (1997)].
Modified bosonic gas trapped in a generic 3-dim power law potential
NASA Astrophysics Data System (ADS)
Castellanos, E.; Laemmerzahl, C.
2014-04-01
We analyze the consequences caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the condensation temperature is shifted as a consequence of such deformation and show that this fact could be used to provide bounds on the deformation parameters. Additionally, we show that the shift in the condensation temperature, described as a non-trivial function of the number of particles and the trap parameters, could be used as a criterion to analyze the effects caused by a deformed dispersion relation in weakly interacting systems and also in finite size systems.
Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential
NASA Astrophysics Data System (ADS)
Koura, Katsuhisa; Matsumoto, Hiroaki
1991-10-01
The variable soft sphere (VSS) molecular model is introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse-power-law (IPL) or Lennard-Jones (LJ) potential. The VSS model has almost the same analytical and computational simplicity (computation time) as the variable hard sphere (VHS) model in the Monte Carlo simulation of rarefied gas flows. The null-collision Monte Carlo method is used to make comparative calculations for the molecular diffusion in a heat-bath gas and the normal shock wave structure in a simple gas. For the most severe test of the VSS model for the IPL potential, the softest practical model corresponding to the Maxwell molecule is chosen. The agreement in the molecular diffusion and shock wave structure between the VSS model and the IPL or LJ potential is remarkably good.
Power law classification scheme of time series correlations. On the example of G20 group
NASA Astrophysics Data System (ADS)
Miśkiewicz, Janusz
2013-05-01
A power law classification scheme (PLCS) of time series correlations is proposed. It is shown that PLCS provides the ability to classify nonlinear correlations and measure their stability. PLCS has been applied to gross domestic product (GDP) per capita of G20 members and their correlations analysed. It has been shown that the method does not only recognise linear correlations properly, but also allows to point out converging time series as well as to distinguish nonlinear correlations. PLCS is capable of crash recognition as it is shown in the Argentina example. Finally the strength of correlations and the stability of correlation matrices have been used to construct a minimum spanning tree (MST). The results were compared with those based on the ultrametric distance (UD). Comparing the structures of MST, UD and PLCS indicates that the latter one is more complicated, but better fits the expected economic relations within the G20.
Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses
NASA Astrophysics Data System (ADS)
Garcia, O. E.; Theodorsen, A.
2017-02-01
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For a constant pulse duration, this is shown to result in an exponential power spectral density for the stationary process. A random distribution of pulse durations modifies the frequency spectrum, and several examples are shown to result in power law spectra. The distribution of pulse durations does not influence the characteristic function and thus neither the moments nor the probability density function of the random variable. It is demonstrated that the fluctuations are intrinsically intermittent through a large excess kurtosis moment in the limit of weak pulse overlap. These results allow for estimation of the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.
Power law of shear viscosity in Einstein-Maxwell-Dilaton-Axion model
NASA Astrophysics Data System (ADS)
Ling, Yi; Xian, Zhuoyu; Zhou, Zhenhua
2017-02-01
We construct charged black hole solutions with hyperscaling violation in the infrared (IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is verified numerically at low temperature T, namely, η/s ∼ T κ , where the values of exponent κ coincide with the analytical results. We also find that the exponent κ is not affected by irrelevant current, but is reduced by the relevant current. Supported by National Natural Science Foundation of China (11275208, 11575195), Opening Project of Shanghai Key Laboratory of High Temperature Superconductors (14DZ2260700) and Jiangxi Young Scientists (JingGang Star) Program and 555 Talent Project of Jiangxi Province
Semiclassical trace formula for the two-dimensional radial power-law potentials.
Magner, A G; Vlasenko, A A; Arita, K
2013-06-01
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate up to a constant shift the radial dependence of the Woods-Saxon potential and its quantum spectra in a bound region, was derived by the improved stationary phase method. The specific analytical results are obtained for the powers α=4 and 6. The enhancement of periodic-orbit contribution to the level density near the bifurcations are found to be significant for the description of the fine shell structure. The semiclassical trace formulas for the shell corrections to the level density and the energy of many-fermion systems reproduce the quantum results with good accuracy through all the bifurcation (symmetry breaking) catastrophe points, where the standard stationary-phase method breaks down. Various limits (including the harmonic oscillator and the spherical billiard) are obtained from the same analytical trace formula.
