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1

Power-Law Behavior in Geometric Characteristics of Full Binary Trees

NASA Astrophysics Data System (ADS)

Natural river networks exhibit regular scaling laws in their topological organization. Here, we investigate whether these scaling laws are unique characteristics of river networks or can be applicable to general binary tree networks. We generate numerous binary trees, ranging from purely ordered trees to completely random trees. For each generated binary tree, we analyze whether the tree exhibits any scaling property found in river networks, i.e., the power-laws in the size distribution, the length distribution, the distance-load relationship, and the power spectrum of width function. We found that partially random trees generated on the basis of two distinct types of deterministic trees, i.e., deterministic critical and supercritical trees, show contrasting characteristics. Partially random trees generated on the basis of deterministic critical trees exhibit all power-law characteristics investigated in this study with their fitted exponents close to the values observed in natural river networks over a wide range of random-degree. On the other hand, partially random trees generated on the basis of deterministic supercritical trees rarely follow scaling laws of river networks.

Paik, Kyungrock; Kumar, Praveen

2011-02-01

2

Predictions of tensile strength of binary tablets using linear and power law mixing rules.

There has recently been an increased interest in predicting the tensile strength of binary tablets from the properties of the individual components. In this paper, measurements are reported for tensile strength of tablets compressed from single-component and binary powder mixtures of lactose with microcrystalline cellulose (MCC), and lactose with two types of silicified microcrystalline cellulose (SMCC and SMCC-HD), which are different in compressibility. Measurements show the tensile strength increases with the relative density for single powders, and both with the relative density and the mass fraction of cellulose in the mixtures. It was also observed, for binary mixtures compacted at 50 and 150 MPa, that there was a slight variation in porosity with the mass fraction of celluloses. The predictions of the tensile strength of binary tablets from the characteristics of the single-components was analysed with the extended Ryshkewitch-Duckworth model by assuming both linear and power law mixing rules for the determination of the parameters "tensile strength at zero porosity and bonding capacity constant". As consequence, four models were analysed and compared with measurements using criteria based on the standard deviation from the mean values. Results showed a good prediction using a linear mixing rule combined with the power law. However, as the predictions of these models depend on the powders and the porosity range for the characterization of single-components, none of them can be systematically considered as being the best to predict binary behaviour from data for individual powders. PMID:17097245

Michrafy, A; Michrafy, M; Kadiri, M S; Dodds, J A

2007-03-21

3

The Causal Connection Between Disc and Power-Law Variability in Hard State Black Hole X-Ray Binaries

NASA Technical Reports Server (NTRS)

We use the XMM-Newton EPIC-pn instrument in timing mode to extend spectral time-lag studies of hard state black hole X-ray binaries into the soft X-ray band. \\Ve show that variations of the disc blackbody emission substantially lead variations in the power-law emission, by tenths of a second on variability time-scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time-delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time-scales less than a second the disc lags the power-law variations by a few ms, consistent with the disc variations being dominated by X-ray heating by the power-law, with the short lag corresponding to the light-travel time between the power-law emitting region and the disc. Our results indicate that instabilities in the accretion disc are responsible for continuum variability on time-scales of seconds or longer and probably also on shorter time-scales.

Uttley, P.; Wilkinson, T.; Cassatella, P.; Wilms, J.; Pottschimdt, K.; Hanke, M.; Boeck, M.

2010-01-01

4

Zipf's law, power laws and maximum entropy

NASA Astrophysics Data System (ADS)

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.

Visser, Matt

2013-04-01

5

Entropic force in black hole binaries and Newton's law from an adiabatic Hilbert action

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive

2011-01-01

6

Rain, power laws, and advection.

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters, Phys. Rev. Lett. 88, 018701 (2002)

Dickman, Ronald

2003-03-14

7

The power law Starobinsky model

We consider a power law $\\frac{1}{M^2}R^{\\beta}$ correction to Einstein gravity as a model for inflation. The interesting feature of this form of generalization is that small deviations from the Starobinsky limit $\\beta=2$ can change the value of tensor to scalar ratio from $r \\sim \\mathcal{O}(10^{-3})$ to $r\\sim \\mathcal{O}(0.1)$. We find that in order to get large tensor perturbation $r= 0.2^{+0.07}_{-0.05}$ as indicated by BICEP2 measurements, we require the value of $\\beta \\simeq 1.818$ thereby breaking global Weyl symmetry. We show that the general $R^\\beta$ model can be obtained from a SUGRA construction by adding a power law $(\\Phi +\\bar \\Phi)^n$ term to the minimal no-scale SUGRA model. We further show that this two parameter power law generalization of the Starobinsky model is equivalent to generalized non-minimal curvature coupled models of the form $\\xi \\phi^{a} R^{b} + \\lambda \\phi^{4(1+\\gamma)}$ and thus the power law Starobinsky model is the most economical parametrization of such models.

Girish Kumar Chakravarty; Subhendra Mohanty

2015-01-19

8

Binary power multiplier for electromagnetic energy

A technique for converting electromagnetic pulses to higher power amplitude and shorter duration, in binary multiples, splits an input pulse into two channels, and subjects the pulses in the two channels to a number of binary pulse compression operations. Each pulse compression operation entails combining the pulses in both input channels and selectively steering the combined power to one output channel during the leading half of the pulses and to the other output channel during the trailing half of the pulses, and then delaying the pulse in the first output channel by an amount equal to half the initial pulse duration. Apparatus for carrying out each of the binary multiplication operation preferably includes a four-port coupler (such as a 3 dB hybrid), which operates on power inputs at a pair of input ports by directing the combined power to either of a pair of output ports, depending on the relative phase of the inputs. Therefore, by appropriately phase coding the pulses prior to any of the pulse compression stages, the entire pulse compression (with associated binary power multiplication) can be carried out solely with passive elements.

Farkas, Zoltan D. (203 Leland Ave., Menlo Park, CA 94025)

1988-01-01

9

Power-Law Distributions: Beyond Paretian Fractality

The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six classes of probability laws - all equally entitled to be ordained fractal, all possessing a characteristic power-law structure, and all being the unique fixed

Iddo Eliazar; Joseph Klafter

2008-01-01

10

New Directions for Power Law Research

1 New Directions for Power Law Research Michael Mitzenmacher Harvard University #12;2 Internet;6 Models Â· After observation, the natural step is to explain/model the behavior. Â· Outcome: lots tests of power law behavior. Â· Question: how to differentiate them empirically? ( ) 2 2 2 ln 2lnln

Chen, Yiling

11

Tachyonic (phantom) power-law cosmology

NASA Astrophysics Data System (ADS)

Tachyonic scalar field-driven late universe with dust matter content is considered. The cosmic expansion is modeled with power-law and phantom power-law expansion at late time, i.e. z?0.45. WMAP7 and its combined data are used to constraint the model. The forms of potential and the field solution are different for quintessence and tachyonic cases. Power-law cosmology model (driven by either quintessence or tachyonic field) predicts unmatched equation of state parameter to the observational value, hence the power-law model is excluded for both quintessence and tachyonic field. In the opposite, the phantom power-law model predicts agreeing valued of equation of state parameter with the observational data for both quintessence and tachyonic cases, i.e. (WMAP7+BAO+ H 0) and (WMAP7). The phantom-power law exponent ? must be less than about -6, so that the -2< w ?,0<-1. The phantom power-law tachyonic potential is reconstructed. We found that dimensionless potential slope variable ? at present is about 1.5. The tachyonic potential reduced to V= V 0 ? -2 in the limit ? m,0?0.

Rangdee, Rachan; Gumjudpai, Burin

2014-02-01

12

Power law inflation with electromagnetism

We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ?{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},?{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,?,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}, ?{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.

Luo, Xianghui; Isenberg, James, E-mail: isenberg@uoregon.edu

2013-07-15

13

Limit Laws for Functions of Fringe trees for Binary Search Trees and Recursive Trees

Limit Laws for Functions of Fringe trees for Binary Search Trees and Recursive Trees Cecilia of binary search trees and random recursive trees. In particular, we give simple new proofs of the fact that the number of fringe trees of size k = kn in the binary search tree and the random recursive tree (of total

Janson, Svante

14

Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---

NASA Astrophysics Data System (ADS)

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^{-?}, with an exponent that moves in the range of 1.09 < ? < 1.27. Furthermore, we found that as the power-law exponents ? approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.

Kaizoji, T.

15

The first and second laws of thermodynamics were used to analyze a novel thermodynamic cycle proposed by Goswami in 1995 that uses an ammonia–water binary mixture as the working fluid, while producing both power and refrigeration simultaneously. The thermodynamic performance of the cycle was optimized for maximum second law efficiency using a commercially available optimization program. A maximum second law

Afif Akel Hasan; D. Yogi Goswami; Sanjay Vijayaraghavan

2002-01-01

16

Hierarchical networks, power laws, and neuronal avalanches

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions—even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws. PMID:23556972

Friedman, Eric J.; Landsberg, Adam S.

2013-01-01

17

Hierarchical networks, power laws, and neuronal avalanches.

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws. PMID:23556972

Friedman, Eric J; Landsberg, Adam S

2013-03-01

18

43 CFR 4.1121 - Powers of administrative law judges.

Code of Federal Regulations, 2010 CFR

...2010-10-01 false Powers of administrative law judges. 4.1121...HEARINGS AND APPEALS PROCEDURES Special Rules Applicable...Hearings § 4.1121 Powers of administrative law judges. (a...an administrative law judge may—...

2010-10-01

19

The power law character of off-site power failures

A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency-duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power failure duration follow Frechet distribution, which is a type II asymptotic distribution, strengthening our assumption of power law for the parent distribution. The extreme value distributions obtained are used to extrapolate for failure durations beyond the observed range.

Arul, A J; Marimuthu, S; Singh, O P; Singh, Om Pal

2003-01-01

20

On Distinguishing between Internet Power Law Topology Generators

On Distinguishing between Internet Power Law Topology Generators Tian Bu and Don Towsley Department exhibit power laws. Since then several algorithms have been proposed to generate such power law graphs developed power law topology generators, [5] [6] [10] [20] for generating repreÂ sentative Internet

Massachusetts at Amherst, University of

21

On Distinguishing between Internet Power Law Topology Generators

On Distinguishing between Internet Power Law Topology Generators Tian Bu and Don Towsley Department power laws. Since then several algorithms have been proposed to generate such power law graphs developed power law topology generators, [5] [6] [10] [20] for generating repre- sentative Internet

Massachusetts at Amherst, University of

22

On Power Law Inflation in DBI Models

Inflationary models in string theory which identify the inflaton with an open string modulus lead to effective field theories with non-canonical kinetic terms: Dirac-Born-Infeld scalar field theories. In the case of a $D$-brane moving in an AdS throat with a quadratic scalar field potential DBI kinetic terms allow a novel realization of power law inflation. This note adresses the question of whether this behaviour is special to this particular choice of throat geometry and potential. The answer is that for any throat geometry one can explicitly find a potential which leads to power law inflation. This generalizes the well known fact that an exponential potential gives power law inflation in the case of canonical kinetic terms.

Michal Spalinski

2007-04-26

23

The power law character of off-site power failures

A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency–duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power

A. John Arul; C. Senthil Kumar; S. Marimuthu; Om Pal Singh

2003-01-01

24

The power law character of off-site power failures

A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency-duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power

A. John Arul; C. Senthil Kumar; S. Marimuthu; Om Pal Singh

2003-01-01

25

Power-laws and Non-Power-laws in Dark Matter Halos

Simulated dark matter profiles are often modelled as a `NFW' density profile rather than a single power law. Recently, attention has turned to the rather rigorous power-law behaviour exhibited by the `pseudo phase-space density' of the dark matter halo, which is defined dimensionally in terms of the local density and velocity dispersion of the dark matter particles. The non-power-law behaviour of the density profile is generally taken to exclude simple scale-free, in-fall models; however the power-law behaviour of the `pseudo-density' is a counter indication. We argue in this paper that both behaviours may be at least qualitatively understood in terms of a dynamically evolving self-similarity, rather than the form for self-similar infall that is fixed by cosmological initial conditions. The evolution is likely due to collective relaxation such as that provided by the radial-orbit instability on large scales. We deduce, from a distribution function given by first order coarse-graining, both the NFW-type density profile and the power-law pseudo-density profile. The results are not greatly sensitive to variation about 3 in the power of the velocity dispersion used in the definition of the phase space pseudo-density. We suggest that the power 2 may create the more physical quantity, whose deviations from a power-law are a diagnostic of incomplete relaxation.

R. N. Henriksen

2006-09-05

26

Universal Power Law Governing Pedestrian Interactions

NASA Astrophysics Data System (ADS)

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.

Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.

2014-12-01

27

Universal power law governing pedestrian interactions.

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena. PMID:25526171

Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J

2014-12-01

28

Power laws governing epidemics in isolated populations

NASA Astrophysics Data System (ADS)

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.

Rhodes, C. J.; Anderson, R. M.

1996-06-01

29

Variational Principle for the Pareto Power Law

NASA Astrophysics Data System (ADS)

A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system.

Chakraborti, Anirban; Patriarca, Marco

2009-11-01

30

Power-law tailed spectra from equilibrium

We propose that power-law tailed hadron spectra may be viewed as stemming from a matter in an unconventional equilibrium state typical for non-extensive thermodynamics. A non-extensive Boltzmann equation, which is able to form such spectra as a stationary solution, is utilized as a rough model of quark matter hadronization. Basic ideas about non-extensive simulation of the QCD equation of state on the lattice are presented.

T. S. Biro; G. Purcsel; G. Gyorgyi; A. Jakovac; Zs. Schram

2005-10-03

31

29 CFR 417.6 - Powers of Administrative Law Judge.

Code of Federal Regulations, 2010 CFR

...2010-07-01 false Powers of Administrative Law Judge. 417.6...LABOR-MANAGEMENT STANDARDS PROCEDURE FOR REMOVAL OF LOCAL...ORGANIZATION OFFICERS Procedures To Determine Adequacy...Organizations § 417.6 Powers of Administrative Law Judge. The...

2010-07-01

32

Kant on causal laws and powers.

The aim of the paper is threefold. Its first aim is to defend Eric Watkins's claim that for Kant, a cause is not an event but a causal power: a power that is borne by a substance, and that, when active, brings about its effect, i.e. a change of the states of another substance, by generating a continuous flow of intermediate states of that substance. The second aim of the paper is to argue against Watkins that the Kantian concept of causal power is not the pre-critical concept of real ground but the category of causality, and that Kant holds with Hume that causal laws cannot be inferred non-inductively (that he accordingly has no intention to show in the Second analogy or elsewhere that events fall under causal laws). The third aim of the paper is to compare the Kantian position on causality with central tenets of contemporary powers ontology: it argues that unlike the variants endorsed by contemporary powers theorists, the Kantian variants of these tenets are resistant to objections that neo-Humeans raise to these tenets. PMID:25571742

Henschen, Tobias

2014-12-01

33

Rate-Controlling Mechanisms in Five-Power-Law Creep

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

Michael E. Kassner

2004-01-01

34

Power laws in economics and elsewhere J. Doyne Farmer

Power laws in economics and elsewhere J. Doyne Farmer and John Geanakoplos May 14, 2008 Abstract We review power laws in financial economics. This is a chapter from a preliminary draft of a book called of it applies to power laws in general Â the nouns may change, but the underlying questions are similar in many

35

Poissonian renormalizations, exponentials, and power laws

NASA Astrophysics Data System (ADS)

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Eliazar, Iddo

2013-05-01

36

Poissonian renormalizations, exponentials, and power laws.

This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises. PMID:23767505

Eliazar, Iddo

2013-05-01

37

Finite Disks with Power-Law Potentials

We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff at some radius Ro. First we discuss circular disks whose circular rotation speed v is proportional to r^alpha, with any alpha> -1/2. The surface-density of the disks is expressed in terms of hypergeometric functions of 1-(Ro/r)^2. We give closed expressions for the full 3-D potentials in terms of hypergeometric functions of two variables. We express the potential and acceleration in the plane at r>Ro, and along the rotation axis, in terms of simple hypergeometric functions. All the multipoles of the disk are given. We then generalize to non-axisymmetric disks. The potential in the midplane is given in terms of the hypergeometric function of two variables. For integer values of 2 alpha the above quantities are given in more elementary terms. All these results follow straightforwardly from formulae we derive for the general, cutoff, power-law, triaxial ellipsoid.

R. Brada; M. Milgrom

1994-08-08

38

Power-law Solutions from Heterotic Strings

In this paper we search for accelerating power-law and ekpyrotic solutions in heterotic string theory with NS-NS fluxes compactified on half-flat and generalized half-flat manifolds. We restrict our searches to the STZ sector of the theory and include linear order $\\alpha'$ corrections when looking for accelerating solutions. We find two ekpyrotic solutions in the case when the heterotic string theory is compactified on generalized half-flat manifolds. We do not find accelerating solutions in any of the models.

Tibra Ali; S. Shajidul Haque

2014-05-09

39

The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory

First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly circular orbit. Our calculation is valid through 3PN order and includes, in addition, the contributions of logarithmic terms at 4PN and 5PN orders. This first law of binary point-particle mechanics is then derived from first principles in general relativity, and analogies are drawn with the single and binary black hole cases. Some consequences of the first law are explored for PN spacetimes. As one such consequence, a simple relation between the PN binding energy of the binary system and Detweiler's redshift observable is established. Through it, we are able to determine with high precision the numerical values of some previously unknown high order PN coefficients in the circular-orbit binding energy. Finally, we propose new gauge invariant notions for the energy and angular momentum of a particle in a binary system.

Alexandre Le Tiec; Luc Blanchet; Bernard F. Whiting

2011-11-23

40

Power Laws and Fragility in Flow Networks

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.

Shore, Jesse; Bianchi, Matt T

2013-01-01

41

Anisotropic power-law k-inflation

NASA Astrophysics Data System (ADS)

It is known that power-law k-inflation can be realized for the Lagrangian P=Xg(Y), where X=-(??)2/2 is the kinetic energy of a scalar field ? and g is an arbitrary function in terms of Y=Xe??/Mpl (? is a constant and Mpl is the reduced Planck mass). In the presence of a vector field coupled to the inflaton with an exponential coupling f(?)?e??/Mpl, we show that the models with the Lagrangian P=Xg(Y) generally give rise to anisotropic inflationary solutions with ?/H=constant, where ? is an anisotropic shear and H is an isotropic expansion rate. Provided these anisotropic solutions exist in the regime where the ratio ?/H is much smaller than 1, they are stable attractors irrespective of the forms of g(Y). We apply our results to concrete models of k-inflation such as the generalized dilatonic ghost condensate and the Dirac-Born-Infeld model and we numerically show that the solutions with different initial conditions converge to the anisotropic power-law inflationary attractors. Even in the de Sitter limit (??0) such solutions can exist, but in this case the null energy condition is generally violated. The latter property is consistent with the Wald’s cosmic conjecture stating that the anisotropic hair does not survive on the de Sitter background in the presence of matter respecting the dominant/strong energy conditions.

Ohashi, Junko; Soda, Jiro; Tsujikawa, Shinji

2013-11-01

42

Fractional power-law spatial dispersion in electrodynamics

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.

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation); Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain); Trujillo, Juan J., E-mail: jtrujill@ullmat.es [Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain)

2013-07-15

43

Routing and Congestion in Power Law Graphs

NASA Astrophysics Data System (ADS)

We investigate a simple model of packet routing on a power law (scale free) graph where packets arrive at each node at a given rate and are routed to a randomly chosen destination along the shortest path between the source and destination. This mimics the Shortest Path Routing protocol used in the internet. It was previously found that there is a critical rate of packet arrival beyond which there is an onset of congestion and packets start accumulating on the network. This critical rate depends on the maximum betweenness incurred on the network when shortest path routing is used. We analytically find a bound on the maximal betweenness incurred in shortest path routing and compare it to the optimal (least possible) maximal betweenness that can be acheived using an arbitrary routing protocol. This provides an effective quantitative measure of the optimality of Shortest Path Routing.