Scalar field probes of power-law space-time singularities
NASA Astrophysics Data System (ADS)
Blau, Matthias; Frank, Denis; Weiss, Sebastian
2006-08-01
We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x-2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x-2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
NASA Astrophysics Data System (ADS)
Liu, Chao; Li, Rong
2016-09-01
An evolutionary prisoner's dilemma game (PDG) with players located on Barabási-Albert scale-free networks is studied. The impact of players' heterogeneous temporal activity pattern on the evolution of cooperation is investigated. To this end, the normal procedure that players update their strategies immediately after a round of game is discarded. Instead, players update strategies according to their assigned reproduction time, which follows a power-law distribution. We find that the temporal heterogeneity of players' activities facilitates the prosperity of cooperation, indicating the important role of hubs in the maintenance of cooperation on scale-free networks. When the reproduction time is assigned to individuals negatively related to their degrees, a fluctuation of the cooperation level with the increase of the exponent β is observed.
NASA Technical Reports Server (NTRS)
Choi, Sung R.; Gyekenyesi, John P.
2002-01-01
The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.
Slow synaptic dynamics in a network: From exponential to power-law forgetting
NASA Astrophysics Data System (ADS)
Luck, J. M.; Mehta, A.
2014-09-01
We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√t relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.
NASA Astrophysics Data System (ADS)
Fan, Qingju; Wu, Yonghong
2015-08-01
In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.
Conductance statistics for the power-law banded random matrix model
Martinez-Mendoza, A. J.; Mendez-Bermudez, J. A.; Varga, Imre
2010-12-21
We study numerically the conductance statistics of the one-dimensional (1D) Anderson model with random long-range hoppings described by the Power-law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single-mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT){proportional_to}T{sup M2/2}, for T<<
A comment on power-law inflation with a dark radiation component
NASA Astrophysics Data System (ADS)
Di Valentino, Eleonora; Bouchet, François R.
2016-10-01
Tram et al. 2016 recently pointed out in [1] that power-law inflation in presence of a dark radiation component may relieve the 3.3 σ tension which exists within standard ΛCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) [2] and the value derived from CMB anisotropy data [3] by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the σ8 tension between the Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from Planck HFI data [4] are included in the analysis, the H0 tension reappears and this scenario looses appeal.
Cohen, Joel E
2014-05-01
Taylor's power law of fluctuation scaling (TL) states that for population density, population abundance, biomass density, biomass abundance, cell mass, protein copy number, or any other nonnegative-valued random variable in which the mean and the variance are positive, variance=a(mean)(b),a>0, or equivalently log variance=loga+b×log mean. Many empirical examples and practical applications of TL are known, but understanding of TL's origins and interpretations remains incomplete. We show here that, as time becomes large, TL arises from multiplicative population growth in which successive random factors are chosen by a Markov chain. We give exact formulas for a and b in terms of the Markov transition matrix and the values of the successive multiplicative factors. In this model, the mean and variance asymptotically increase exponentially if and only if b>2 and asymptotically decrease exponentially if and only if b<2.
Origins of power-law degree distribution in the heterogeneity of human activity in social networks.
Muchnik, Lev; Pei, Sen; Parra, Lucas C; Reis, Saulo D S; Andrade, José S; Havlin, Shlomo; Makse, Hernán A
2013-01-01
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.
Phase scintillations due to equatorial F region irregularities with two-component power law spectrum
NASA Astrophysics Data System (ADS)
Bhattacharyya, A.; Rastogi, R. G.
1986-10-01
Power spectra of weak phase scintillations on a 140-MHz signal, transmitted from the geostationary satellite ATS 6 and observed during premidnight and postmidnight periods at an equatorial station Ootacamund (magnetic dip 6 N), show that the nighttime equatorial F region irregularities in the wavelength range of about hundred meters to a few kilometers exhibit a two-component power law spectrum. The long- and short-wavelength spectral indices and the break scale at which the transition from a shallow to a steep slope occurs are determined self-consistently using both the phase and amplitude scintillation data. As the power spectra of phase scintillations do not exhibit the effect of Fresnel filtering, they provide fairly accurate estimates of the spectral indices and the break scale. These estimated parameters are utilized in a model calculation of the dependence of the S4 index on signal frequency based on weak scattering theory.
Architectures engender crises: The emergence of power laws in social networks
NASA Astrophysics Data System (ADS)
Tohmé, Fernando; Larrosa, Juan M. C.
2016-05-01
Recent financial crises posed a number of questions. The most salient were related to the cogency of derivatives and other sophisticated hedging instruments. One claim is that all those instruments rely heavily on the assumption that events in the world are guided by normal distributions while, instead, all the evidence shows that they actually follow fat-tailed power laws. Our conjecture is that it is the very financial architecture that engenders extreme events. Not on purpose but just because of its complexity. That is, the system has an internal connection structure that is able to propagate and enhance initially small disturbances. The final outcome ends up not being correlated with its triggering event. To support this claim, we appeal to the intuition drawn from the behavior of social networks. Most of the interesting cases constitute scale-free structures. In particular, we contend, those that arise from strategic decisions of the agents.