Sreenivasan, Sameet; Lopez, Eduardo; Toroczkai, Zoltan

2006-03-01

44

Modulated power-law behaviour in Stirling's approximation

Modulated power-law behaviour in Stirling's approximation Les Hatton CISM, University of Kingston. This argument used Stirling's approximation which limits its relevance to larger component sizes. Although power to broaden Stirling's approximation to see if it corresponds with the departures from power-law observed

Hatton, Les

45

On Power-law Relationships of the Internet Topology

Despite the apparent randomness of the Internet, we discover some surprisingly simple power-laws of the Internet topology. These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period. We show that our power-laws fit the real data very well resulting in correlation coefficients of 96% or

Michalis Faloutsos; Petros Faloutsos; Christos Faloutsos

1999-01-01

46

Compressed Image Quality Evaluation using Power Law Models

Abstract This paper ,presents a compressed ,image ,quality measure based on the properties of Zipf law, which is a power-law model ,adapted from linguistic analysis. It describes the frequency distribution of image patterns, and can be used ,to put ,into evidence image ,details which are affected by compression.,Two image quality evaluation measures ,based ,on Zipf ,law have ,been proposed and

Yves Caron; Nicole Vincent

2006-01-01

47

Code of Federal Regulations, 2010 CFR

...of administrative law judges; stipulations...to administrative law judges or to the Board; assignment and powers of settlement judges...REGULATIONS, SERIES 8 Procedure Under Section...35 Duties and powers of administrative law judges;...

2010-07-01

48

Helmholtz solitons in power-law optical materials

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.

Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P. [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

2007-09-15

49

Rate-Controlling Mechanisms in Five-Power-Law Creep

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.

Michael E. Kassner

2004-04-20

50

On Distinguishing between Internet Power Law Topology Generators

Recent work has shown that the node degree in the WWW induced graph and the AS-level Internet topology exhibit power laws. Since then several algorithms have been proposed to generate such power law graphs. In this paper we evaluate the effectiveness of these generators to generate representative AS-level topologies. Our conclusions are mixed. Although they (mostly) do a reasonable job

Tian Bu; Donald F. Towsley

2002-01-01

51

Power law rank-abundance relationships in marine phage populations

in the marine ecosystem5,6. The second assumption is that there is a strong and specific interaction between1 Power law rank-abundance relationships in marine phage populations Karl Heinz Hoffmann1 , Beltran Sciences, San Diego State University, San Diego, CA 92182 Running Title: Power law for marine phage

Salamon, Peter

52

ORIGINAL PAPER Undersampling power-law size distributions: effect

Government 2014 Abstract The effect of undersampling on estimating the size of extreme natural hazards fromORIGINAL PAPER Undersampling power-law size distributions: effect on the assessment of extreme to account for estimation dependence between the power-law scaling exponent and the corner size parameter

53

Do wealth distributions follow power laws? Evidence from ‘rich lists’

NASA Astrophysics Data System (ADS)

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.

Brzezinski, Michal

2014-07-01

54

Distortion of power law blinking with binning and thresholding

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 ?{sub on/off} ? 1.6, especially if ?{sub on} ? ?{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.

Amecke, Nicole; Heber, André; Cichos, Frank, E-mail: cichos@physik.uni-leipzig.de [Molecular Nanophotonics Group, Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig (Germany)] [Molecular Nanophotonics Group, Institute of Experimental Physics I, Universität Leipzig, Linnéstraße 5, 04103 Leipzig (Germany)

2014-03-21

55

Development of Jet Noise Power Spectral Laws

NASA Technical Reports Server (NTRS)

High-quality jet noise spectral data measured at the Aero-Acoustic Propulsion Laboratory (AAPL) at NASA Glenn is used to develop jet noise scaling laws. A FORTRAN algorithm was written that provides detailed spectral prediction of component jet noise at user-specified conditions. The model generates quick estimates of the jet mixing noise and the broadband shock-associated noise (BBSN) in single-stream, axis-symmetric jets within a wide range of nozzle operating conditions. Shock noise is emitted when supersonic jets exit a nozzle at imperfectly expanded conditions. A successful scaling of the BBSN allows for this noise component to be predicted in both convergent and convergent-divergent nozzles. Configurations considered in this study consisted of convergent and convergent- divergent nozzles. Velocity exponents for the jet mixing noise were evaluated as a function of observer angle and jet temperature. Similar intensity laws were developed for the broadband shock-associated noise in supersonic jets. A computer program called sJet was developed that provides a quick estimate of component noise in single-stream jets at a wide range of operating conditions. A number of features have been incorporated into the data bank and subsequent scaling in order to improve jet noise predictions. Measurements have been converted to a lossless format. Set points have been carefully selected to minimize the instability-related noise at small aft angles. Regression parameters have been scrutinized for error bounds at each angle. Screech-related amplification noise has been kept to a minimum to ensure that the velocity exponents for the jet mixing noise remain free of amplifications. A shock-noise-intensity scaling has been developed independent of the nozzle design point. The computer program provides detailed narrow-band spectral predictions for component noise (mixing noise and shock associated noise), as well as the total noise. Although the methodology is confined to single streams, efforts are underway to generate a data bank and algorithm applicable to dual-stream jets. Shock-associated noise in high-powered jets such as military aircraft can benefit from these predictions.

Khavaran, Abbas; Bridges, James

2011-01-01

56

Evolution of power law distributions in science and society.

Power law distributions have been observed in numerous physical and social systems; for example, the size distributions of particles, aerosols, corporations, and cities are often power laws. Each system is an ensemble of clusters, comprising units that combine with or dissociate from the cluster. Constructing models and investigating their properties are needed to understand how such clusters evolve. To describe the growth of clusters, we hypothesize that a distribution obeys a governing population dynamics equation based on a reversible association-dissociation process. The rate coefficients are considered to depend on the cluster size as power expressions, thus providing an explanation for the asymptotic evolution of power law distributions. PMID:16241617

Jeon, Young-Pyo; McCoy, Benjamin J

2005-09-01

57

Advanced binary geothermal power plants: Limits of performance

The Heat Cycle Research Program is currently investigating the potential improvements to power cycles utilizing moderate temperature geothermal resources to produce electrical power. Investigations have specifically examined Rankine cycle binary power systems. Binary Rankine cycles are more efficient than the flash steam cycles at moderate resource temperatures, achieving a higher net brine effectiveness. At resource conditions similar to those at the Heber binary plant, it has been shown that mixtures of saturated hydrocarbons (alkanes) or halogenated hydrocarbons operating with a supercritical Rankine cycle gave improved performance over Rankine cycles with the pure working fluids executing single boiling cycles. Recently, in addition to the supercritical Rankine Cycle, other types of cycles have been proposed for binary geothermal service. This paper explores the limits on efficiency of a feasibility plant and discusses the methods used in these advanced concept plants to achieve the maximum possible efficiency. The advanced plants considered appear to be approaching the feasible limit of performance so that the designer must weigh all considerations to find the best plant for a given service. 16 refs., 12 figs.

Bliem, C.J.; Mines, G.L.

1990-01-01

58

Statistical analyses support power law distributions found in neuronal avalanches.

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. PMID:21720544

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

59

ISPM, Division of Biostatistics Modelling power-law spread

ISPM, Division of Biostatistics Modelling power-law spread of infectious diseases Sebastian Meyer 2013 Page 1 #12;ISPM, Division of Biostatistics Epidemic Modelling Â Prospective surveillance: outbreak-law spread of infectious diseases Page 2 #12;ISPM, Division of Biostatistics Mobility networks determine

Zurich, University of

60

29 CFR 1955.12 - Administrative law judge; powers and duties.

Code of Federal Regulations, 2010 CFR

...Administrative law judge; powers and duties...CONTINUED) PROCEDURES FOR WITHDRAWAL...Administrative law judge; powers and duties...Administrative Law Judge to preside...shall have all powers necessary...Administrative Procedure Act, 5...

2010-07-01

61

14 CFR 406.109 - Administrative law judges-powers and limitations.

Code of Federal Regulations, 2010 CFR

...false Administrative law judges-powers and limitations...OF TRANSPORTATION PROCEDURE INVESTIGATIONS...109 Administrative law judges—powers and limitations. (a) Powers of an administrative law judge. In...

2010-01-01

62

Punctuated equilibrium and power law in economic dynamics

NASA Astrophysics Data System (ADS)

This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called 'feedback' was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of 'fitness' and 'selection' in the present model of economic evolution.

Gupta, Abhijit Kar

2012-02-01

63

Fractal ladder models and power law wave equations.

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

Kelly, James F; McGough, Robert J

2009-10-01

64

Fractal ladder models and power law wave equations

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

Kelly, James F.; McGough, Robert J.

2009-01-01

65

The laminar axisymmetric wake for power-law fluids

Summary An analytic solution is given for the asymptotic structure of the axisymmetric laminar wake of a power-law fluid valid for rheological indicesn>1\\/3. For dilatant fluids (n>1) the lateral extent of the wake is finite, a feature not found in Newtonian fluid flows. Velocity profiles are compared with previously published results for two-dimensional laminar wakes of power-law fluids at selected

P. D. Weidman; C. W. Van Atta

2001-01-01

66

Convergent Multiplicative Processes Repelled from Zero: Power Laws and Truncated Power Laws

NASA Astrophysics Data System (ADS)

Levy and Solomon have found that random multiplicative processes w_t =?_1?_2...?_t (with ?_j > 0) lead, in the presence of a boundary constraint, to a distribution P(w_t) in the form of a power law w_t^{-(1+?)}. We provide a simple exact physically intuitive derivation of this result based on a random walk analogy and show the following: 1) the result applies to the asymptotic (trightarrow infty) distribution of w_t and should be distinguished from the central limit theorem which is a statement on the asymptotic distribution of the reduced variable frac{1}{sqrt t}(log w_t - <~ngle log w_trangle); 2) the two necessary and sufficient conditions for P(w_t) to be a power law are that <~ngle log?_jrangle < 0 (corresponding to a drift w_t rightarrow 0) and that w_t not be allowed to become too small. We discuss several models, previously thought unrelated, showing the common underlying mechanism for the generation of power laws by multiplicative processes: the variable log w_t undergoes a random walk repelled from -infty, which we describe by a Fokker-Planck equation. 3) For all these models, we obtain the exact result that ? is solution of <~ngle?^?rangle = 1 and thus depends on the distribution of ?. 4) For finite t, the power law is cut-off by a log-normal tail, reflecting the fact that the random walk has not the time to scatter off the repulsive force to diffusively transport the information far in the tail. Levy et Solomon ont montré qu'un processus mutiplicatif du type w_t =?_1?_2...?_t (avec ?_j > 0) conduit, en présence d'une contrainte de bord, à une distribution P(w_t) en loi de puissance w_t^{-(1+?)}. Nous proposons une dérivation simple, intuitive et exacte de ce résultat basée sur une analogie avec une marche aléatoire. Nous obtenons les résultats suivants: 1) le régime de loi de puissance décrit la distribution asymptotique de w_t aux grands temps et doit être distingué du théorème limite central décrivant la convergence de la variable réduite frac{1}{sqrt t}(log w_t - <~ngle log w_trangle) vers la loi Gaussienne; 2) les deux conditions nécessaires et suffisantes pour que P(w_t) soit une loi de puissance sont <~ngle log?_jrangle < 0 (correspondant à une dérive vers zéro) et la contrainte que w_t soit empêchée de trop s'approcher de zéro. Cette contrainte peut être mise en oeuvre de manière variée, généralisant à une grande classe de modèles le cas d'une barrière réfléchissante examiné par Levy et Solomon. Nous donnons aussi un traitement approximatif, devenant exact dans la limite où la distribution de ? est étroite ou log-normale en terme d'équation de Fokker-Planck. 3) Pour tous ces modèles, nous obtenons le résultat général exact que l'exposant ? est la solution de l'équation <~ngle?^?rangle = 1. ? est donc non-universet et dépend de la spécificité de la distribution de ?. 4) Pour des t finis, la loi de puissance est tronquée par une queue log-normale due à une exploration finie de la marche aléatoire.

Sornette, Didier; Cont, Rama

1997-03-01

67

Advanced binary geothermal power plants: Limits of performance

The Heat Cycle Research Program is investigating potential improvements to power cycles utilizing moderate temperature geothermal resources to produce electrical power. Investigations have specifically examined Rankine cycle binary power systems. Binary Rankine cycles are more efficient than the flash steam cycles at moderate resource temperature, achieving a higher net brine effectiveness. At resource conditions similar to those at the Heber binary plant, it has been shown that mixtures of saturated hydrocarbons (alkanes) or halogenated hydrocarbons operating in a supercritical Rankine cycle gave improved performance over Rankine cycles with the pure working fluids executing single or dual boiling cycles or supercritical cycles. Recently, other types of cycles have been proposed for binary geothermal service. This report explores the feasible limits on efficiency of a plant given practical limits on equipment performance and discusses the methods used in these advanced concept plants to achieve the maximum possible efficiency. (Here feasible is intended to mean reasonably achievable and not cost-effective.) No direct economic analysis has been made because of the sensitivity of economic results to site specific input. The limit of performance of three advanced plants were considered in this report. The performance predictions were taken from the developers of each concept. The advanced plants considered appear to be approaching the feasible limit of performance. Ultimately, the plant designer must weigh the advantages and disadvantages of the the different cycles to find the best plant for a given service. In addition, this report presents a standard of comparison of the work which has been done in the Heat Cycle Research Program and in the industrial sector by Exergy, Inc. and Polythermal Technologies. 18 refs., 16 figs., 1 tab.

Bliem, C.J.; Mines, G.L.

1991-01-01

68

Relaxation Dynamics of Non-Power-Law Fluids

NASA Astrophysics Data System (ADS)

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.

Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong

2013-12-01

69

NASA Technical Reports Server (NTRS)

The indeterminacy inherent to the formal extension of Arrhenius' law to reactions in turbulent flows is shown to be surmountable in the case of a binary exchange reaction with a sufficiently high activation energy. A preliminary calculation predicts that the turbulent reaction rate is invariant in the Arrhenius form except for an equivalently lowered activation energy. This is a reflection of turbulence-augmented molecular vigor, and causes an appreciable increase in the reaction rate. A similarity to the tunnel effect in quantum mechanics is indicated. The anomaly associated with the mild ignition of oxy-hydrogen mixtures is discussed in this light.

Tsuge, S.; Sagara, K.

1978-01-01

70

Power-law friction in closely-packed granular materials

In order to understand the nature of friction in closely-packed granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the shear rate, the exponent of which does not depend on the material constants. Using a nondimensional parameter that is known as the inertial number, the power-law can be cast in a generalized form so that the friction coefficients at different confining pressures collapse on the same curve. We show that the volume fraction also obeys a power-law.

Takahiro Hatano

2007-05-08

71

Power-law connections: From Zipf to Heaps and beyond

In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf’s law, Pareto’s law, and Heaps’ law—three elemental empirical power-laws that are ubiquitously observed in the sciences. -- Highlights: ? The large-ensemble asymptotic statistics of rank distributions are explored. ? Lorenzian, oligarchic, and Heapsian asymptotic analyses are applied. ? Associated oligarchy sizes and induced innovation rates are analyzed. ? General elemental statistical connections are established. ? The underlying connections between Zipf’s, Pareto’s and Heaps’ laws are unveiled.

Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il [Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel); Cohen, Morrel H., E-mail: mcohen@physics.rutgers.edu [Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019 (United States); Department of Chemistry, Princeton University, Princeton, NJ 08544 (United States)

2013-05-15

72

24 CFR 1720.140 - Administrative law judge, powers and duties.

Code of Federal Regulations, 2010 CFR

...false Administrative law judge, powers and duties. 1720...REGISTRATION PROGRAM) FORMAL PROCEDURES AND RULES OF PRACTICE...140 Administrative law judge, powers and duties. (a...qualified administrative law judge who shall...

2010-04-01

73

5 CFR 2423.31 - Powers and duties of the Administrative Law Judge at the hearing.

Code of Federal Regulations, 2010 CFR

...Administrative Law Judge at the...PROCEEDINGS Hearing Procedures § 2423.31 Powers and duties of the Administrative Law Judge at the...to limit the powers of the Administrative Law Judge provided...Administrative Procedure Act....

2010-01-01

74

Primordial scalar perturbations in tachyonic power-law inflation

In this work we determine the power spectrum of the gravitational potential of the primordial fluctuations for an inflationary model whose \\emph{inflaton} is a non-canonical scalar field of the tachyon-type. The respective background field equations for an inverse-square potential produce a power-law inflation, and it is explicitly shown that for such a potential the power spectrum tends to be scale-independent for highly accelerated regimes in the inflationary expansion.

Rudinei C. de Souza; Gilberto M. Kremer

2014-01-31

75

Second-law analysis of composite power plants

Optimization of composite power plants (combined-cycle or cogeneration plants, for instance) demands a second-law analysis to define the thermodynamic efficiencies of such complex processes. In a general study of cycle combination and cogeneration, the University of Florence first performed a direct second-law analysis, then introduced a modular energy-loss procedure to calculate the contribution of each unit's performance to the overall

S. Stecco; G. Manfrida

1982-01-01

76

A COSMIC COINCIDENCE: THE POWER-LAW GALAXY CORRELATION FUNCTION

We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of {xi}(r), the galaxy two-point correlation function. While {xi}(r) at large scales is set by primordial fluctuations, departures from a power law are governed by galaxy pair counts at small scales, subject to nonlinear dynamics. We assume that galaxies reside within dark matter halos and subhalos. Therefore, the shape of the correlation function at small scales depends on the amount of halo substructure. We use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal mass loss and, to a lesser extent, dynamical friction dramatically deplete the number of subhalos within larger host halos over time, resulting in a {approx}90% reduction by z = 0 compared to the number of distinct mergers that occur during the assembly of a host halo. We show that these nonlinear processes resulting in this depletion are essential for achieving a power law {xi}(r). We investigate how the shape of {xi}(r) depends on subhalo mass (or luminosity) and redshift. We find that {xi}(r) breaks from a power law at high masses, implying that only galaxies of luminosities {approx}< L{sub *} should exhibit power-law clustering. Moreover, we demonstrate that {xi}(r) evolves from being far from a power law at high redshift, toward a near power-law shape at z = 0. We argue that {xi}(r) will once again evolve away from a power law in the future. This is in large part caused by the evolving competition between the accretion and destruction rates of subhalos over time, which happen to strike just the right balance at z {approx} 0. We then investigate the conditions required for {xi}(r) to be a power law in a general context. We use the halo model, along with simple parameterizations of the halo occupation distribution, to probe galaxy occupation at various masses and redshifts. We show that the key ingredients determining the shape of {xi}(r) are the fraction of galaxies that are satellites, the relative difference in mass between the halos of isolated galaxies and halos that contain a single satellite on average, and the rareness of halos that host galaxies. These pieces are intertwined and we find no simple, universal rule for which a power law {xi}(r) will occur. However, we do show that the physics responsible for setting the galaxy content of halos do not care about the conditions needed to achieve a power law {xi}(r) and that these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of {xi}(r) for L{sub *} and fainter galaxy samples at low redshift is a cosmic coincidence.

Watson, Douglas F.; Berlind, Andreas A. [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States); Zentner, Andrew R. [Department of Physics and Astronomy, The University of Pittsburgh, Pittsburgh, PA 15260 (United States)

2011-09-01

77

Modelling power-law spread of infectious diseases

Short-time human travel behaviour can be well described by a power law with respect to distance. We incorporate this information in space-time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a space-time point process model for individual point-referenced data, and a multivariate time series model for aggregated count data. In both frameworks, the power-law spread is embedded into the epidemic component and its decay parameter is estimated simultaneously with all other unknown parameters using (penalised) likelihood inference. The performance of the new approach is investigated by a re-analysis of individual cases of invasive meningococcal disease in Germany (2002-2008), and count data on influenza in 140 administrative districts of Southern Germany (2001-2008). In both applications, the power-law formulations substantially ...