Validation of a power-law noise model for simulating small-scale breast tissue
NASA Astrophysics Data System (ADS)
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.
NASA Technical Reports Server (NTRS)
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.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
NASA Technical Reports Server (NTRS)
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Supernova blast waves in wind-blown bubbles, turbulent, and power-law ambient media
NASA Astrophysics Data System (ADS)
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.
Effect of phase morphology on bulk strength for power-law materials
NASA Astrophysics Data System (ADS)
Gerbi, Christopher; Johnson, Scott E.; Cook, Alden; Vel, Senthil S.
2015-01-01
The strength of a polyphase aggregate comprising power-law materials is a function of the constitutive laws of the phases present, the arrangement of those phases and environmental conditions such as temperature. Primarily for geological applications, we consider the degree to which the arrangement of the phases has a significant influence on bulk strength. Calculations based on current single-mineral experimental data indicate that the absolute and relative strength differences between the upper and lower theoretical bounds vary widely with mineral pair, environmental conditions and strain rate. For example, at 850 °C, some pairs, such as plagioclase-clinopyroxene, are highly sensitive to phase morphology, whereas others, such as quartz-plagioclase, are not. Using a finite-element implementation of asymptotic expansion homogenization, we have calculated the bulk strength of natural and synthetic microstructures across macroscale strain gradients. We find that phase morphology does not change sufficiently in most cases to be the dominant factor in bulk strength variation. Thus on its own, phase morphology in an aggregate of power-law materials does not appear to be a major control on bulk strength under typical viscous geological conditions. However, phase morphology does affect microscale stress and strain rate patterns, which in turn can induce microscale variations in constitutive laws and diffusional pathways. These factors, including reactions and changing deformation mechanisms, are strongly influenced by phase morphology and do cause strength variation in rocks. As a result, any parametrization of rock strength needs to account for evolving modal mineralogy and deformation mechanisms in addition to morphological changes alone.
A power-law approximation for fluvial incision by tools and bed coverage processes
NASA Astrophysics Data System (ADS)
Brandon, M. T.; Gasparini, N. M.
2005-12-01
The stream-power model is widely used to represent fluvial incision in bedrock channels. The model does not account for the amount of sediment in the channel, which can abrade the channel at low concentrations or armor the channel at high concentrations. Here we use a natural example (Clearwater River, Washington State, USA) and numerical experiments to explore how sediment flux influences bedrock incision at a drainage-wide scale. We have generated numerical landscapes with different uplift patterns using the CHILD numerical model and incision rules that include a tools-and-coverage formulation. We then use regression analysis to fit a power-law function I=K*Am*Sn*, where I is incision rate, S slope, and A drainage area, and K*, m*, and n* are fit parameters. We find that this formulation works very well for the Clearwater and all of our numerical experiments. The function has the same form as the stream-power model, but the parameters are empirically defined (as indicated by the asterisks) and can take on values quite different than those inferred from process-based arguments. The best-fit parameters appear to be constant at the scale of a single drainage, but they vary between drainages depending on the pattern of uplift, and whether or not the landscape has reached steady-state. In all cases, slope-area steepness analysis works well for estimating relative incision rates. Our analysis indicates that, in some cases, m* can be quite low, apparently due to the fact that bed coverage increases with increasing area. We conclude that the power-law formulation provides a good functional representation of fluvial incision, but that there are no universal values for m* and n*. These conclusions have important implications for the size of mountain belts and feedbacks between tectonic uplift and surface processes.
A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4
Chakrabarty, Deepto; Nowak, Michael A.; Tomsick, John A.; Boggs, Steven E.; Craig, William W.; Grefenstette, Brian W.; Fürst, Felix; Harrison, Fiona A.; Rana, Vikram; Psaltis, Dimitrios; Bachetti, Matteo; Barret, Didier; Christensen, Finn E.; Hailey, Charles J.; Kaspi, Victoria M.; Miller, Jon M.; Stern, Daniel; Wik, Daniel R.; Zhang, William W.; Wilms, Jörn
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.
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
Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology
NASA Astrophysics Data System (ADS)
Wu, Patrick; Wang, Hansheng
2008-10-01
Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology ( n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A ˜ 10 -35 Pa -3 s -1 for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.
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
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.
From the Cover: Musical rhythm spectra from Bach to Joplin obey a 1/f power law
NASA Astrophysics Data System (ADS)
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-03-01
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.
Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements
NASA Astrophysics Data System (ADS)
Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun
2015-01-01
Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass meff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation νt and change in spectral index for scalar perturbation νst to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of ns=0.96 by having a non-zero value of effective mass of the inflaton field m2eff/H2. The analysis with WP + Planck likelihood shows a non-zero detection of m2eff/H2 with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m2eff/H2 = -0.0237 ± 0.0135 which is consistent with zero.
Blair, Clancy
2006-04-01
This target article considers the relation of fluid cognitive functioning to general intelligence. A neurobiological model differentiating working memory/executive function cognitive processes of the prefrontal cortex from aspects of psychometrically defined general intelligence is presented. Work examining the rise in mean intelligence-test performance between normative cohorts, the neuropsychology and neuroscience of cognitive function in typically and atypically developing human populations, and stress, brain development, and corticolimbic connectivity in human and nonhuman animal models is reviewed and found to provide evidence of mechanisms through which early experience affects the development of an aspect of cognition closely related to, but distinct from, general intelligence. Particular emphasis is placed on the role of emotion in fluid cognition and on research indicating fluid cognitive deficits associated with early hippocampal pathology and with dysregulation of the hypothalamic-pituitary-adrenal axis stress-response system. Findings are seen to be consistent with the idea of an independent fluid cognitive construct and to assist with the interpretation of findings from the study of early compensatory education for children facing psychosocial adversity and from behavior genetic research on intelligence. It is concluded that ongoing development of neurobiologically grounded measures of fluid cognitive skills appropriate for young children will play a key role in understanding early mental development and the adaptive success to which it is related, particularly for young children facing social and economic disadvantage. Specifically, in the evaluation of the efficacy of compensatory education efforts such as Head Start and the readiness for school of children from diverse backgrounds, it is important to distinguish fluid cognition from psychometrically defined general intelligence.
A growth model for directed complex networks with power-law shape in the out-degree distribution
Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.
2015-01-01
Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141
Fluid physics phenomena of resistojet thrusters
NASA Technical Reports Server (NTRS)
DeWitt, Kenneth J. (Principal Investigator)
1996-01-01
This final report includes a list of publications and part of an M.S. thesis titled 'Analyses in Theoretical and Experimental Fluid Flow', by Tony G. Howell. The thesis discusses analyses of momentum and heat transfer occurring in a laminar boundary layer of a non-Newtonian power-law fluid, and experiments completed in a simulated space thruster's plume for prediction comparison.
Well behaved parametric class of relativistic charged fluid ball in general relativity
NASA Astrophysics Data System (ADS)
Pant, Neeraj
2011-04-01
The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤ K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).
A generalized hydrodynamic model for acoustic mode stability in viscoelastic plasma fluid
NASA Astrophysics Data System (ADS)
Borah, B.; Haloi, A.; Karmakar, P. K.
2016-05-01
In this paper a generalized hydrodynamic (GH) model to investigate acoustic-mode excitation and stability in simplified strongly coupled bi-component plasma is proposed. The goal is centered in seeing the viscoelasticity-influences on the instability properties. The dispersive and nondispersive features are methodologically explored followed by numerical illustrations. It is seen that, unlike usual plasma acoustic mode, here the mode stability is drastically modified due to the considered viscoelastic effects contributed from both the electronic and ionic fluids. For example, it is found that there exists an excitation threshold value on angular wavenumber, K ≈3 in the K-space on the Debye scale, beyond which only dispersive characteristic features prevail. Further, it is demonstrated that the viscoelastic relaxation time plays a stabilizing influential role on the wave dynamics. In contrast, it is just opposite for the effective viscoelastic relaxation effect. Consistency with the usual viscoelasticity-free situations, with and without plasma approximation taken into account, is also established and explained. It is identified and conjectured that the plasma fluid viscoelasticity acts as unavoidable dispersive agency in attributing several new characteristics to acoustic wave excitation and propagation. The analysis is also exploited to derive a quantitative glimpse on the various basic properties and dimensionless numbers of the viscoelastic plasma. Finally, extended implications of our results tentative to different cosmic, space and astrophysical situations, amid the entailed facts and faults, are highlighted together with indicated future directions.
Prasad, N.E.; Malakondaiah, G.; Kutumbarao, V.V.
1997-09-01
Aluminium-lithium alloys, like many other aerospace structural alloys, exhibit bilinearity in power-law relationships between high strain, low cycle fatigue life (in terms of number of reversals to failure, 2N{sub f}) and plastic strain amplitude ({Delta}{epsilon}{sub p}/2) or average stress amplitude ({Delta}{sigma}/2) or average plastic strain energy per cycle ({Delta}W{sub p}). In the present paper the micromechanisms leading to bilinear fatigue power-law relationships, especially the Coffin-Manson (C-M) relationship, in aluminium-lithium alloys are compiled and discussed.