Meyer, Sebastian

2013-01-01

78

Power-law velocity distributions in granular gases

NASA Astrophysics Data System (ADS)

The kinetic theory of granular gases is studied for spatially homogeneous systems. At large velocities, the equation governing the velocity distribution becomes linear, and it admits stationary solutions with a power-law tail, f(v)˜v-? . This behavior holds in arbitrary dimension for arbitrary collision rates including both hard spheres and Maxwell molecules. Numerical simulations show that driven steady states with the same power-law tail can be realized by injecting energy into the system at very high energies. In one dimension, we also obtain self-similar time-dependent solutions where the velocities collapse to zero. At small velocities there is a steady state and a power-law tail but at large velocities, the behavior is time dependent with a stretched exponential decay.

Ben-Naim, E.; Machta, B.; Machta, J.

2005-08-01

79

Statistical Models of Power-law Distributions in Homogeneous Plasmas

A variety of in-situ measurements in space plasmas point out to an intermittent formation of distribution functions with elongated tails and power-law at high energies. Power-laws form ubiquitous signature of many complex systems, plasma being a good example of a non-Boltzmann behavior for distribution functions of energetic particles. Particles, which either undergo mutual collisions or are scattered in phase space by electromagnetic fluctuations, exhibit statistical properties, which are determined by the transition probability density function of a single interaction, while their non-asymptotic evolution may determine the observed high-energy populations. It is shown that relaxation of the Brownian motion assumptions leads to non-analytical characteristic functions and to generalization of the Fokker-Planck equation with fractional derivatives that result in power law solutions parameterized by the probability density function.

Roth, Ilan [Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States)

2011-01-04

80

Estimation in a fluctuating medium and power-law distributions

NASA Astrophysics Data System (ADS)

We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power-law probability distributions. Beck, Cohen and others have provided plausible mechanisms explaining how power-law probability distributions naturally emerge in scenarios characterized by either finite dimension or fluctuation effects. This Letter tries to further contribute to such an idea. As an application, a new and multivariate version of the central limit theorem is obtained that provides a convenient alternative to the one recently presented in [S. Umarov, C. Tsallis, S. Steinberg, cond-mat/0603593].

Vignat, C.; Plastino, A.

2007-01-01

81

Power-Law Creep from Discrete Dislocation Dynamics

NASA Astrophysics Data System (ADS)

We report two-dimensional discrete dislocation dynamics simulations of combined dislocation glide and climb leading to “power-law” creep in a model aluminum crystal. The approach fully accounts for matter transport due to vacancy diffusion and its coupling with dislocation motion. The existence of quasiequilibrium or jammed states under the applied creep stresses enables observations of diffusion and climb over time scales relevant to power-law creep. The predictions for the creep rates and stress exponents fall within experimental ranges, indicating that the underlying physics is well captured.

Keralavarma, Shyam M.; Cagin, T.; Arsenlis, A.; Benzerga, A. Amine

2012-12-01

82

Medical practices display power law behaviors similar to spoken languages

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

2013-01-01

83

The Origin of Power-Laws in Internet Topologies Revisited

In a recent paper, Faloutsos et al. (1) found that the inter Autonomous System (AS) topology exhibits a power-law vertex degree dis- tribution. This result was quite unexpected in the networking community and stirred significant interest in exploring the possible causes of this phe- nomenon. The work of Barabasi and Albert (2) and its application to net- work topology generation

Qian Chen; Hyunseok Chang; Ramesh Govindan; Sugih Jamin; Scott J. Shenker; Walter Willinger

2002-01-01

84

From Power Laws to Fractional Diffusion: the Direct Way

Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for the waiting times, between 0 and 2 for the jumps. By stating the relevant lemmata (of Tauber type) for

Rudolf Gorenflo; Entsar A. A. Abdel-Rehim

2007-01-01

85

The power-law and the logarithmic potentials

In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The results are in very good agreement with exact numerical results.

Hakan Ciftci; Engin Ateser; Hueyin Koru

2002-12-26

86

Particle Deposition in Laminar Crossflow Filtration of Power Law Slurry

A theoretical model for predicting the probability of particle deposition in crossflow filtration of power law slurry is developed. The model is based on the critical angle of friction between depositing particles, which can be estimated by analyzing the forces exerted on the particles. The binding force between the particles due to polymer adsorption plays an important role in the

Kuo-Jen Hwang; Wei-Ming Lu

1997-01-01

87

On the origin of power laws in Internet topologies

Recent empirical studies [6] have shown that Internet topologies exhibit power laws of the form y = x ? for the following relationships: (P1) outdegree of node (domain or router) versus rank; (P2) number of nodes versus outdegree; (P3) number of node pairs within a neighborhood versus neighborhood size (in hops); and (P4) eigenvalues of the adjacency matrix versus rank.

Alberto Medina; Ibrahim Matta; John W. Byers

2000-01-01

88

Power scaling laws and dimensional transitions in solid mechanics

Physicists have often observed a scaling behaviour of the main physical quantities during experiments on systems exhibiting a phase transition. The main assumption of a scaling theory is that these characteristic quantities are self-similar functions of the independent variables of the phenomenon and, therefore, such a scaling can be interpreted be means of power-laws. Since a characteristic feature of phase

Alberto Carpinteri; Bernardino Chiaia

1996-01-01

89

Second law analysis of a conventional steam power plant

NASA Technical Reports Server (NTRS)

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.

Liu, Geng; Turner, Robert H.; Cengel, Yunus A.

1993-01-01

90

Spectral geometry of power-law potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

It is supposed that a single particle moves in openR3 in an attractive central power-law potential V(q)(r)=sgn(q)rq, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues Enl(q) of the Hamiltonian H=-?+V(q) depend on the power parameter q\\? Pure power-law potentials have the elementary property that, for p

Hall, Richard L.

1989-06-01

91

Engineering inverse power law decoherence of a qubit

NASA Astrophysics Data System (ADS)

The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a bath of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoirs are sub-ohmic at low frequencies and inverse power law at high frequencies. The exact dynamics of the qubit is described analytically through Fox H-functions. Over estimated long time scales, decoherence results in inverse power laws with powers decreasing continuously to unity, according to the particular choice of the engineered reservoir. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is considerably hindered.

Petruccione, Francesco; Giraldi, Filippo

2011-03-01

92

Scaling range of power laws that originate from fluctuation analysis

NASA Astrophysics Data System (ADS)

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.

Grech, Dariusz; Mazur, Zygmunt

2013-05-01

93

New exact solutions for power-law inflation Friedmann models

We consider the spatially flat Friedmann model. For a(t) = t^p, especially, if p is larger or equal to 1, this is called power-law inflation. For the Lagrangian L = R^m with p = - (m - 1)(2m - 1)/(m - 2), power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field Phi in an exponential potential V(Phi) = exp(mu Phi) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we use another gauge. Finally, special solutions for the closed and open Friedmann model are found.

H. -J. Schmidt

2001-09-04

94

Power-laws in recurrence networks from dynamical systems

Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in classical mechanics. In this Letter, we demonstrate that recurrence networks obtained from various deterministic model systems as well as experimental data naturally display power-law degree distributions with scaling exponents $\\gamma$ that can be derived exclusively from the systems' invariant densities. For one-dimensional maps, we show analytically that $\\gamma$ is not related to the fractal dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent $\\gamma$ depending on a suitable notion of local dimension, and such with fixed $\\gamma=1$.

Y. Zou; J. Heitzig; R. V. Donner; J. F. Donges; J. D. Farmer; R. Meucci; S. Euzzor; N. Marwan; J. Kurths

2012-03-15

95

Double power-law in aggregation-chipping processes

NASA Astrophysics Data System (ADS)

Temporal evolution of a distribution function P(X,t) for X clusters is analyzed in aggregation-chipping processes, which is a model incorporating simultaneously aggregation and the chipping off of a monomeric unit from a randomly chosen aggregate. Numerical simulations show that P(1,t) exhibits the singular time dependence P(1,t)-P(1,?)?t-2/3 . Using this time dependence, we find a notable double power-law distribution of P(X,t) with universal exponents -5/2 and -3/2 at a sufficiently large t . In finite systems, clusters in the second power law with the exponent -3/2 eventually coagulate into one “monopolized” cluster. These analyses are in good agreement with the results of the simulation.

Yamamoto, Hiroshi; Ohtsuki, Toshiya; Fujihara, Akihiro

2008-06-01

96

Probability distributions and confidence intervals for simulated power law noise.

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 ?, 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. PMID:25585396

Ashby, Neil

2015-01-01

97

The Origin of Power Law Distributions in Protein Synthesis

NASA Astrophysics Data System (ADS)

A genetically identical bacteria population will show heterogeneous gene expression due to the stochastic nature of the protein production mechanism. Therefore, the probability distribution of the resulting protein(s) can be used to gain information about these underlying processes. The experiments of Chapman-McQuistion et. al. show that under certain circumstances the protein probability distribution has a power law form p(n) ˜n^-? at small n. Our simulations and analysis find, in agreement with work by Friedlander and Brenner, that a linear protein production rate will produce a power law distribution with the exponent depending on the amplitude of the production rate. We also find that a protein distribution generated by rare occurrences of large bursts will produce a distribution of the form p(n) ˜1/n.

Barker, Jeffrey; Yeung, Chuck; Wu, Xiao-Lun; Chapman-McQuiston, Emily

2009-03-01

98

Power law behavior of the zigzag transition in Yukawa clusters

NASA Astrophysics Data System (ADS)

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.

Sheridan, T. E.; Magyar, Andrew L.

2010-11-01

99

Power-law tailed statistical distributions and Lorentz transformations

NASA Astrophysics Data System (ADS)

The present Letter, deals with the statistical theory [G. Kaniadakis, Phys. Rev. E 66 (2002) 056125; G. Kaniadakis, Phys. Rev. E 72 (2005) 036108], which predicts the probability distribution p(E)?exp?(-I), where, I??E-??, is the collision invariant, and exp?(x)=(x+?x)1/?, with ?<1. This, experimentally observed distribution, at low energies behaves as the Maxwell-Boltzmann exponential distribution, while at high energies presents power law tails. Here we show that the function exp?(x) and its inverse ln?(x), can be obtained within the one-particle relativistic dynamics, in a very simple and transparent way, without invoking any extra principle or assumption, starting directly from the Lorentz transformations. The achievements support the idea that the power law tailed distributions are enforced by the Lorentz relativistic microscopic dynamics, like in the case of the exponential distribution which follows from the Newton classical microscopic dynamics.

Kaniadakis, G.

2011-01-01

100

Power-law cosmology, SN Ia, and BAO

NASA Astrophysics Data System (ADS)

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? with ? close to 3/2 in a spatially flat universe is a good fit to these data.

Dolgov, Aleksander; Halenka, Vitali; Tkachev, Igor

2014-10-01

101

Power law tails in the Italian personal income distribution

We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977–2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of

Fabio Clementi; Mauro Gallegati

2005-01-01

102

London house prices are power-law distributed

In this pilot study we explore the house price distributions for London, Manchester, Bristol, Newcastle, Birmingham and Leeds. We find Pareto (power law) behaviour in their upper tails, which is clearly distinct from lognormal behaviour in the cases of London and Manchester. We propose an index of Housing Wealth Inequality based on the Pareto exponent and analogous to the Gini coefficient, and comment on its possible uses.

MacKay, Niall

2010-01-01

103

Power-law correlations of landslide areas in central Italy

We have studied the frequency–area statistics of landslides in central Italy. We consider two data sets. Data set A contains 16?809 landslide areas in the Umbria–Marche area of central Italy; they represent a reconnaissance inventory of very old, old, and recent (modern) landslides. The noncumulative frequency–area distribution of these landslides correlates well with a power-law relation, exponent ?2.5, over the

Fausto Guzzetti; Bruce D Malamud; Donald L Turcotte; Paola Reichenbach

2002-01-01

104

24 CFR 26.32 - Powers and duties of the Administrative Law Judge (ALJ).

Code of Federal Regulations, 2010 CFR

...2010-04-01 false Powers and duties of the Administrative Law Judge (ALJ). ...Development HEARING PROCEDURES Hearings Pursuant to the Administrative Procedure Act Administrative Law Judge § 26.32 Powers and duties of...

2010-04-01

105

5 CFR 2423.24 - Powers and duties of the Administrative Law Judge during prehearing proceedings.

Code of Federal Regulations, 2010 CFR

...Prehearing Procedures § 2423.24 Powers and duties...Administrative Law Judge during...Prehearing procedures. The Administrative...Administrative Law Judge may...the motions procedure in § 2423...limited to, the power to:...

2010-01-01

106

30 CFR 44.22 - Administrative law judges; powers and duties.

Code of Federal Regulations, 2010 CFR

...and duties. (a) Powers. An administrative law judge designated to...hearing shall have all powers necessary or appropriate...When an administrative law judge deems himself...Federal Rules of Civil Procedure and Evidence....

2010-07-01

107

Published online 1 May 2002 The fractal nature of nature: power laws, ecological

Published online 1 May 2002 The fractal nature of nature: power laws, ecological complexity of ecology is order that re ects the operation of funda- mental physical and biological processes. Power laws of magnitude. Power laws allow extrapolation and predic- tion over a wide range of scales. Some appear

Brown, James H.

108

PERSISTENCE AND PERMANENCE OF MASS-ACTION AND POWER-LAW DYNAMICAL SYSTEMS

PERSISTENCE AND PERMANENCE OF MASS-ACTION AND POWER-LAW DYNAMICAL SYSTEMS GHEORGHE CRACIUN, FEDOR apply to power-law systems and other nonlinear dynamical systems. In addition, ideas behind and permanence for mass-action systems, and the more general power-law systems. A dynamical system on Rn >0

Craciun, Gheorghe

109

Log-Periodic Power Law as a Predictor of Catastrophic Events: A New Mathematical

Log-Periodic Power Law as a Predictor of Catastrophic Events: A New Mathematical Justification describe this behavior in detail. The emergence of log-periodic power law in disaster prediction. The history of log-periodic power law applications started with space exploration. To be able to safely return

Kreinovich, Vladik

110

POWER LAWS FOR MONKEYS TYPINGS RANDOMLY: THE CASE OF UNEQUAL PROBABILITIES

POWER LAWS FOR MONKEYS TYPINGS RANDOMLY: THE CASE OF UNEQUAL PROBABILITIES BRIAN CONRAD AND MICHAEL MITZENMACHER Abstract. An early result in the history of power laws, due to Miller, concerned the following)/N. Miller proved that in this experiment, the rank-frequency distribution of words follows a power law

Conrad, Brian

111

Power law deformation of Wishart Laguerre ensembles of random matrices

NASA Astrophysics Data System (ADS)

We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index ? = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of ?, in terms of the orthogonal polynomials of the standard Wishart-Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Mar?enko-Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on ? and the difference M-N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart-Laguerre ensembles. To illustrate these findings, the generalized Mar?enko-Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices.

Akemann, Gernot; Vivo, Pierpaolo

2008-09-01

112

Interfacial pattern formation in confined power-law fluids.

The interfacial pattern formation problem in an injection-driven radial Hele-Shaw flow is studied for the situation in which a Newtonian fluid of negligible viscosity displaces a viscous non-Newtonian power-law fluid. By utilizing a Darcy-law-like formulation, we tackle the fluid-fluid interface evolution problem perturbatively, and we derive second-order mode-coupling equations that describe the time evolution of the perturbation amplitudes. This allows us to investigate analytically how the non-Newtonian nature of the dislocated fluid determines the morphology of the emerging interfacial patterns. If the pushed fluid is shear-thinning, our results indicate the development of side-branching structures. On the other hand, if the displaced fluid is shear-thickening, one detects the formation of petal-like shapes, markedly characterized by strong tip-splitting events. Finally, a time-dependent injection protocol is presented that is able to restrain finger proliferation via side-branching and tip-splitting. This permits the emergence of symmetric n-fold interfacial shapes for which the number of fingers remains fixed as time progresses. This procedure generalizes existing controlling strategies for purely Newtonian flow circumstances to the case of a non-Newtonian, displaced power-law fluid. PMID:25122375

Brandão, Rodolfo; Fontana, João V; Miranda, José A

2014-07-01

113

Interfacial pattern formation in confined power-law fluids

NASA Astrophysics Data System (ADS)

The interfacial pattern formation problem in an injection-driven radial Hele-Shaw flow is studied for the situation in which a Newtonian fluid of negligible viscosity displaces a viscous non-Newtonian power-law fluid. By utilizing a Darcy-law-like formulation, we tackle the fluid-fluid interface evolution problem perturbatively, and we derive second-order mode-coupling equations that describe the time evolution of the perturbation amplitudes. This allows us to investigate analytically how the non-Newtonian nature of the dislocated fluid determines the morphology of the emerging interfacial patterns. If the pushed fluid is shear-thinning, our results indicate the development of side-branching structures. On the other hand, if the displaced fluid is shear-thickening, one detects the formation of petal-like shapes, markedly characterized by strong tip-splitting events. Finally, a time-dependent injection protocol is presented that is able to restrain finger proliferation via side-branching and tip-splitting. This permits the emergence of symmetric n-fold interfacial shapes for which the number of fingers remains fixed as time progresses. This procedure generalizes existing controlling strategies for purely Newtonian flow circumstances to the case of a non-Newtonian, displaced power-law fluid.

Brandão, Rodolfo; Fontana, João V.; Miranda, José A.

2014-07-01

114

SHJAR Jet Noise Data and Power Spectral Laws

NASA Technical Reports Server (NTRS)

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. The measured spectral data are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of 0.0 to 10.0. The measured data are reported as lossless (i.e., atmospheric attenuation is added to measurements), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter (200-in.) arc. Following the work of Viswanathan, velocity power factors are evaluated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit and the confidence margins for the two regression parameters are studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. As an immediate application of the velocity power laws, spectral density in shockcontaining jets are decomposed into components attributed to jet mixing noise and shock noise. From this analysis, jet noise prediction tools can be developed with different spectral components derived from different physics.

Khavaran, Abbas; Bridges, James

2009-01-01

115

Adhesion of nanoscale asperities with power-law profiles

NASA Astrophysics Data System (ADS)

The behavior of single-asperity micro- and nanoscale contacts in which adhesion is present is important for the performance of many small-scale mechanical systems and processes, such as atomic force microscopy (AFM). When analyzing such problems, the bodies in contact are often assumed to have paraboloidal shapes, thus allowing the application of the familiar Johnson-Kendall-Roberts (JKR), Derjaguin-Müller-Toporov (DMT), or Maugis-Dugdale (M-D) adhesive contact models. However, in many situations the asperities do not have paraboloidal shapes and, instead, have geometries that may be better described by a power-law function. An M-D-n analytical model has recently been developed to extend the M-D model to asperities with power-law profiles. We use a combination of M-D-n analytical modeling, finite element (FE) analysis, and experimental measurements to investigate the behavior of nanoscale adhesive contacts with non-paraboloidal geometries. Specifically, we examine the relationship between pull-off force, work of adhesion, and range of adhesion for asperities with power-law-shaped geometries. FE analysis is used to validate the M-D-n model and examine the effect of the shape of the adhesive interaction potential on the pull-off force. In the experiments, the extended M-D model is applied to analyze pull-off force measurements made on nanoscale tips that are engineered via gradual wear to have power-law shapes. The experimental and modeling results demonstrate that the range of the adhesive interaction is a crucial parameter when quantifying the adhesion of non-paraboloidal tips, quite different than the familiar paraboloidal case. The application of the M-D-n model to the experimental results yields an unusually large adhesion range of 4-5 nm, a finding we attribute to either the presence of long-range van der Waals forces or deviations from continuum theory due to atomic-scale roughness of the tips. Finally, an adhesion map to aid in analysis of pull-off force measurements of non-paraboloidal tips is presented. The map delineates the cases in which a simplified rigid analysis can be used to analyze experimental data.

Grierson, David S.; Liu, Jingjing; Carpick, Robert W.; Turner, Kevin T.

2013-02-01

116

Power laws, discontinuities and regional city size distributions

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.

Garmestani, A.S.; Allen, C.R.; Gallagher, C.M.

2008-01-01

117

Elastohydrodynamic analysis using a power law pressure-viscosity relation

NASA Technical Reports Server (NTRS)

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.

Loewenthal, S. H.; Zaretsky, E. V.

1973-01-01

118

Gravitational wave generation in power-law inflationary models

We investigate the generation of gravitational waves in power-law inflationary models. The energy spectrum of the gravitational waves is calculated using the method of continuous Bogoliubov coefficients. We show that, by looking at the interval of frequencies between 10^(-5) and 10^5 Hz and also at the GHz range, important information can be obtained, both about the inflationary period itself and about the thermalization regime between the end of inflation and the beginning of the radiation-dominated era. We thus deem the development of gravitational wave detectors, covering the MHz/GHz range of frequencies, to be an important task for the future.

Paulo M. Sá; Alfredo B. Henriques

2008-04-21

119

The power-law expansion universe and dark energy evolution

In order to depict the transition from deceleration to acceleration expansion of the universe we use a power-law expansion scale factor, $a\\sim t^{n_0+bt^m}$, with $n_0$, $b$ and $m$ three parameters determined by $H_0$, $q_0$ and $z_T$. For the spatially flat, isotropic and homogeneous universe, such a scale factor leads to the results that the dark energy density is slowly changing currently, and predicts the equation of state $w_X$ changes from $w_X>-1$ to $w_X<-1$.

Yi-Huan Wei

2005-02-03

120

Power-law photoluminescence decay in quantum dots

Some quantum dot samples show a long-time (power-law) behavior of their luminescence intensity decay. This effect has been recently explained as being due to a cooperation of many tunneling channels transferring electrons from small quantum dots with triplet exciton to quantum dots at which the electrons can recombine with the holes in the valence band states. In this work we show that the long-time character of the sample luminescence decay can also be caused by an intrinsic property of a single dot, namely, by a non-adiabatic effect of the electron occupation up-conversion caused by the electron-phonon multiple scattering mechanism.

Král, Karel [Institute of Physics, Academy of Sciences of Czech Republic, v.v.i., Na Slovance 2, 18221 Prague 8 (Czech Republic); Menšík, Miroslav [Institute of Macromolecular Chemistry, Academy of Sciences of Czech Republic, v.v.i., Heyrovského nám. 2, 162 06 Prague 6 (Czech Republic)

2014-05-15

121

Inference of Statistical Patterns in Complex Geosystems: Fitting Power-law Distributions.

NASA Astrophysics Data System (ADS)

Power-law distributions contain precious information about a large variety of physical processes. Although there are sound theoretical grounds for these distributions, the empirical evidence giving support to power laws has been traditionally weak. Recently, Clauset et al. have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method fails to recognize true (simulated) power-law tails in some instances, rejecting the power-law hypothesis. Moreover, the method does not perform well when it is extended to power-law distributions with an upper truncation. We present an alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. We will test the performance of our method on several empirical data which were previously analyzed with less systematic approaches.

Deluca, Anna; Corral, Alvaro

2014-05-01

122

Optimized dynamical decoupling for power-law noise spectra

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.

Pasini, S.; Uhrig, G. S. [Lehrstuhl fuer Theoretische Physik I, TU Dortmund, Otto-Hahn Strasse 4, D-44221 Dortmund (Germany)

2010-01-15

123

Natural orbit approximations in single power-law potentials

In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to improve accuracy, especially for nearly radial orbits. 1) It is found that moderately improved orbital fits can be achieved with higher order perturbation expansions (in eccentricity), with the addition of `harmonic' terms to the solution. 2) Alternately, a matching of the extreme radial excursions of an orbit can be imposed, and a more accurate estimate of the eccentricity parameter is obtained. However, the error in the precession frequency is usually increased. 3) A correction function of small magnitude corrects the frequency problem. With this correction, even first order approximations yield excellent fits at quite high eccentricity over a range of potential indices that includes flat and falling rotation curve cases. 4) Adding a first harmonic term to fit the breadt...

Struck, Curtis

2014-01-01

124

Power Law Scaling of Variability of Discrete Signals.

NASA Astrophysics Data System (ADS)

Data were taken for a variety of systems of discrete signals, including heart rate and background radiation. These sets of data were individually analyzed comparing the standard deviation and the average number of counts as functions of time (or length). It is well known that for random systems, such as nuclear decay, the standard deviation is proportional to the average number of counts raised to the 1/2 power. This was found not to be true for the background radiation and heart rate data. To analyze the data, a computer code was written in C++. The method of analyzing discrete signal data by finding a power-law relationship between standard deviation and average may be used over a wide range of disciplines in areas including, but not limited to, health science, computer science, business, life science, and physics. It may be especially useful in modeling non-linear discrete data.

Thompson, Emily

2004-05-01

125

Power-Law and Long-Memory Characteristics of the Atmospheric General Circulation DMITRY I. VYUSHIN memory'' or ``power-law'' model. Such a model fits a temporal spectrum to a single power-law function, which thereby accumulates more power at lower frequencies than an AR1 fit. In this study, several power-law

126

Concerning the Nature of the Cosmic Ray Power Law Exponents

We have recently shown that the cosmic ray energy distributions as detected on earthbound, low flying balloon or high flying satellite detectors can be computed by employing the heats of evaporation of high energy particles from astrophysical sources. In this manner, the experimentally well known power law exponents of the cosmic ray energy distribution have been theoretically computed as 2.701178 for the case of ideal Bose statistics, 3.000000 for the case of ideal Boltzmann statistics and 3.151374 for the case of ideal Fermi statistics. By "ideal" we mean virtually zero mass (i.e. ultra-relativistic) and noninteracting. These results are in excellent agreement with the experimental indices of 2.7 with a shift to 3.1 at the high energy ~ PeV "knee" in the energy distribution. Our purpose here is to discuss the nature of cosmic ray power law exponents obtained by employing conventional thermal quantum field theoretical models such as quantum chromodynamics to the cosmic ray sources in a thermodynamic scheme w...

Widom, A; Srivastava, Y N

2014-01-01

127

Power Laws in Real Estate Prices during Bubble Periods

NASA Astrophysics Data System (ADS)

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.

Ohnishi, Takaaki; Mizuno, Takayuki; Shimizu, Chihiro; Watanabe, Tsutomu

128

A poly(dimethylsiloxane) viscometer for microliter power law fluids

NASA Astrophysics Data System (ADS)

This paper describes a poly(dimethylsiloxane) (PDMS) microfluidic device for measuring the viscosity of power law fluids. The viscometer utilized the high solubility and permeability of air in PDMS to generate vacuum and drive the Poiseuille flow in the degassed PDMS microchannels. Wide ranges of shear rates in PDMS microchannels were generated by controlling the chamber sizes of the PDMS viscometer. By measuring the distance the fluids traveled and the flow velocity in the PDMS microchannel, the flow behavior index n was determined and the viscosity profile of the sample fluid under a range of shear rates was obtained. Only 5 µL or less volume was consumed for the viscosity measurement. Viscosities of poly(ethylene oxide) solutions and blood control standard were successfully measured under shear rates varying from 10 to 500 s-1, and the results were consistent with those from conventional cone-plate rheometers. The PDMS viscometer was applicable to a broad range of power law fluids, such as diluted polymeric solutions and colloidal suspensions.

Han, Zuoyan; Zheng, Bo

2009-11-01

129

Power law statistics of force and acoustic emission from a slowly penetrated granular bed

NASA Astrophysics Data System (ADS)

Penetration-resistant force and acoustic emission (AE) from a plunged granular bed are experimentally investigated through their power law distribution forms. An AE sensor is buried in a glass bead bed. Then, the bed is slowly penetrated by a solid sphere. During the penetration, the resistant force exerted on the sphere and the AE signal are measured. The resistant force shows power law relation to the penetration depth. The power law exponent is independent of the penetration speed, while it seems to depend on the container's size. For the AE signal, we find that the size distribution of AE events obeys power laws. The power law exponent depends on grain size. Using the energy scaling, the experimentally observed power law exponents are discussed and compared to the Gutenberg-Richter (GR) law.

Matsuyama, K.; Katsuragi, H.

2014-01-01

130

Power-Law Template for IR Point Source Clustering

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 < l < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 um; 1000 < l < 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 l^-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^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 arou...

Addison, Graeme E; Hajian, Amir; Viero, Marco; Bond, J Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renée; Marriage, Tobias A; Moodley, Kavilan; Page, Lyman A; Reese, Erik D; Scott, Douglas; Spergel, David N; Staggs, Suzanne T; Wollack, Edward

2011-01-01

131

Power-law versus log-law in wall-bounded turbulence: A large-eddy simulation perspective

NASA Astrophysics Data System (ADS)

The debate whether the mean streamwise velocity in wall-bounded turbulent flows obeys a log-law or a power-law scaling originated over two decades ago, and continues to ferment in recent years. As experiments and direct numerical simulation can not provide sufficient clues, in this study we present an insight into this debate from a large-eddy simulation (LES) viewpoint. The LES organically combines state-of-the-art models (the stretched-vortex model and inflow rescaling method) with a virtual-wall model derived under different scaling law assumptions (the log-law or the power-law by George and Castillo ["Zero-pressure-gradient turbulent boundary layer," Appl. Mech. Rev. 50, 689 (1997)]). Comparison of LES results for Re? ranging from 105 to 1011 for zero-pressure-gradient turbulent boundary layer flows are carried out for the mean streamwise velocity, its gradient and its scaled gradient. Our results provide strong evidence that for both sets of modeling assumption (log law or power law), the turbulence gravitates naturally towards the log-law scaling at extremely large Reynolds numbers.

Cheng, W.; Samtaney, R.

2014-01-01

132

Federal Register 2010, 2011, 2012, 2013

...State or local law enforcement...immigration law enforcement powers would be less...efficient than the procedures already established...precise activation procedures. (3) Written...statement of the powers, privileges...State or local law...

2002-07-24

133

Unexpected power-law stress relaxation of entangled ring polymers

NASA Astrophysics Data System (ADS)

After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers.

Kapnistos, M.; Lang, M.; Vlassopoulos, D.; Pyckhout-Hintzen, W.; Richter, D.; Cho, D.; Chang, T.; Rubinstein, M.

2008-12-01

134

Persistence of locality in systems with power-law interactions

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\\alpha}$ interactions with $\\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \\emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems.

Zhe-Xuan Gong; Michael Foss-Feig; Spyridon Michalakis; Alexey V. Gorshkov

2014-07-07

135

Molecular clouds have power-law probability distribution functions

In this Letter we investigate the shape of the probability distribution of column densities (PDF) in molecular clouds. Through the use of low-noise, extinction-calibrated \\textit{Herschel}/\\textit{Planck} emission data for eight molecular clouds, we demonstrate that, contrary to common belief, the PDFs of molecular clouds are not described well by log-normal functions, but are instead power laws with exponents close to two and with breaks between $A_K \\simeq 0.1$ and $0.2\\,\\mathrm{mag}$, so close to the CO self-shielding limit and not far from the transition between molecular and atomic gas. Additionally, we argue that the intrinsic functional form of the PDF cannot be securely determined below $A_K \\simeq 0.1\\,\\mathrm{mag}$, limiting our ability to investigate more complex models for the shape of the cloud PDF.

Lombardi, Marco; Lada, Charles J

2015-01-01

136

Power-law inflation with a nonminimally coupled scalar field

We consider the dynamics of power-law inflation with a nonminimally coupled scalar field $\\phi$. It is well known that multiple scalar fields with exponential potentials $V(\\phi)=V_0 {\\rm exp}(-\\sqrt{16\\pi/p m_{\\rm pl}^2} \\phi)$ lead to an inflationary solution even if the each scalar field is not capable to sustain inflation. In this paper, we show that inflation can be assisted even in the one-field case by the effect of nonminimal coupling. When $\\xi$ is positive, since an effective potential which arises by a conformal transformation becomes flatter compared with the case of $\\xi=0$ for $\\phi>0$, we have an inflationary solution even when the universe evolves as non-inflationary in the minimally coupled case. For the negative $\\xi$, the assisted inflation can take place when $\\phi$ evolves in the region of $\\phi<0$ \\.

Tsujikawa, S

2000-01-01

137

An effective quintessence field with a power-law potential

In this paper, we consider an effective quintessence scalar field with a power-law potential interacting with a $P_{b}=\\xi q\\rho_{b}$ barotropic fluid as a first model, where $q$ is a deceleration parameter. For the second model we assume viscous polytropic gas interacting with the scalar field. We investigate problem numerically and analyze behavior of different cosmological parameter concerning to components and behavior of Universe. We also compare our results with observational data to fix parameters of the models. We find some instabilities in the first model which may disappear in the second model for the appropriate parameters. Therefore, we can propose interacting quintessence dark energy with viscous polytropic gas as a successful model to describe Universe.

M. Khurshudyan; B. Pourhassan; R. Myrzakulov; S. Chattopadhyay

2014-03-15

138

Controlling total spot power from holographic laser by superimposing a binary phase grating.

By superimposing a tunable binary phase grating with a conventional computer-generated hologram, the total power of multiple holographic 3D spots can be easily controlled by changing the phase depth of grating with high accuracy to a random power value for real-time optical manipulation without extra power loss. Simulation and experiment results indicate that a resolution of 0.002 can be achieved at a lower time cost for normalized total spot power. PMID:21643099

Liu, Xiang; Zhang, Jian; Gan, Yu; Wu, Liying

2011-04-25

139

POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING

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.

Addison, Graeme E.; Dunkley, Joanna [Sub-department of Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH (United Kingdom); Hajian, Amir; Das, Sudeep; Hincks, Adam D.; Page, Lyman A.; Staggs, Suzanne T. [Joseph Henry Laboratories of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544 (United States); Viero, Marco [Department of Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Bond, J. Richard [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada); Devlin, Mark J.; Reese, Erik D. [Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104 (United States); Halpern, Mark; Scott, Douglas [Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z4 (Canada); Hlozek, Renee; Marriage, Tobias A.; Spergel, David N. [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544 (United States); Moodley, Kavilan [Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041 (South Africa); Wollack, Edward [NASA/Goddard Space Flight Center, Code 665, Greenbelt, MD 20771 (United States)

2012-06-20

140

Power-Law Template for IR Point Source Clustering

NASA Technical Reports Server (NTRS)

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.

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

141

Anisotropic power-law inflation for the Dirac-Born-Infeld theory

NASA Astrophysics Data System (ADS)

We find a new set of the Bianchi type I power-law expanding solutions in a string-motivated Dirac-Born-Infeld theory. Stability analysis shows that these power-law inflationary solutions remain stable with or without the contribution of the Dirac-Born-Infeld effect. We also find a new set of Bianchi type I expanding power-law solutions in a two scalar Dirac-Born-Infeld model with an additional phantom field. It is shown that the inclusion of the phantom field turns the Bianchi type I power-law solutions unstable during the inflationary phase.

Do, Tuan Q.; Kao, W. F.

2011-12-01

142

Universal fractional noncubic power law for density of metallic glasses.

As a fundamental property of a material, density is controlled by the interatomic distances and the packing of microscopic constituents. The most prominent atomistic feature in a metallic glass (MG) that can be measured is its principal diffraction peak position (q1) observable by x-ray, electron, or neutron diffraction, which is closely associated with the average interatomic distance in the first shell. Density (and volume) would naturally be expected to vary under compression in proportion to the cube of the one-dimensional interatomic distance. However, by using high pressure as a clean tuning parameter and high-resolution in situ techniques developed specifically for probing the density of amorphous materials, we surprisingly found that the density of a MG varies with the 5/2 power of q1, instead of the expected cubic relationship. Further studies of MGs of different compositions repeatedly produced the same fractional power law of 5/2 in all three MGs we investigated, suggesting a universal feature in MG. PMID:24856706

Zeng, Qiaoshi; Kono, Yoshio; Lin, Yu; Zeng, Zhidan; Wang, Junyue; Sinogeikin, Stanislav V; Park, Changyong; Meng, Yue; Yang, Wenge; Mao, Ho-Kwang; Mao, Wendy L

2014-05-01

143

NASA Astrophysics Data System (ADS)

The conservation laws for the (1+2)-dimensional Zakharov—Kuznetsov modified equal width (ZK-MEW) equation with power law nonlinearity are constructed by using Noether's approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. Finally, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.

Han, Zhong; Zhang, Yu-Feng; Zhao, Zhong-Long

2013-12-01

144

Natural orbit approximations in single power-law potentials

NASA Astrophysics Data System (ADS)

In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here, I explore several extensions of these approximations to improve accuracy, especially for nearly radial orbits. (1) It is found that moderately improved orbital fits can be achieved with higher order perturbation expansions (in eccentricity), with the addition of `harmonic' terms to the solution. (2) Alternately, a matching of the extreme radial excursions of an orbit can be imposed, and a more accurate estimate of the eccentricity parameter is obtained. However, the error in the precession frequency is usually increased. (3) A correction function of small magnitude corrects the frequency problem. With this correction, even first-order approximations yield excellent fits at quite high eccentricity over a range of potential indices that includes flat and falling rotation-curve cases. (4) Adding a first harmonic term to fit the breadth of the orbital loops, and determining the fundamental and harmonic coefficients by matching to three orbital positions further improves the fit. With a couple of additional small corrections, one obtains excellent fits to orbits with radial ranges of more than a thousand for some potentials. These simple corrections to the basic p-ellipse are basically in the form of several successive approximations, and can provide high accuracy. They suggest new results including that the apsidal precession rate scales approximately as log(1 - e) at very high eccentricities e. New insights are also provided on the occurrence of periodic orbits in various potentials, especially at high eccentricity.

Struck, Curtis

2015-01-01

145

Interpolating between types and tokens by estimating power-law generators

Standard statistical models of language fail to capture one of the most striking properties of natural languages: the power-law distribution in the frequencies of word tokens. We present a framework for developing statistical models that generically produce power-laws, augmenting stan- dard generative models with an adaptor that produces the appropriate pattern of token frequencies. We show that taking a particular

Sharon Goldwater; Tom Griffiths; Mark Johnson

2005-01-01

146

Numerical Simulation of the Flow of a Power Law Fluid in an Elbow Bend

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several...

Kanakamedala, Karthik

2010-07-14

147

The fractal nature of nature: power laws, ecological complexity and biodiversity

Underlying the diversity of life and the complexity of ecology is order that reè ects the operation of funda- mental 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

James H. Brown; Vijay K. Gupta; Bai-Lian Li; Bruce T. Milne; Carla Restrepo; Geoffrey B. West

2002-01-01

148

Behavioral/Systems/Cognitive Power-Law Dynamics in an Auditory-Nerve Model Can

Behavioral/Systems/Cognitive Power-Law Dynamics in an Auditory-Nerve Model Can Account for Neural. Inclusion of power-law dynamics in a phenomenological model of the inner hair cell (IHC)Âauditory nerve (AN Neurons in the auditory system respond to recent stimulus-level history by adapting their response

Carney, Laurel H.

149

Laminar heat transfer for power-law fluids in thermal entrance region of annular sector ducts

Laminar heat transfer of a power law fluid in the thermal entrance region of an annular sector duct is analyzed. The effect of geometric shape, power law index, axial conduction and viscous dissipation are investigated. Both boundary conditions of uniform temperature and uniform heat flux peripherally are considered. The annular sector duct flow configuration is one of the common arrangements

Rong Ping Hsia

1993-01-01

150

Power law fitting procedures: The electrical conductance of coalescing nanocluster films

NASA Astrophysics Data System (ADS)

The electrical conductance of bismuth nanocluster films deposited in vacuum has been observed to increase after the end of deposition. This evolution Gexp(t) can be successfully fitted with a power law. However, it is well known that interpretation of power law fits can be problematic. To investigate the physical meaning of the fitted power law exponent a percolation model with coalescence built into it was developed. In this model the evolution of the conductance of necks between neighboring occupied sites is defined as a power law with exponent ? resulting in model conductance data Gmod(t). The Gmod(t) data are fitted with a power law and we show that the fitted exponent is close to the original exponent ?, so long as the power law expression is chosen correctly. The fits to the synthetic Gmod(t) data provide confidence in the fitting procedure and in the power law exponents obtained from fits to the experimental data. The experimental power law exponents are found to be much smaller than expected from previous theories of micron scale particle coalescence.

Convers, Pierre Y.; Sattar, Abdul; Brown, Simon A.; Hendy, Shaun C.

2011-01-01

151

Heat transfer enhancement in laminar slurry pipe flows with power law thermal conductivities

Generalized theoretical results for heat transfer in laminar pipe flow with power law varying thermal conductivities are presented. The study is motivated by experimental observations that above a threshold shear rate the effective thermal conductivity for disperse two-phase mixtures increases with shear rate. Using a relatively general three parameter power law model for conductivity as a function of shear rate,

C. W. Sohn; M. M. Chen

1984-01-01

152

Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics?

Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics? Jonathan Touboul1 with no ambiguity that the avalanche size is distributed as a power-law. We conclude that logarithmic and Neuronal Avalanches Arise from Stochastic Dynamics? PLoS ONE 5(2): e8982. doi:10.1371/ journal.pone.0008982

Destexhe, Alain

153

ELSEVIER Physica A 242 (1997) 90-94 New evidence for the power-law distribution

PHYSiCA ELSEVIER Physica A 242 (1997) 90-94 New evidence for the power-law distribution of wealth the distribution of wealth in society. We analyze data from the 1996 Forbes 400 list of the richest people in the US. Our results confirm that wealth is distributed according to a power law. The measured exponent

154

Power-law forgetting in synapses with metaplasticity

NASA Astrophysics Data System (ADS)

The idea of using metaplastic synapses to incorporate the separate storage of long- and short-term memories via an array of hidden states was put forward in the cascade model of Fusi et al. In this paper, we devise and investigate two models of a metaplastic synapse based on these general principles. The main difference between the two models lies in their available mechanisms of decay, when a contrarian event occurs after the build-up of a long-term memory. In one case, this leads to the conversion of the long-term memory to a short-term memory of the opposite kind, while in the other, a long-term memory of the opposite kind may be generated as a result. Appropriately enough, the response of both models to short-term events is not affected by this difference in architecture. On the contrary, the transient response of both models, after long-term memories have been created by the passage of sustained signals, is rather different. The asymptotic behaviour of both models is, however, characterised by power-law forgetting with the same universal exponent.

Mehta, A.; Luck, J. M.

2011-09-01

155

Statistical tests for power-law cross-correlated processes

NASA Astrophysics Data System (ADS)

For stationary time series, the cross-covariance and the cross-correlation as functions of time lag n serve to quantify the similarity of two time series. The latter measure is also used to assess whether the cross-correlations are statistically significant. For nonstationary time series, the analogous measures are detrended cross-correlations analysis (DCCA) and the recently proposed detrended cross-correlation coefficient, ?DCCA(T,n), where T is the total length of the time series and n the window size. For ?DCCA(T,n), we numerically calculated the Cauchy inequality -1??DCCA(T,n)?1. Here we derive -1??DCCA(T,n)?1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ?DCCA within which the cross-correlations become statistically significant. For overlapping windows we numerically determine—and for nonoverlapping windows we derive—that the standard deviation of ?DCCA(T,n) tends with increasing T to 1/T. Using ?DCCA(T,n) we show that the Chinese financial market's tendency to follow the U.S. market is extremely weak. We also propose an additional statistical test that can be used to quantify the existence of cross-correlations between two power-law correlated time series.

Podobnik, Boris; Jiang, Zhi-Qiang; Zhou, Wei-Xing; Stanley, H. Eugene

2011-12-01

156

Binary optics used in high-power laser shaping

NASA Astrophysics Data System (ADS)

On the basis of the analysis of the existed optimization algorithms, three kinds of hybrid algorithms are developed for phase design of the Binary Optical Element to realize beam shaping, including Global/local united search algorithm (GLUSA), the modified GLUSA, and the modified GLUSA with multi-resolution. Four masks have been used to produce a (phi) 50 mm binary phase plate with 16-phase level relief surface structure for wavelength 0.6328 micrometers and an optical CT method has been used for measuring the intensity distribution. A continuous phase plate, with operating wavelength 1.053 micrometers and diameter 100 mm, is manufactured by ion-etching technique with gray-scale mask on the K9- glass substrate. The intensity distribution of the focused spot is measured by a common CCD and multi-attenuators with which the measurement dynamic range is increased. The experimental results after data processing show that the focused spot with steep edge, low side lobe and a certain uniformity of the main lobe without sharp peak at the zero order is obtained.

Jin, Guofan; Tan, Qiaofeng; Yan, Yingbai; Wu, Minxian

1999-09-01

157

Exergy analysis of a dual-level binary geothermal power plant

Exergy analysis of a 12.4 MW existing binary geothermal power plant is performed using actual plant data to assess the plant performance and pinpoint sites of primary exergy destruction. Exergy destruction throughout the plant is quantified and illustrated using an exergy flow diagram, and compared to the energy flow diagram. The causes of exergy destruction in the plant include the

Mehmet Kanoglu

2002-01-01

158

The generalized linear mixed model (GLIMMIX) provides a powerful technique to model correlated outcomes with different types of distributions. The model can now be easily implemented with SAS PROC GLIMMIX in version 9.1. For binary outcomes, linearization methods of penalized quasilikelihood (PQL) or marginal quasi-likelihood (MQL) provide relatively accurate variance estimates for fixed effects. Using GLIMMIX based on these linearization methods, we derived formulas for power and sample size calculations for longitudinal designs with attrition over time. We found that the power and sample size estimates depend on the within-subject correlation and the size of random effects. In this article, we present tables of minimum sample sizes commonly used to test hypotheses for longitudinal studies. A simulation study was used to compare the results. We also provide a Web link to the SAS macro that we developed to compute power and sample sizes for correlated binary outcomes. PMID:18462826

Dang, Qianyu; Mazumdar, Sati; Houck, Patricia R.

2008-01-01

159

Zeotropic mixtures of halocarbons as working fluids in binary geothermal power generation cycles

The performance of Rankine cycle binary systems for geothermal power generation using a hydrothermal resource has been investigated. To date, in addition to many pure fluids, mixtures of Paraffin-type hydrocarbons and water-ammonia mixtures have been investigated. This paper gives the results of consideration of mixtures of halocarbons as working fluids in these power cycles. The performance of mixtures of Refrigerant-114

Bliem

1987-01-01

160

Swings between rotation and accretion power in a binary millisecond pulsar.

It is thought that neutron stars in low-mass binary systems can accrete matter and angular momentum from the companion star and be spun-up to millisecond rotational periods. During the accretion stage, the system is called a low-mass X-ray binary, and bright X-ray emission is observed. When the rate of mass transfer decreases in the later evolutionary stages, these binaries host a radio millisecond pulsar whose emission is powered by the neutron star's rotating magnetic field. This evolutionary model is supported by the detection of millisecond X-ray pulsations from several accreting neutron stars and also by the evidence for a past accretion disc in a rotation-powered millisecond pulsar. It has been proposed that a rotation-powered pulsar may temporarily switch on during periods of low mass inflow in some such systems. Only indirect evidence for this transition has hitherto been observed. Here we report observations of accretion-powered, millisecond X-ray pulsations from a neutron star previously seen as a rotation-powered radio pulsar. Within a few days after a month-long X-ray outburst, radio pulses were again detected. This not only shows the evolutionary link between accretion and rotation-powered millisecond pulsars, but also that some systems can swing between the two states on very short timescales. PMID:24067710

Papitto, A; Ferrigno, C; Bozzo, E; Rea, N; Pavan, L; Burderi, L; Burgay, M; Campana, S; Di Salvo, T; Falanga, M; Filipovi?, M D; Freire, P C C; Hessels, J W T; Possenti, A; Ransom, S M; Riggio, A; Romano, P; Sarkissian, J M; Stairs, I H; Stella, L; Torres, D F; Wieringa, M H; Wong, G F

2013-09-26

161

??Power-laws provide a means for investigating snow avalanche frequency/magnitude relationships and their contributing factors. This research uses power-laws to explore variations in avalanche size proportions… (more)

Naisbitt, Adam

2008-01-01

162

On the origin of power-law X-ray spectra of active galactic nuclei

NASA Technical Reports Server (NTRS)

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.

Schlosman, I.; Shaham, J.; Shaviv, G.

1984-01-01

163

Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales

NASA Technical Reports Server (NTRS)

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.

Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.

2006-01-01

164

Analytical time-domain Green's functions for power-law media.

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation ["Time domain wave-equations for lossy media obeying a frequency power-law," J. Acoust. Soc. Am. 96, 491-500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green's functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1/3, 1/2, 2/3, 3/2, and 2, the Green's function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green's functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green's functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green's function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green's function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

Kelly, James F; McGough, Robert J; Meerschaert, Mark M

2008-11-01

165

Analytical time-domain Green’s functions for power-law media

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1?3, 1?2, 2?3, 3?2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

2008-01-01

166

Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection

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

Adler, Miri; Mayo, Avi; Alon, Uri

2014-01-01

167

Performance analysis of the Chena binary geothermal power plant

In this paper, the IPSEpro model of the Chena Geothermal ORC Power Plant had been developed and validated using the real data. The validated model was used to investigate the effect of variation in the geothermal source temperature on plant performance.The analysis showed that the variation of the geothermal source temperature affects the plant behaviour. Increase in the geothermal source

Mathew Aneke; Brian Agnew; Chris Underwood

2011-01-01

168

A Power-Law Formulation of Laminar Flow in Short Pipes Max Sherman

A Power-Law Formulation of Laminar Flow in Short Pipes Max Sherman Indoor Environment Program-law representation between the air flow and applied pressure for laminar flow in short pipes. It is found that short of interest. The system studied herein is the flow of an incompressible, viscous fluid through a short pipe

169

Stochastic mixing model with power law decay of variance Sergei Fedotov,1

Stochastic mixing model with power law decay of variance Sergei Fedotov,1 Matthias Ihme,2 and Heinz; published 14 January 2005 A stochastic mixing model based on the law of large numbers is presented- . A general Lagrangian mixing process is modeled by a stochastic difference equation where the mixing

Fedotov, Sergei

170

Power-Law Sensitivity To Initial Conditions In Sea Clutter , Jianbo Gao1

Power-Law Sensitivity To Initial Conditions In Sea Clutter Jing Hu1 , Jianbo Gao1 , and Kung Yao2 1-law sensitivity to initial conditions, sea clutter, target detection ABSTRACT Understanding the nature of sea clutter is crucial to the successful modeling of sea clutter as well as to facilitate target detection

Gao, Jianbo

171

Binary generators - you'll wonder where the power went

There has been a surge of interest in electric power generation from low-temperature geothermal energy. The organic Rankine cycle is reviewed for efficiency. A pressure-enthalpy diagram for R-114 (the refrigerant chosen for this study) is given. In the cycle, refrigerant is vaporized, then expanded, to turn the shaft, then condensed, then pumped back into the cycle. The cycle depends on

Ryan

1983-01-01

172

Comment on 'Generalized Heisenberg algebra coherent states for power-law potentials'

We argue that the statistical features of generalized coherent states for power-law potentials based on Heisenberg algebra, presented in a recent paper by Berrada et al (Phys. Lett. A, 375, 298 (2011)) are incorrect.

Shahid Iqbal; Farhan Saif

2011-10-24

173

Research on power-law acoustic transient signal detection based on wavelet transform

NASA Astrophysics Data System (ADS)

Aiming at the characteristics of acoustic transient signal emitted from antisubmarine weapon which is being dropped into water (torpedo, aerial sonobuoy and rocket assisted depth charge etc.), such as short duration, low SNR, abruptness and instability, based on traditional power-law detector, a new method to detect acoustic transient signal is proposed. Firstly wavelet transform is used to de-noise signal, removes random spectrum components and improves SNR. Then Power- Law detector is adopted to detect transient signal. The simulation results show the method can effectively extract envelop characteristic of transient signal on the condition of low SNR. The performance of WT-Power-Law markedly outgoes that of traditional Power-Law detection method.

Han, Jian-hui; Yang, Ri-jie; Wang, Wei

2007-11-01

174

Tunable power law in the desynchronization events of coupled chaotic electronic circuits

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.

Gilson F. de Oliveira Jr.; Hugo L. D. de Souza Cavalcante; Orlando di Lorenzo; Martine Chevrollier; Thierry Passerat de Silans; Marcos Oriá

2013-09-12

175

NASA Astrophysics Data System (ADS)

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.

Sato, Aki-Hiro

2004-04-01

176

Tunable power law in the desynchronization events of coupled chaotic electronic circuits

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.

Oliveira, Gilson F. de, E-mail: gilson@otica.ufpb.br; Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos [Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB (Brazil)] [Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB (Brazil); Souza Cavalcante, Hugo L. D. de [Departamento de Informática, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB (Brazil)

2014-03-15

177

Bimodal Diffusion in Power-Law Shear Flows E. Ben-Naim and S. Redner

Bimodal Diffusion in Power-Law Shear Flows E. Ben-Naim and S. Redner Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215 D. ben-Avraham Department of Physics, Clarkson

Ben-Naim, Eli

178

Bimodal Di usion in Power-Law Shear Flows E. Ben-Naim and S. Redner

Bimodal Di#11;usion in Power-Law Shear Flows E. Ben-Naim and S. Redner Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215 D. ben-Avraham Department of Physics, Clarkson

Ben-Naim, Eli

179

Power law scaling of tsunami run-up heights and probabilistic forecasting

Many natural systems have cumulative number-size distributions that follow a power law or an upper-truncated power law. A well-known example is the Gutenberg-Richter scaling relationship for earthquakes where the b-value is the scaling exponent. Tsunamis are a natural hazard for many coastal regions and are often triggered by earthquakes. Tsunami size is measured as run-up height, which may be measured

S. Burroughs; S. Tebbens

2003-01-01

180

Power Law Spectra in the Nature: Analogies with the Cosmic Ray Spectrum

Examples of the power law spectra observations in the Nature are given. It is shown that the observed meteoroid mass spectrum is very similar to the observed cosmic ray energy spectrum. It is concluded that the "knees" observed in both spectra have a similar origin: the Earth's atmosphere. Both spectra are studied by indirect methods through secondary components and specific behavior of these components in the atmosphere could produce the "knee" even in a case when primary spectrum follows a pure power law.

Yuri V. Stenkin

2005-07-01

181

The shape of the two-point correlation function - Evidence for a double power law

NASA Astrophysics Data System (ADS)

The two-point galaxy correlation functions for three samples of galaxies are studied to determine a suitable model based on a Chi-square analysis. A double-power-law model is shown to generally describe the samples over the large range of separations, and the fit obtained agrees with studies based on redshift separations. The analysis suggests that the double power law is geometrical, and the function for galactic clusters is the same as that for large-scale galactic formations.

Calzetti, Daniela; Giavalisco, Mauro; Meiksin, Avery

1992-10-01

182

ERIC Educational Resources Information Center

I am pleased to be part of this symposium to celebrate the life and work of Peter Bachrach. Although my focus is the relevance of Peter's ideas of power to law, I want to begin with some personal comments as well as raise some final thoughts, drawing on others' contributions. Like so many of Peter's other students, I adored him. Peter's joy in…

Schneider, Elizabeth M.

2010-01-01

183

Two Power-Law States of the Ultraluminous X-Ray Source IC 342 X-1

NASA Astrophysics Data System (ADS)

In order to elucidate the emission properties of ultraluminous X-ray sources (ULXs) during their power-law (PL) state, we examined long-term X-ray spectral data of IC 342 X-1 during its PL state by using our own Suzaku data and archival data by XMM-Newton, Chandra, and Swift observations. The PL state of this source seems to be classified into two sub-states in terms of the X-ray luminosities in the 0.5-10 keV band: the low-luminosity PL state with (4-6) × 1039 erg s-1 and the high-luminosity one with (1.1-1.4) × 1040 erg s-1 . During Suzaku observations, which were made in 2010 August and 2011 March, X-1 stayed in the low-luminosity PL state. The observed X-ray luminosity (4.9-5.6 × 1039 erg s-1) and the spectral shape (photon index = 1.67-1.83) slightly changed between the two observations. Using the Suzaku PIN detector, we for the first time confirmed a PL tail extending up to at least 20 keV with no signatures of a high-energy turnover in both of the Suzaku observations. In contrast, a turnover at about 6 keV was observed during the high-luminosity PL state in 2004 and 2005 with XMM-Newton. Importantly, the photon indices are similar between the two PL states, and so are the Compton y-parameters of y ˜ 1, which indicates a similar energy balance (between the corona and the accretion disk) holding in the two PL states despite different electron temperatures. From spectral similarities with recent studies about other ULXs, and the Galactic black-hole binary GRS 1915+ 105, IC 342 X-1 is also likely to be in a state with a supercritical accretion rate, although more sensitive higher energy observations would be necessary to make any conclusion.

Yoshida, Tessei; Isobe, Naoki; Mineshige, Shin; Kubota, Aya; Mizuno, Tsunefumi; Saitou, Kei

2013-04-01

184

ANN based optimization of supercritical ORC-Binary geothermal power plant: Simav case study

Artificial neural network is a new tool, which works rapidly for decision making and modeling of the processes within the expertise. Therefore, ANN can be a solution for the design and optimization of complex power cycles, such as ORC-Binary. In the present study, the back-propagation learning algorithm with three different variants, namely Levenberg–Marguardt (LM), Pola-Ribiere Conjugate Gradient (CGP), and Scaled

Oguz Arslan; Ozge Yetik

2011-01-01

185

In this paper we determine the tidal distortion parameter k_m of the secondary partner (mass loser) of the semi-detached eclipsing binary system V621 Cen by comparing the phenomenologically determined orbital period P_b=3.683549(11) d to the Keplerian one P^Kep computed with the values of the relevant system's parameters determined independently of the third Kepler law itself. Our result is k_m = -1.5 +/- 0.6. Using the periastron precession, as traditionally done with other eclipsing binaries in eccentric orbits, would have not been possible because of the circularity of the V621 Cen path.

Lorenzo Iorio

2008-01-06

186

Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

NASA Astrophysics Data System (ADS)

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.

Sibatov, R. T.

2011-08-01

187

Power law scaling in synchronization of brain signals depends on cognitive load

As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors. PMID:24822039

Tinker, Jesse; Velazquez, Jose Luis Perez

2014-01-01

188

Exergy analysis of a cogeneration heat and power (CHP) system (first and second law analysis)

The present study deals with an Analysis of power generation systems are of scientific interest and also essential for the efficient utilization of energy resources. The most commonly-used method for analysis of an energy conversion process is the first law of thennodynamics. Therefore, the effect of key parameters on the out put power and efficiency are so important. In this

A. Ganjeh Kaviri; M. N. Mohd Jafar; M. L. Tholudin; H. Barzegar Avval

2011-01-01

189

Modified power law equations for vertical wind profiles. [in investigation of windpower plant siting

NASA Technical Reports Server (NTRS)

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.

Spera, D. A.; Richards, T. R.

1979-01-01

190

How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor's law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution. PMID:25550506

Lagrue, Clément; Poulin, Robert; Cohen, Joel E

2015-02-10

191

In this paper we determine the tidal distortion parameter km of the secondary partner (mass loser) of the semi-detached eclipsing binary system V621 Cen by comparing the phenomenologically determined orbital period Pb=3.683549(11)d to the Keplerian one PKep computed with the values of the relevant system’s parameters determined independently of the third Kepler law itself. Our result is km=-1.5±0.6. Using the

Lorenzo Iorio

2008-01-01

192

Power law behavior associated with a Fibonacci Lucas model and generalized statistical models

A Fibonacci-Lucas based statistical model and several other related models are studied. The canonical and grand canonical partition functions for these models are developed.Partition structure such as the distribution of sizes as in a cluster distribution is explored.Ensemble averaging over all partitions leads to a scale invariant power law behavior at a particular critical like point. The canonical ensemble of the Fibonacci-Lucas case involves the Gegenbauer polynomial.The model has a hyperbolic power law behavior, a feature linked to the golden mean ratio of two adjacent Fibonacci numbers and also the connection of Lucas numbers to the golden mean. The relation to other power law behavior, such as Zipf and Pareto laws, is mentioned. For the cases considered, the grand canonical ensemble involves the Gauss hypergeometric function F(a,b,c,z) with specific values for a,b,c. The general case has a variable power law behavior with tau exponent equal to1+c-a-b. An application with a=1/2, b=1, c=3 and thus tau=5/2 very closely approximates Bose-Einstein condensation. The zeta function zeta(3/2)=2.61 of the exact theory is replaced with 8/3 and zeta(5/2)= 1.34 with 4/3. At the condensation point the number of cycles of length falls as a scale invariant power law. The cycles, which arise from permutation symmetries associated with Bose-Einstein statistics, can be viewed as links in a complex network of connections between particles. This scale invariant power law parallels that seen in complex networks. The growth of the network is developed using recurrence properties of the model. Constraints imposed by the canonical ensemble and associates correlations lead to some number theoretic connections between Fibonacci and Lucas numbers as an incidental consequence of this approach.

Aram Z. Mekjian

2009-10-13

193

Federal Register 2010, 2011, 2012, 2013

...authorize State or local law enforcement officers...contain precise activation procedures. (3) Written agreements...requirements: (i) The powers, privileges, or duties that State or local law enforcement officers...in accordance with the procedures set forth in...

1999-04-08

194

Constraints on the tensor-to-scalar ratio for non-power-law models

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 2.5? C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r{sub LD} = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

Vázquez, J. Alberto; Bridges, M. [Kavli Institute for Cosmology, Madingley Road,Cambridge CB3 0HA (United Kingdom); Ma, Yin-Zhe [Department of Physics and Astronomy, University of British Columbia, Agricultural Road, Vancouver BC V6T 1Z1 (Canada); Hobson, M.P., E-mail: jv292@cam.ac.uk, E-mail: mb435@mrao.cam.ac.uk, E-mail: mayinzhe@phas.ubc.ca, E-mail: mph@mrao.cam.ac.uk [Astrophysics Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge, CB3 0HE (United Kingdom)

2013-08-01

195

NASA Technical Reports Server (NTRS)

Magnetospheric radio frequency emission power has been shown to vary as a function of both solar wind and planetary values such as magnetic field by Kaiser and Desch (1984). Planetary magnetic fields have been shown to scale with planetary variables such as density and angular momentum by numerous researchers. This paper combines two magnetic scaling laws with the radiometric law to yield 'Bode's'-type laws governing planetary radio emissions. Further analysis allows the reduction of variables to planetary mass and orbital distance. These generalized laws are then used to predict the power otuput of Neptune to be about 1.6 x 10 to the 7th W; with the intensity peaking at about 3 MHz.

Million, M. A.; Goertz, C. K.

1988-01-01

196

Presidential Power over International Law: Restoring the Balance

The vast majority of U.S. international agreements today are made by the President acting alone. Little noticed and rarely discussed, the agreements are concluded in a process almost completely hidden from outside view. This state of affairs is the result of a longterm transformation. Over the course of more than a century, Congress gradually yielded power to the President to

Oona A Hathaway

2009-01-01

197

Second law analysis of a conventional steam power plant

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine\\/generator sets from thermal to electrical. Combustion and heat transfer inside the

Geng Liu; Robert H. Turner; Yunus A. Cengel

1993-01-01

198

Phase diagram of power law and Lennard-Jones systems: crystal phases.

An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed. PMID:25362319

Travesset, Alex

2014-10-28

199

Phase diagram of power law and Lennard-Jones systems: Crystal phases

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.

Travesset, Alex [Ames Laboratory

2014-10-28

200

Human mobility has been empirically observed to exhibit Levy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we analyze urban human mobility and we propose to explain the Levy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bicycle, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an e...

Zhao, Kai; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu

2014-01-01

201

Phase diagram of power law and Lennard-Jones systems: Crystal phases

NASA Astrophysics Data System (ADS)

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.

Travesset, Alex

2014-10-01

202

Power law behavior associated with a Fibonacci Lucas model and generalized statistical models

A Fibonacci-Lucas based statistical model and several other related models are studied. The canonical and grand canonical partition functions for these models are developed.Partition structure such as the distribution of sizes as in a cluster distribution is explored.Ensemble averaging over all partitions leads to a scale invariant power law behavior at a particular critical like point. The canonical ensemble of the Fibonacci-Lucas case involves the Gegenbauer polynomial.The model has a hyperbolic power law behavior, a feature linked to the golden mean ratio of two adjacent Fibonacci numbers and also the connection of Lucas numbers to the golden mean. The relation to other power law behavior, such as Zipf and Pareto laws, is mentioned. For the cases considered, the grand canonical ensemble involves the Gauss hypergeometric function F(a,b,c,z) with specific values for a,b,c. The general case has a variable power law behavior with tau exponent equal to1+c-a-b. An application with a=1/2, b=1, c=3 and thus tau=5/...

Mekjian, Aram Z

2009-01-01

203

Numerical study of non-Darcy natural convection of a power-law fluid in a porous cavity

A numerical study of laminar natural convection in a porous enclosure saturated with a power-law fluid was performed. Hydrodynamic and heat transfer results are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated. The flow in the porous medium was modeled using th modified Brinkman-Forchheimer-extended Darcy model for power-law fluids. Parametric studies were conducted to examine the effects of Darcy number, Rayleigh number, and power law index. The results indicate that when the power law index was decreased, the circulation within the enclosure increased leading to a higher Nusselt number and these effects were enhanced as the Darcy number was increased. As the power law index was decreased, the boundary layer regime was shifted from a higher range of Darcy number to a lower range. An increase in Rayleigh number produced similar effects as a decrease in power law index.

Hadim, H.A.; Chen, G. [Stevens Inst. of Tech., Hoboken, NJ (United States). Dept. of Mechanical Engineering

1995-12-31

204

Power law scaling of topographic depressions and their hydrologic connectivity

NASA Astrophysics Data System (ADS)

Topographic depressions, areas of no lateral surface flow, are ubiquitous characteristics of the land surface that control many ecosystem and biogeochemical processes. High density of depressions increases the surface storage capacity, whereas lower depression density increases runoff, thus influencing soil moisture states, hydrologic connectivity, and the climate-soil-vegetation interactions. With the widespread availability of high-resolution lidar-based digital elevation model (lDEM) data, it is now possible to identify and characterize the structure of the spatial distribution of topographic depressions for incorporation in ecohydrologic and biogeochemical studies. Here we use lDEM data to document the prevalence and patterns of topographic depressions across five different landscapes in the United States and quantitatively characterize the probability distribution of attributes, such as surface area, storage volume, and the distance to the nearest neighbor. Through the use of a depression identification algorithm, we show that these probability distributions of attributes follow scaling laws indicative of a structure in which a large fraction of land surface areas can consist of high number of topographic depressions of all sizes and can account for 4 to 21 mm of depression storage. This implies that the impacts of small-scale topographic depressions in the landscapes on the redistribution of material fluxes, evaporation, and hydrologic connectivity are quite significant.

Le, Phong V. V.; Kumar, Praveen

2014-03-01

205

Stochastic Mixing Model with Power Law Decay of Variance

NASA Technical Reports Server (NTRS)

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.

Fedotov, S.; Ihme, M.; Pitsch, H.

2003-01-01

206

NASA Technical Reports Server (NTRS)

A characteristic feature of the Fourier Power Density Spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broad band-limited noise, characterized by a constant below some frequency (a "break" frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time to is related to the phenomenological break frequency, while the PDS power-law slope above the "break" is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black hole and neutron star) during an evolution of theses sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power P(sub x), decreases approximately as a square root of the characteristic frequency of the driving oscillations v(sub dr). The RXTE observations of Cyg X-1 allow us to infer P(sub dr), and t(sub o) as a function of v(sub dr). We also apply the basic parameters of observed PDSs, power-law index and low frequency quasiperiodic oscillations. to infer Reynolds (Re) number from the observations using the method developed in our previous paper. Our analysis shows that Re-number increases from values about 10 in low/hard state to that about 70 during the high/soft state. Subject headings: accretion, accretion disks-black hole physics-stars:individual (Cyg X-1) :radiation mechanisms: nonthermal-physical data and processes

Titarchuk, Lev; Shaposhinikov, Nikolai

2007-01-01

207

Origin of power-law composition dependence in ionic transport glasses

NASA Astrophysics Data System (ADS)

The origin of a power-law correlation between ionic conductivity and cation-contents, found commonly in oxide and chalcogenide glasses, is discussed using the concept of configuration entropy. It is suggested that power-law dependence is primarily attributed to an increase in configuration entropy with mixing cation components into glasses. This effect reduces the potential barrier height to be surmounted by mobile ions, which results in a higher diffusion coefficient (and hence conductivity). The origin of anomalous pre-exponential factors of diffusion coefficient and conductivity can be interpreted in terms of the present context.

Shimakawa, K.; Wagner, T.

2013-04-01

208

One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase

We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|{sup {beta}}, with {beta}>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 {beta} 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.

Dalmonte, M. [Dipartimento di Fisica dell'Universita di Bologna and INFN, via Irnerio 46, 40127 Bologna (Italy); IQOQI and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Pupillo, G. [IQOQI and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Zoller, P. [IQOQI and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125 (United States)

2010-10-01

209

Power Law Inflation and the Cosmic No Hair Theorem in Brane World

We study the cosmic no hair theorem for anisotropic Bianchi models that admit power law inflation with a scalar field in the framework of Brane world. The power law inflationary solution obtained here is driven by the curvature term in the modified field equation in Brane. It is found that all Bianchi models except Bianchi type IX, transit to an inflationary regime with vanishing anisotropy. We note that in the Brane world anisotropic universe isotropizes much faster than that in the general theory of relativity.

Paul, B. C. [Physics Department, North Bengal University, Siliguri, Pin: 734 013 (India); Beesham, A. [Department of Mathematical Sciences, Zululand University, Kwadlangezwa (South Africa)

2006-11-03

210

Power-law Behavior of High Energy String Scatterings in Compact Spaces

We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. We obtain infinite linear relations among high energy scattering amplitudes. For some kinematic regimes, we discover that some linear relations break down and, simultaneously, the amplitudes enhance to power-law behavior due to the space-time T-duality symmetry in the compact direction. This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out prevously. It is also reminiscent of hard (power-law) string scatterings in warped spacetime proposed by Polchinski and Strassler.

Jen-Chi Lee; Yi Yang

2007-09-28

211

FREQUENCY DEPENDENCE OF THE POWER-LAW INDEX OF SOLAR RADIO BURSTS

We process solar flare observations of Nobeyama Radio Polarimeters with an improved maximum likelihood method developed recently by Clauset et al. The method accurately extracts power-law behaviors of the peak fluxes in 486 radio bursts at six frequencies (1-35 GHz) and shows an excellent performance in this study. The power-law indices on 1-35 GHz given by this study vary around 1.74-1.87, which is consistent with earlier statistics in different solar cycles and very close to the simulations of the avalanche model by Lu.

Song Qiwu; Huang Guangli [Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China); Tan Baolin, E-mail: songqw@pmo.ac.cn, E-mail: glhuang@pmo.ac.cn, E-mail: bltan@bao.ac.cn [Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China)

2012-05-10

212

Evidence of microstructure evolution in solid elastic media based on a power law analysis

NASA Astrophysics Data System (ADS)

Complex and consolidated granular media or microcracked composites and metals usually exhibit a high level of nonlinearity in their elastic response already at low amplitudes of excitation. To quantify it, a proper nonlinear indicator y is introduced and its dependence on the excitation amplitude x is studied. The dependence of y on x is found in experiments to be a power law. Here we show that the different power law exponents measured for different materials could be predicted by proper classes of discrete models. An application is presented to link the exponent evolution and the changes of the microstructure due to the progression of damage mechanically induced.

Scalerandi, M.; Idjimarene, S.; Bentahar, M.; El Guerjouma, R.

2015-05-01

213

Gamma-rays from nebulae around binary systems containing energetic rotation-powered pulsars

NASA Astrophysics Data System (ADS)

We consider nebulae which are created around binary systems containing rotation-powered pulsars and companion stars with strong stellar winds. It is proposed that the stellar and pulsar winds have to mix at some distance from the binary system, defined by the orbital period of the companion stars and the velocity of the stellar wind. The mixed pulsar-stellar wind expands with a specific velocity determined by the pulsar power and the mass loss rate of the companion star. Relativistic particles, either from the inner pulsar magnetosphere and/or accelerated at the shocks between stellar and pulsar winds, are expected to be captured and isotropized in the reference frame of the mixed wind. Therefore, they can efficiently Comptonize stellar radiation producing GeV-TeV ?-rays in the inverse Compton process. We calculate the ?-ray spectra expected in such scenario for the two example binary systems: J1816+4510 which is the Redback-type millisecond binary and LS 5039 which is supposed to contain energetic pulsar. It is concluded that the steady TeV ?-ray emission from J1816+4510 should be on the 100 h sensitivity limit of the planned Cherenkov Telescope Array, provided that ? ˜ 10 per cent of the rotational energy lost by the pulsar is transferred to TeV electrons. On the other hand, the comparison of the predicted steady TeV ?-ray emission, expected from ?-ray binary LS 5039, with the observations of the TeV emission in a low state, reported by the High Energy Stereoscopic System Collaboration, allows us to put stringent upper limit on the product of the part of the hemisphere in which the mixed pulsar-stellar wind is confined, ?mix, and the energy conversion efficiency, ?, from the supposed pulsar to the TeV electrons injected in this system, ?mix ? < 1 per cent. This lower limit can be understood provided that either the acceleration efficiency of electrons is rather low (? ˜ 1 per cent), or the parameters of the stellar wind from the companion star are less extreme than expected, or the injection/acceleration process of electrons occurs highly anisotropically with the predominance towards the companion star.

Bednarek, W.; Sitarek, J.

2013-04-01

214

NASA Astrophysics Data System (ADS)

An alternate two layers theory, based on four new scalings for transitional wall roughness variables, is presented for large appropriate roughness Reynolds numbers. For velocity profile the matching of inner and outer layers in the overlap region, by Izakson-Millikan-Kolmogorov hypothesis (Afzal, N. 2005 Proc. Royal Society A: PME 461, 1889-1910) leads to functional solutions that are universal log laws, as well as universal power laws, that explicitly independent of transitional wall roughness, having same constants as in smooth wall case. The universal log or power laws velocity profile and skin friction, if expressed in terms of traditional Reynolds numbers also yield log law and power laws that depend on surface roughness. The skin friction, in traditional variables, is predicted by a single relation for inflectional type of Nikuradse roughness for sand grain type roughness data and Colebrook commercial monotonic roughness. The extensive experimental data for various types of wall transitional roughness provide very good support to present theory of universal log laws as well as new predictions in traditional log laws . The experimental data from various sources (Osaka and Mochizuki, Kameda et al, Antonia and Krogstad, Smalley et al, Schultz and Flack and Leonardi et al for boundary layers and Nikuradse, Shockling and Bakken for pipes/Channels) provide strong support to the new scaling for log and power laws. Moody type diagram for inflectional roughness for boundary layer and pipe flows are presented.

Afzal, Noor

2006-11-01

215

Inverse free steering law for small satellite attitude control and power tracking with VSCMGs

NASA Astrophysics Data System (ADS)

Recent developments in integrated power and attitude control systems (IPACSs) for small satellite, has opened a new dimension to more complex and demanding space missions. This paper presents a new inverse free steering approach for integrated power and attitude control systems using variable-speed single gimbal control moment gyroscope. The proposed inverse free steering law computes the VSCMG steering commands (gimbal rates and wheel accelerations) such that error signal (difference in command and output) in feedback loop is driven to zero. H? norm optimization approach is employed to synthesize the static matrix elements of steering law for a static state of VSCMG. Later these matrix elements are suitably made dynamic in order for the adaptation. In order to improve the performance of proposed steering law while passing through a singular state of CMG cluster (no torque output), the matrix element of steering law is suitably modified. Therefore, this steering law is capable of escaping internal singularities and using the full momentum capacity of CMG cluster. Finally, two numerical examples for a satellite in a low earth orbit are simulated to test the proposed steering law.

Malik, M. S. I.; Asghar, Sajjad

2014-01-01

216

Dynamical Explanation for the Emergence of Power Law in a Stock Market Model

data regarding the performance of the stock in order to estimate the future stock performance. EachDynamical Explanation for the Emergence of Power Law in a Stock Market Model by Moshe Levy regime of a previously introduced dynamical microscopic model of the stock market. We nd scaling

217

A Power Law for the Lowest Eigenvalue in Localized Massive Gravity

This short note contains a detailed analysis to find the right power law the lowest eigenvalue of a localized massive graviton bound state in a four dimensional AdS background has to satisfy. In contrast to a linear dependence of the cosmological constant we find a quadratic one [hep-th\\/0011156].

André Miemiec

2001-01-01

218

A power law for the lowest eigenvalue in localized massive gravity

This short note contains a detailed analysis to find the right power law the lowest eigenvalue of a localized massive graviton bound state in a four dimensional AdS background has to satisfy. In contrast to a linear dependence of the cosmological constant we find a quadratic one [hep-th/0011156].

Andre Miemiec

2000-11-17

219

Power-law cosmic expansion in f(R) gravity models

We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for 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.

Goheer, Naureen; Larena, Julien [Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, Cape Town (South Africa); Dunsby, Peter K. S. [Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, Cape Town (South Africa); South African Astronomical Observatory, Observatory 7925, Cape Town (South Africa)

2009-09-15

220

Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?

ERIC Educational Resources Information Center

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…

Bauer, Ben

2009-01-01

221

Power-law cosmic expansion in f(R) gravity models

We show that within the class of f(R) gravity theories, FLRW power-law perfect fluid solutions only exist for R^n gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard General Relativity.

Naureen Goheer; Julien Larena; Peter K. S. Dunsby

2009-06-21

222

Kobe University Law Department Workshop Is Japan a Viable Hard Power in the Academe?

Kobe University Law Department Workshop Is Japan a Viable Hard Power in the Academe? Following up of Japanese Studies in North America, it became quite evident that the state of Japanese studies was in midst majorities of new generation of scholars of East Asia were now shifting their academic focus towards China

Banbara, Mutsunori

223

On the distributions of seasonal river flows: Lognormal or power law?

NASA Astrophysics Data System (ADS)

Distributional analysis of river discharge time series is an important task in many areas of hydrological engineering, including optimal design of water storage and drainage networks, management of extreme events, risk assessment for water supply, and environmental flow management, among many others. Having diverging moments, heavy-tailed power law distributions have attracted widespread attention, especially for the modeling of the likelihood of extreme events such as floods and droughts. However, straightforward distributional analysis does not connect well with the complicated dynamics of river flows, including fractal and multifractal behavior, chaos-like dynamics, and seasonality. To better reflect river flow dynamics, we propose to carry out distributional analysis of river flow time series according to three "flow seasons": dry, wet, and transitional. We present a concrete statistical procedure to partition river flow data into three such seasons and fit data in these seasons using two types of distributions, power law and lognormal. The latter distribution is a salient property of the cascade multiplicative multifractal model, which is among the best models for turbulence and rainfall. We show that while both power law and lognormal distributions are relevant to dry seasons, river flow data in wet seasons are typically better fitted by lognormal distributions than by power law distributions.

Bowers, M. C.; Tung, W. W.; Gao, J. B.

2012-05-01

224

The horizontal dam break problem for slow non-Newtonian power-law fluids

The horizontal dam break problem for slow non-Newtonian power-law fluids P. Saramito a C. Smutek bLaboratoire gÂ´eosciences Â IPGP et universitÂ´e de La RÂ´eunion, France Abstract Â The dam break problem shallow for the horizontal dam break problem. Keywords Â viscoplastic fluid; dam break problem; shallow flows. 1

225

The Pareto, Zipf and other power laws. William J. Reed1

for which power-law behaviour has been claimed include those of sand particle sizes; of meteor impacts on the moon; of numbers of species per genus in flowering plants; of frequencies of words in long sequences a varying, but size independent proportional growth rate, which mathematically can be modelled by geometric

Reed, W.J.

226

This paper presents a unified treatment of cloud particle fall velocities for both liquid and crystalline cloud particles over the entire size range observed in the atmosphere. The fall velocity representation is formulated in terms of the Best (or Davies) number X, and the Reynolds number Re. For the power-law representations used in many applications, the coefficients are found as

Vitaly I. Khvorostyanov; Judith A. Curry

2002-01-01

227

NASA Astrophysics Data System (ADS)

In a recent publication [Phys. Rev. E 63, 047201 (2001)], Ausloos and Ivanova report power-law probability distributions, fractal properties, and antipersistent long-range correlations in the southern oscillation index. As a comparison with artificial short-range correlated data shows, most of these findings are possibly due to misleading interpretation of the analysis techniques used.

Metzler, Richard

2003-01-01

228

Frequency variations of solar radio zebras and their power-law spectra

NASA Astrophysics Data System (ADS)

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 ?pe is much higher than the electron-cyclotron frequency ?ce, the Fourier power spectra are interpreted to be those of the electron plasma density in zebra radio sources.

Karlický, M.

2014-01-01

229

The Extended Power Law as Intrinsic Signature For a Black Hole

We analyze the exact general relativistic exact integro-differential equation of radiative transfer describing the interaction of low energy photons with a Maxwellian distribution of hot electrons in gravitational field of a Schwarzschild black hole. We prove that due to Comptonization an initial arbitrary spectrum of low energy photons unavoidably results in spectra characterized by an extended power-law feature. We examine the spectral index by using both analytical and numerical methods for a variety of physical parameters as such the plasma temperature and the mass accretion rate. The presence of the event horizon as well as the behaviour of the null geodesics in its vicinity largely determine the dependence of the spectral index on the flow parameters. We come to the conclusion that the bulk motion of a converging flow is more efficient in upscattering photons than thermal Comptonization provided that the electron temperature in the flow is of order of a few keV or less. In this case, the spectrum observed at infinity consists of a soft component produced by those input photons that escape after a few scatterings without any significant energy change and of hard component (described by a power law) produced by the photons that underwent significant upscattering. The luminosity of the power-law component is relatively small compared to that of the soft component. For accretion into black hole the spectral energy index of the power-law is always higher than one for plasma temperature of order of a few keV. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black-hole X-ray sources.

Lev Titarchuk; Thomas Zannias

1997-08-27

230

Summary 1. Ecologists are obtaining ever-increasing amounts of data concerning animal movement. A movement strategy that has been concluded for a broad variety of animals is that of Lévy flights, which are random walks whose step lengths come from probability distributions with heavy power-law tails. 2. The exponent that parameterizes the power-law tail, denoted ? , has repeatedly been found

Andrew M. Edwards

2008-01-01

231

Disorder and Power-law Tails of DNA Sequence Self-Alignment Concentrations in Molecular Evolution

Self-alignment concentrations, $c(x)$, as functions of the length $x$ of the identically matching maximal segments in the genomes of a variety of species, present typically power-law tails extending to the largest scales, $c(x) \\propto x^{\\alpha}$, with similar or different negative $\\alpha$s ($<-2$ as observed so far). The relevant fundamental processes of molecular evolution are segmental duplication and point mutation, and that the stick fragmentation phenomenology has been used to account the neutral evolution [F. Massip and P. Arndt, Phys. Rev. Lett., {\\bf 110} 148101 (2012)]. Disorder is intrinsic and, applying quenching, we systematically show with decaying, steady-state and the general full time-dependent solutions that disorders in the configurations of a simple fragmentation system facilitate the various power-law tails. The full time-dependent solution show the possibility of distinct power law(s) at intermediate scales, which seems to be confirmed by some species, such as rice.

Gao, Kun; Zhu, Jian-Zhou

2014-01-01

232

Strain-rate Dependence of Power-law Creep and Folding of Rocks

NASA Astrophysics Data System (ADS)

Kocks (1987) proposed how the kinetics of deformation associated with different stress levels results in different shear stress-shear strain rate behaviours, with a cross-over or threshold from thermally activated dislocation motion at low stresses to viscous glide at some critical shear stress. Cordier (pers. comm.; Carrez et al., 2010) clarified this transition at least for MgO through atomistic, single dislocation and Dislocation Dynamics calculations. These studies indicate that the power-law relations observed experimentally for deforming rocks may be different for geological strain-rates, in that rate laws may become relatively strain-rate insensitive at low strain-rates. This transition from power law behaviour with relatively small values of the stress exponent, N, (N = 1 to 5) to large values of N (N = 5 to 20) has important implications for the development of localised behaviour during deformation as has been demonstrated at the other end of the spectrum for high stresses by Schmalholz and Fletcher (2011). Since localisation of fold systems arises from softening of the tangential viscosity, large values of N mean that little softening occurs with changes in strain rate, and sinusoidal folds are expected. There is therefore a critical range of N-values where localised, natural looking, folds develop. We explore the implications for folding of linear viscous single layers embedded in power-law viscous materials with N that varies with the stress level. The strain-rate dependence of the power law parameters results in strongly localised, aperiodic folding as opposed to the fold styles that arise from the linear Biot theory of folding. Also developed are axial plane shear fabrics. These structures resemble natural ones more than those that arise from simple Newtonian viscous or power-law behaviour with constant N. The results show that new studies of folded rocks and associated axial plane structures in the field may give important information on the transition from thermally activated dislocation motion to viscous glide. References. Amodeo, J., Carrez, Ph., Devincre, B., & Cordier, P. 2011. Multiscale modelling of MgO plasticity. Acta Materialia, 59, 2291-2301. Kocks, U. F. 1987. Constitutive behavior based on crystal plasticity. In: Unified Constitutive Equations for Creep and Plasticity. Ed. by A. K. Miller, Elsevier, pp. 1-88. Schmalholz, S. M., & Fletcher, R. C. 2011. The exponential flow law applied to necking and folding of a ductile layer. Geophys. J. Int., 184, 83-89.

Ord, A.; Hobbs, B. E.

2011-12-01

233

Second-order small-disturbance solutions for hypersonic flow over power-law bodies

NASA Technical Reports Server (NTRS)

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.

Townsend, J. C.

1975-01-01

234

High-index asymptotics of spherical Bessel products averaged with modulated Gaussian power laws

NASA Astrophysics Data System (ADS)

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.

Tomaschitz, Roman

2014-12-01

235

A generalized power-law detection algorithm for humpback whale vocalizations.

Conventional detection of humpback vocalizations is often based on frequency summation of band-limited spectrograms under the assumption that energy (square of the Fourier amplitude) is the appropriate metric. Power-law detectors allow for a higher power of the Fourier amplitude, appropriate when the signal occupies a limited but unknown subset of these frequencies. Shipping noise is non-stationary and colored and problematic for many marine mammal detection algorithms. Modifications to the standard power-law form are introduced to minimize the effects of this noise. These same modifications also allow for a fixed detection threshold, applicable to broadly varying ocean acoustic environments. The detection algorithm is general enough to detect all types of humpback vocalizations. Tests presented in this paper show this algorithm matches human detection performance with an acceptably small probability of false alarms (P(FA) < 6%) for even the noisiest environments. The detector outperforms energy detection techniques, providing a probability of detection P(D) = 95% for P(FA) < 5% for three acoustic deployments, compared to P(FA) > 40% for two energy-based techniques. The generalized power-law detector also can be used for basic parameter estimation and can be adapted for other types of transient sounds. PMID:22501048

Helble, Tyler A; Ierley, Glenn R; D'Spain, Gerald L; Roch, Marie A; Hildebrand, John A

2012-04-01

236

Pacific Northwest Electric Power Planning and Conservation Act, with Index (Public Law 96-501).

The Pacific Northwest Electric Power Planning and Conservation Act was enacted by the Senate and House of Representatives of the United States of America. It was enacted to assist the electrical consumers of the Pacific Northwest through use of the Federal columbia River Power System to achieve cost-effective energy conservation, to encourage the development of renewable energy resources, to establish a representative regional power planning process, to assure the region of an efficient and adequate power supply, and for other purposes. Contents of the Act are: short title and table of contents; purposes; definitions; regional planning and participation; sale of power; conservation and resource acquisition; rates; amendments to existing law; administrative provisions; savings provisions; effective date; and severability.

Not Available

1991-12-01

237

Fractionally integrated process with power-law correlations in variables and magnitudes

NASA Astrophysics Data System (ADS)

Motivated by the fact that many empirical time series—including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values—exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two parameters, where one controls the correlations in the variables and the other controls the correlations in their magnitudes. We apply the process to time series of heartbeat interval changes and air temperature changes and find that the statistical properties of the modeled time series are in agreement with those observed in the data.

Podobnik, Boris; Ivanov, Plamen Ch.; Biljakovic, Katica; Horvatic, Davor; Stanley, H. Eugene; Grosse, Ivo

2005-08-01

238

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 ? ? B(2)/(4?nm(e)c(2))>1 and when the system size is sufficiently large. In the limit ? ? 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. PMID:25375716

Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin

2014-10-10

239

Power-law solutions and accelerated expansion in scalar-tensor theories

We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and the deceleration parameter in the Jordan frame may be different from the signs of their Einstein-frame counterparts. For special parameter combinations we identify these solutions with asymptotic attractors that have been obtained in the literature through dynamical-system analysis. We establish an effective general-relativistic description for which the geometrical equivalent of dark energy is associated with a time dependent equation of state. The present value of the latter is consistent with the observed cosmological 'constant'. We demonstrate that this type of power-law solution for accelerated expansion cannot be realized in f(R) theories.

Batista, C. E. M.; Zimdahl, W. [Universidade Federal do Espirito Santo, Departamento de Fisica, Av. Fernando Ferrari, 514, Campus de Goiabeiras, CEP 29075-910, Vitoria, Espirito Santo (Brazil)

2010-07-15

240

Finite sample properties of power-law cross-correlations estimators

NASA Astrophysics Data System (ADS)

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.

Kristoufek, Ladislav

2015-02-01

241

Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow

NASA Astrophysics Data System (ADS)

Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.

Matsubara, Yoshitsugu; Hieida, Yasuhiro; Tadaki, Shin-ichi

2013-09-01

242

The relationship between randomness and power-law distributed move lengths in random walk algorithms

NASA Astrophysics Data System (ADS)

Recently, we proposed a new random walk algorithm, termed the REV algorithm, in which the agent alters the directional rule that governs it using the most recent four random numbers. Here, we examined how a non-bounded number, i.e., "randomness" regarding move direction, was important for optimal searching and power-law distributed step lengths in rule change. We proposed two algorithms: the REV and REV-bounded algorithms. In the REV algorithm, one of the four random numbers used to change the rule is non-bounded. In contrast, all four random numbers in the REV-bounded algorithm are bounded. We showed that the REV algorithm exhibited more consistent power-law distributed step lengths and flexible searching behavior.

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2014-05-01

243

Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.

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. PMID:24433745

Holm, Sverre; Näsholm, Sven Peter

2014-04-01

244

Gelled propellant flow: Boundary layer theory for power-law fluids in a converging planar channel

A boundary layer theory for the flow of power-law fluids in a converging planar channel has been developed. This theory suggests a Reynolds number for such flows, and following numerical integration, a boundary layer thickness. This boundary layer thickness has been used in the generation of a finite element mesh for the finite element code FIDAP. FIDAP was then used to simulate the flow of power-law fluids through a converging channel. Comparison of the analytic and finite element results shows the two to be in very good agreement in regions where entrance and exit effects (not considered in the boundary layer theory) can be neglected. 6 refs., 8 figs., 1 tab.

Kraynik, A.M.; Geller, A.S.; Glick, J.H.

1989-10-01

245

Laboratory constraints on chameleon dark energy and power-law fields.

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. PMID:21231645

Steffen, J H; Upadhye, A; Baumbaugh, A; Chou, A S; Mazur, P O; Tomlin, R; Weltman, A; Wester, W

2010-12-31

246

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Mirels, Harold

1959-01-01

247

Dark optical solitons of Biswas-Milovic equation with dual-power law nonlinearity

NASA Astrophysics Data System (ADS)

This paper studies the Biswas-Milovic equation, which is a generalized version of the nonlinear Schrödinger equation, with dual-power law nonlinearity. The G'/ G-expansion method is employed to extract the dark 1-soliton solution from the equation. The results have a similar setting to the ones obtained earlier by the ansatz approach. Both constant and time-dependent coefficients are taken into consideration.

Mirzazadeh, M.; Eslami, M.; Arnous, Ahmed Hassan

2015-01-01

248

Shell structures in single-particle energy spectra are investigated against regular tetrahedral type deformation using radial power-law potential model. Employing a natural way of shape parametrization which interpolates sphere and regular tetrahedron, we find prominent shell effects at rather large tetrahedral deformations, which bring about shell energies much larger than the cases of spherical and quadrupole type shapes. We discuss the semiclassical origin of these anomalous shell structures using periodic orbit theory.

Ken-ichiro Arita; Yasunori Mukumoto

2014-05-09

249

Power-law and exponential tails in a stochastic priority-based model queue

NASA Astrophysics Data System (ADS)

We derive exact asymptotic results for a stochastic queueing model in which tasks are executed according to a continuous-valued priority. The distribution P(?) of the waiting times ? of executed tasks for this model is shown to behave asymptotically as a power law, P(?)˜?-3/2 , when the average rates of task arrival ? and execution ? satisfy ??? (as was earlier noted empirically). For ?>? , P(?)˜?-5/2exp[-(?-?)2?] .

Grinstein, G.; Linsker, R.

2008-01-01

250

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

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.

Howell, L. W., Jr.

2003-01-01

251

Two-phase power-law modeling of pipe flows displaying shear-thinning phenomena

This paper describes work in modeling concentrated liquid-solids flows in pipes. COMMIX-M, a three-dimensional transient and steady-state computer program developed at Argonne National Laboratory, was used to compute velocities and concentrations. Based on the authors' previous analyses, some concentrated liquid-solids suspension flows display shear-thinning rather than Newtonian phenomena. Therefore, they developed a two-phase non-Newtonian power-law model that includes the effect

Jianmin Ding; R. W. Lyczkowski; W. T. Sha

1993-01-01

252

NASA Astrophysics Data System (ADS)

In this paper a technique has been developed to determine constant parameters of copper as a power-law hardening material by tensile test approach. A work-hardening process is used to describe the increase of the stress level necessary to continue plastic deformation. A computer program is used to show the variation of the stress-strain relation for different values of stress hardening exponent, n and power-law hardening constant, ? . Due to its close tolerances, excellent corrosion resistance and high material strength, in this analysis copper (Cu) has been selected as the material. As a power-law hardening material, Cu has been used to compute stress hardening exponent, n and power-law hardening constant, ? from tensile test experiment without heat treatment and after heat treatment. A wealth of information about mechanical behavior of a material can be determined by conducting a simple tensile test in which a cylindrical specimen of a uniform cross-section is pulled until it ruptures or fractures into separate pieces. The original cross sectional area and gauge length are measured prior to conducting the test and the applied load and gauge deformation are continuously measured throughout the test. Based on the initial geometry of the sample, the engineering stress-strain behavior (stress-strain curve) can be easily generated from which numerous mechanical properties, such as the yield strength and elastic modulus, can be determined. A universal testing machine is utilized to apply the load in a continuously increasing (ramp) manner according to ASTM specifications. Finally, theoretical results are compared with these obtained from experiments where the nature of curves is found similar to each other. It is observed that there is a significant change of the value of n obtained with and without heat treatment it means the value of n should be determined for the heat treated condition of copper material for their applications in engineering fields.

Kowser, Md. A.; Mahiuddin, Md.

2014-11-01

253

Power-law cosmological solution derived from DGP brane with a brane tachyon field

By studying a tachyon field on the DGP brane model, in order to embed the 4D standard Friedmann equation with a brane tachyon field in 5D bulk, the metric of the 5D spacetime is presented. Then, adopting the inverse square potential of tachyon field, we obtain an expanding universe with power-law on the brane and an exact 5D solution.

Yongli Ping; Lixin Xu; Hongya Liu; Ying Shao

2008-01-01

254

Multiple short time power laws in the orientational relaxation of nematic liquid crystals.

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. PMID:17115789

Jose, Prasanth P; Bagchi, Biman

2006-11-14

255

Asymptotic crack-tip fields for dynamic crack growth in compressive power-law hardening materials

The effect of material compressibility on the stress and strain fields for a mode-I crack propagating steadily in a power-law hardening material is investigated under plane strain conditions. The plastic deformation of materials is characterized by the J2 flow theory within the framework of isotropic hardening and infinitesimal displacement gradient. The asymptotic solutions developed by the present authors [Zhu, X.K.,

Xian-Kui Zhu; Keh-Chih Hwang

2008-01-01

256

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. PMID:21133374

Caduff, Marloes; Huijbregts, Mark A J; Althaus, Hans-Joerg; Hendriks, A Jan

2011-01-15

257

Spin glassiness and power law scaling in anisotropic triangular spin-1/2 antiferromagnets

NASA Astrophysics Data System (ADS)

We discuss the magnetic properties of a class of spin S=1/2 antiferromagnetic quasi-triangular lattice materials, both in the clean limit and in the presence of non-magnetic Zn impurities. These systems are long organic chain intercalated derivatives of copper hydroxy nitrate, with a very large c-axis separation of 24å. In these compounds, we find that a spin glass phase is universally preceded by two different power law regimes in the temperature dependence of the DC magnetic susceptibility, separated by a sharp crossover. This is seen both in the presence as well as in the absence of non-magnetic Zn impurities, where the power law exponents are surprisingly unperturbed by the compositional disorder. We argue that these findings may be consistent with a picture based on a self-generated spin glass in the clean undoped compound, where frustration is the driving mechanism of the glassiness rather than disorder. While AC measurements and time dependent magnetization follow traditional spin glass paradigms, the power law structure found in the DC susceptibility is argued to deviate in various ways from scenarios expected based on Griffiths type physics, and may call for new explanations. [1] J. Wu et al., J. Phys. Condens. Matter, 22, 334211 (2010). [2] J. Wu et al., arXiv:1007.0442

Seidel, Alexander; Wu, Jian; Wildeboer, Julia S.; Werner, Fletcher; Nussinov, Zohar; Solin, S. A.

2011-03-01

258

Effects of diversity and procrastination in priority queuing theory: The different power law regimes

NASA Astrophysics Data System (ADS)

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/t? with 0power 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/t? , with ??(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.

Saichev, A.; Sornette, D.

2010-01-01

259

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile.

The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor. PMID:21682374

O'Boy, Daniel J; Bowyer, Elizabeth P; Krylov, Victor V

2011-06-01

260

Evidence for intermittency and a truncated power law from highly resolved aphid movement data

Power laws are increasingly used to describe animal movement. Despite this, the use of power laws has been criticized on both empirical and theoretical grounds, and alternative models based on extensions of conventional random walk theory (Brownian motion) have been suggested. In this paper, we analyse a large volume of data of aphid walking behaviour (65 068 data points), which provides a highly resolved dataset to investigate the pattern of movement. We show that aphid movement is intermittent—with alternations of a slow movement with frequent change of direction and a fast, relatively directed movement—and that the fast movement consists of two phases—a strongly directed phase that gradually changes into an uncorrelated random walk. By measuring the mean-squared displacement and the duration of non-stop movement episodes we found that both spatial and temporal aspects of aphid movement are best described using a truncated power law approach. We suggest that the observed spatial pattern arises from the duration of non-stop movement phases rather than from correlations in turning angles. We discuss the implications of these findings for interpreting movement data, such as distinguishing between movement and non-movement, and the effect of the range of data used in the analysis on the conclusions. PMID:19474077

Mashanova, Alla; Oliver, Tom H.; Jansen, Vincent A. A.

2010-01-01

261

Power-law behavior in complex organizational communication networks during crisis

NASA Astrophysics Data System (ADS)

Communication networks can be described as patterns of contacts which are created due to the flow of messages and information shared among participating actors. Contemporary organizations are now commonly viewed as dynamic systems of adaptation and evolution containing several parts, which interact with one another both in internal and in external environment. Although there is limited consensus among researchers on the precise definition of organizational crisis, there is evidence of shared meaning: crisis produces individual crisis, crisis can be associated with positive or negative conditions, crises can be situations having been precipitated quickly or suddenly or situations that have developed over time and are predictable etc. In this research, we study the power-law behavior of an organizational email communication network during crisis from complexity perspective. Power law simply describes that, the probability that a randomly selected node has k links (i.e. degree k) follows P(k)?k, where ? is the degree exponent. We used social network analysis tools and techniques to analyze the email communication dataset. We tested two propositions: (1) as organization goes through crisis, a few actors, who are prominent or more active, will become central, and (2) the daily communication network as well as the actors in the communication network exhibit power-law behavior. Our preliminary results support these two propositions. The outcome of this study may provide significant advancement in exploring organizational communication network behavior during crisis.

Uddin, Shahadat; Murshed, Shahriar Tanvir Hasan; Hossain, Liaquat

2011-08-01

262

Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.

EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field. PMID:23229874

Zhao, Cunlu; Yang, Chun

2013-03-01

263

Chaotic inflation with a fractional power-law potential in strongly coupled gauge theories

NASA Astrophysics Data System (ADS)

Models of chaotic inflation with a fractional power-law potential are not only viable but also testable in the foreseeable future. We show that such models can be realized in simple strongly coupled supersymmetric gauge theories. In these models, the energy scale during inflation is dynamically generated by the dimensional transmutation due to the strong gauge dynamics. Therefore, such models not only explain the origin of the fractional power in the inflationary potential but also provide a reason why the energy scale of inflation is much smaller than the Planck scale.

Harigaya, Keisuke; Ibe, Masahiro; Schmitz, Kai; Yanagida, Tsutomu T.

2013-03-01

264

A power law distribution in patients’ lengths of stay in hospital

NASA Astrophysics Data System (ADS)

The distribution of patients’ lengths of stay in English hospitals is measured by using routinely collected data from 11 years. It is found to be well approximated by a power law distribution spanning over more than three decades. To explain this observation, a theoretical resource allocation model is presented. It is based on iterative long-term scheduling of hospital beds, and its main assumption is that future beds are allocated preferentially. This represents a situation where different parts of the health care system compete for resources, with bargaining powers proportional to current resource levels.

Hellervik, A.; Rodgers, G. J.

2007-06-01

265

Length of inflation and WMAP data in the case of power-law inflation

The effect of the length of inflation on the power spectra of scalar and tensor perturbations is estimated using the power-law inflation model with a scale factor of a(t) = t^q. Considering various pre-inflation models with radiation-dominated or matter-dominated periods before inflation in combination with two matching conditions, the power spectrum of curvature perturbations at large scales is calculated. Comparison of the derived angular power spectrum with the Wilkinson Microwave Anisotropy Probe (WMAP) data reveals a possibility that the WMAP can be explained by the finite length of inflation model if the length of inflation is near 60 e-folds and q>200.

Shiro Hirai; Tomoyuki Takami

2005-06-21

266

NASA Astrophysics Data System (ADS)

A large body of evidence within the research literature indicates that mass movements follow a negative power law scaling in their magnitude-frequency distributions over several orders of magnitude. Questions remain as to: (1) Whether this relationship holds for the entire range of the magnitude-frequency distribution. The existence of a rollover in the distribution for smaller events has been the topic of much discussion in the research literature with authors regarding it is a geophysical property of mass movements or as caused by data censoring of smaller magnitude events. (2) The effect that different geological and environmental boundary conditions have on constraining the power law. This research makes use of an ongoing sea cliff monitoring project at Boulby, UK to answer these questions. Monthly surveys using terrestrial laser scanning (TLS) over a period of 7 yrs provides one of the most comprehensive datasets for rock fall in existence. Here we demonstrate that the negative power law scaling holds over six orders of magnitude from 0.01m3 up to 1000 m3 with a characteristic rollover in the distribution for smaller failures. The rollover for the Boulby dataset occurs for rock falls that are three orders of magnitude smaller than other mass movements reported in the research literature and supports the view that it is the result of data censoring rather than a geophysical property inherent to mass movements. Furthermore, we can conclude that our TLS method has a resolution that allows the identification of events from as small as 0.01 m3 to those involving the entire cliff face. Previous research demonstrates that the scaling parameter associated with the slope of the negative power law varies considerably according to regional differences in geology, morphology, hydrology, and climate. At Boulby, the cliffs are composed of horizontally interbedded shales, sandstones, and carbonates allowing for detailed investigation into the geological controls on rock fall occurrence under a wide range of environmental conditions. Stratifying the data in this way gives insight into the constraining influence that these factors have on the magnitude-frequency of rock falls in the area. For example, our results indicate that a decrease in the strength of a rock mass has the effect of steepening the magnitude frequency relation when plotted on logarithmic axes. To date, no project has quantified the geological and environmental constraints on the negative power law scaling of mass movements in this way. Such data will be useful for models of landscape evolution and as a management tool for coastal erosion defences.

Barlow, J.; Rosser, N.; Petley, D. N.

2009-12-01

267

DOUBLE POWER-LAW DISTRIBUTION OF MAGNETIC ENERGY IN THE SOLAR CORONA OVER AN ACTIVE REGION

In this paper, we study the magnetic energy (ME) structure contained in the solar corona over the active region NOAA 11158. The time period is chosen as from 0:00 to 06:00 UT on 2011 February 15, during which an X-class flare occurred. The nonlinear force-free field (NLFFF) and the potential field extrapolation are carried out to model the coronal magnetic field over this active region, using high-quality photospheric vector magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory as boundary conditions. We find that the volume distribution for the density of the ME (B {sup 2}/8{pi}) and the ohmic dissipation power (ODP, j {sup 2}/{sigma}), in which j is the electric current density (c/4{pi}{nabla} Multiplication-Sign B) and {sigma} is the conductivity in the corona, can be readily fitted by a broken-down double-power law. The turn-over density for the spectrum of the ME and ODP is found to be fixed at {approx}1.0 Multiplication-Sign 10{sup 4} erg cm{sup -3} and {approx}2.0 Multiplication-Sign 10{sup -15} W cm{sup -3} (assuming {sigma} = 10{sup 5} {Omega}{sup -1} m{sup -1}), respectively. Compared with their first power-law spectra (fitted below the corresponding turn-over value) which remain unchanged, the second power-law spectra (fitted above the corresponding turn-over value) for the NLFFF's ME and ODP show flare-associated changes. The potential field remains steady. These results indicate that a magnetic field with energy density larger than the turn-over energy density plays a dominant role in powering the flare.

Shen, Jinhua; Ji, Haisheng [Purple Mountain Observatory, 2 West Beijing Road, Nanjing 210008 (China)] [Purple Mountain Observatory, 2 West Beijing Road, Nanjing 210008 (China); Wiegelmann, Thomas; Inhester, Bernd [Max-Planck-Institut fuer sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau (Germany)] [Max-Planck-Institut fuer sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau (Germany)

2013-02-10

268

Swinging between rotation and accretion power in a binary millisecond pulsar

NASA Astrophysics Data System (ADS)

We present the discovery of IGR J18245-2452, the first millisecond pulsar observed to swing between a rotation-powered, radio pulsar state, and an accretion-powered X-ray pulsar state [31]. This transitional source represents the most convincing proof of the evolutionary link shared by accreting neutron stars in low mass X-ray binaries, and radio millisecond pulsars. It demonstrates that swings between these two states take place on the same time-scales of luminosity variations of X-ray transients, and are therefore most easily interpreted in terms of changes in the rate of mass in-flow. While accreting mass, the X-ray emission of IGR J18245-2452 varies dramatically on time-scales ranging from a second to a few hours. We interpret a state characterised by a lower flux and pulsed fraction, and by sudden increases of the hardness of the X-ray emission, in terms of the onset of a magnetospheric centrifugal inhibition of the accretion flow. Prospects of finding new members of the newly established class of transitional pulsars are also briefly discussed.

Papitto, A.; Ferrigno, C.; Bozzo, E.; Rea, N.

2014-01-01

269

System level. First, we show that the topology can be described eÃ?ciently with power-laws. The elegancePower-Laws and the AS-level Internet Topology Georgos Siganos,Michalis Faloutsos,Petros Faloutsos that the power-laws hold even in the most recent and more complete topology [10] with correlation coeÃ?cient above

270

composed by large hydro and thermoelectric power plants, mainly coal fired and natural gas. SING is a 100, the population is becoming progressively more aware of the impact of large hydro power plants and fossil fuelAbstract- The Chilean Electricity Law introduced an obligation to power traders, from 2010 to 2014

Catholic University of Chile (Universidad CatÃ³lica de Chile)

271

Fertility Heterogeneity as a Mechanism for Power Law Distributions of Recurrence Times

We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future events. Specifically, we analyze the impact of the power law distribution of fertilities with exponent \\alpha, where the fertility of an event is the number of aftershocks of first generation that it triggers, on the probability distribution function (pdf) f(\\tau) of the recurrence times \\tau between successive events. The other input of the model is an exponential Omori law quantifying the pdf of waiting times between an event and its first generation aftershocks, whose characteristic time scale is taken as our time unit. At short time scales, we discover two intermediate power law asymptotics, f(\\tau) ~ \\tau^{-(2-\\alpha)} for \\tau << \\tau_c and f(\\tau) ~ \\tau^{-\\alpha} for \\tau_c << \\tau << 1, where \\tau_c is associated with the self-excited cascades of aft...

Saichev, A

2012-01-01

272

All Bright Cold Classical KBOs are Binary

NASA Astrophysics Data System (ADS)

When sorted by absolute magnitude as seen in ground based observations, an extremely high fraction of the brightest Cold Classical (CC) Kuiper Belt objects (KBO) are, in fact resolved as binaries when observed at higher angular resolution. Of the 22 CCs brighter than H=6.1 observed by HST, 16 have been found to be binary yielding a binary fraction of 73±10%. When low inclination interlopers from the hot population and close binaries are considered, this very high fraction is consistent with 100% of bright CCs being binary. At fainter absolute magnitudes, this fraction drops to ~20%. Such a situation is a natural outcome of a broken size distribution with a steep drop-off in the number of CCs with individual component diameters larger than 150 km (for an assumed albedo of 0.15). A sharp cutoff in the size distribution for CCs is consistent with formation models that suggest that most planetesimals form at a preferred modal size of order 100 km.The very high fraction of binaries among the largest CCs also serves to limit the separation distribution of KBO binaries. At most, 27% of the brightest CCs are possible unresolved binaries. The apparent power law distribution of binary separation must cut off near the current observational limits of HST ( 1800 km at 43 AU). It is worth noting, however, that this observation does not constrain how many components of resolved binaries may themselves be unresolved multiples like 47171 1999 TC36. Finally, it is important to point out that, when sorted by the size of the primary rather than absolute magnitude of the unresolved pair, the fraction of binaries is relatively constant with size (Nesvorny et al. 2011, AJ 141, 159) eliminating observational bias as cause of the pile up of binaries among the brightest Cold Classical Kuiper Belt objects.The very high fraction of binaries among the brightest CCs appears to be an effect of the underlying CC size distribution.

Noll, Keith S.; Parker, Alex H.; Grundy, William M.

2014-11-01

273

An Improved Catalog of Halo Wide Binary Candidates

NASA Astrophysics Data System (ADS)

We present an improved catalog of halo wide binaries compiled from an extensive literature search. Most of our binaries stem from the common proper motion binary catalogs by Allen et al. and Chanamé & Gould, but we have also included binaries from the lists of Ryan and Zapatero-Osorio & Martín. All binaries were carefully checked and their distances and systemic radial velocities are included when available. Probable membership to the halo population was tested by means of reduced proper motion diagrams for 251 candidate halo binaries. After eliminating obvious disk binaries, we ended up with 211 probable halo binaries, 150 of which have radial velocities available. We compute galactic orbits for these 150 binaries and calculate the time they spend within the galactic disk. Considering the full sample of 251 candidate halo binaries as well as several subsamples, we find that the distribution of angular separations (or expected major semiaxes) follows a power law f(a) ~ a -1 (Oepik's relation) up to different limits. For the 50 most disk-like binaries, those that spend their entire lives within z = ±500 pc, this limit is found to be 19,000 AU (0.09 pc), while for the 50 most halo-like binaries, those that spend on average only 18% of their lives within z = ±500 pc, the limit is 63,000 AU (0.31 pc). In a companion paper, we employ this catalog to establish limits on the masses of the halo massive perturbers (massive compact halo objects).

Allen, Christine; Monroy-Rodríguez, Miguel A.

2014-08-01

274

Police compliance with the law is one of the most important aspects of a democratic society. Americans expect the police to enforce laws to promote safety and to reduce crime, victimization, and fear, but no one believes that the police should have unlimited power to do so. We expect police to enforce laws fairly according to law and rules that

Wesley G. Skogan; Tracey L. Meares

2004-01-01

275

Power-law entropy-corrected new holographic dark energy in Horava-Lifshitz cosmology

NASA Astrophysics Data System (ADS)

Purpose of this paper is to study power-law entropy-corrected holographic dark energy (PLECHDE) in the frame work of Horava-Lifshitz cosmology with Granda-Oliveros (G-O) IR-cutoff. Considering interacting and non-interacting scenario of PLECHDE with dark matter in a spatially non-flat universe, we investigate the cosmological implications of this model in detail. We obtain equation of state parameter, deceleration parameter and the evolution of dark energy density to explain the expansion of the universe. We also find out these parameters for Ricci scale. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for law red-shifts.

Borah, Bharat; Ansari, M.

2014-12-01

276

NASA Astrophysics Data System (ADS)

In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.

Makinde, O. D.

2014-12-01

277

NASA Technical Reports Server (NTRS)

A multi-input, multi-output control law design methodology, named "CRAFT", is presented. CRAFT stands for the design objectives addressed, namely, Control power, Robustness, Agility, and Flying Qualities Tradeoffs. The methodology makes use of control law design metrics from each of the four design objective areas. It combines eigenspace assignment, which allows for direct specification of eigenvalues and eigenvectors, with a graphical approach for representing the metrics that captures numerous design goals in one composite illustration. Sensitivity of the metrics to eigenspace choice is clearly displayed, enabling the designer to assess the cost of design tradeoffs. This approach enhances the designer's ability to make informed design tradeoffs and to reach effective final designs. An example of the CRAFT methodology applied to an advanced experimental fighter and discussion of associated design issues are provided.

Murphy, Patrick C.; Davidson, John B.

1998-01-01

278

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 ? may arise from a simple, linear partial differential equation. PMID:25393030

Pettersen, Klas H.; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T.

2014-01-01

279

(x) = Ax to an empirical distribution is simple: log x, log y, plot, find the best (perhaps weighted) least the normalizing assumption P( xmin) = 1. This would be the case, for example, for fitting the degree distribution of urban populations in which power laws dampen in the body of the size distribution, as recognized by Zipf

White, Douglas R.

280

We treat numerically in this paper, the transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluids is solved analytically using

N. Luna; F. Méndez; O. Bautista

2005-01-01

281

With the aid of symbolic computation, the new generalized algebraic method is extended to the (1+2)-dimensional nonlinear Schrödinger equation (NLSE) with dual-power law nonlinearity for constructing a series of new exact solutions. Because of the dual-power law nonlinearity, the equation cannot be directly dealt with by the method and require some kinds of techniques. By means of two proper transformations,

Li-Hua Zhang; Jian-Guo Si

2010-01-01

282

Effect of the length of inflation on angular TT and TE power spectra in power-law inflation

The effect of the length of inflation on the power spectra of scalar and tensor perturbations is estimated using the power-law inflation model with a scale factor of a(t) = t^q. Considering various pre-inflation models with radiation-dominated or scalar matter-dominated periods before inflation in combination with two matching conditions, the temperature angular power spectrum (TT) and temperature-polarization cross-power spectrum (TE) are calculated and a likelihood analysis is performed. It is shown that the discrepancies between the Wilkinson Microwave Anisotropy Probe (WMAP) data and the LCDM model, such as suppression of the spectrum at l = 2,3 and oscillatory behavior, may be explained by the finite length of inflation model if the length of inflation is near 60 e-folds and q > 300. The proposed models retain similar values of chi^2 to that achieved by the LCDM model with respect to fit to the WMAP data, but display different characteristics of the angular TE power spectra at l < 20.

Shiro Hirai; Tomoyuki Takami

2005-12-13

283

NASA Astrophysics Data System (ADS)

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

284

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. PMID:24915472

Howard, Robert W

2014-09-01

285

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. PMID:24580259

Langlois, Dominic; Cousineau, Denis; Thivierge, J P

2014-01-01

286

Lower Energy Cutoff Behavior of Negative Power-Law Electrons and Electron-Cyclotron Maser Emission

NASA Astrophysics Data System (ADS)

The electron-cyclotron maser (ECM) emission is one of the most important radio emission mechanisms in astrophysics. It was first pointed out in the late 1950s. Because of the limitation of the nonrelativistic resonant condition, it is difficult to produce an amplified radiation that can escape from plasma. The ECM instability has been extensively applied to various coherent radio-burst phenomena since Wu & Lee (1979) utilized the weakly relativistic resonant condition. Several loss-cone like electron distribution functions have been put forward. Astrophysical observations demonstrate that energetic electrons usually have a negative power-law distribution. However, the negative power-law spectrum of energetic electrons can depress the ECM instability effectively. We need a new and more effective mechanism to drive the radiation. In this thesis, we investigate the ECM emission driven by the lower energy cutoff behavior of power-law electrons, and the effects of anisotropy of energetic electrons in velocity space on ECM. Firstly, Chapter 1 introduces the general knowledge of the observational characteristics of solar radio bursts, and the excitation mechanisms of radio emission. Then, combining with the observations of hard X-ray spectrum, in Chapter 2 we overview the properties of energetic electrons driving the radio emission, and discuss the lower energy cutoff behavior of the negative power-law electrons. We suggest a hyperbolic tangent function to describe the lower energy cutoff behavior. In Chapter 3 we discuss the ECM driven by the lower energy cutoff behavior, and the effects of anisotropy in velocity space on the ECM instability. It is found that: (1) even with isotropic distribution, the power-law electrons with the steepness cutoff can efficiently excite the ECM instability; (2) same as the isotropy case, the power-law electrons with anisotropic distributions can also excite ECM instability efficiently, which have an important effect on the ECM emission. Energetic electrons observed in situ are ubiquitous in the near Earth space plasmas. They are commonly modeled as the so-called Kappa distribution. In Chapter 4 we investigate the ECM instability in space plasmas driven by the Kappa loss-cone distribution. Chapter 5 reports a novel kind of fine structures in solar radio bursts, solar microwave drifting spikes (SMDSs) on 2004 November 3, and makes statistical analysis of microwave spikes on 2006 December 13. We investigate the observational parameters of SMDSs observed on 2004 November 3. The electrons trapped within the solitary kinetic Alfven waves (SKAWs) can be accelerated by the SKAW electric fields, and directly trigger the observed SMDSs by the ECM mechanism. According to the GOES soft X-ray observations, the flare on 2006 December 13 can be separated into the rising phase, peak phase, and decay phase. We make statistical analysis of the observational parameters of the radio spikes, which occurred in all the three phases, and investigate their temporal evolution. Finally, the summary of the whole thesis and outlook are presented in Chapter 6.

Tang, J. F.

2014-01-01

287

Scalar field power-law cosmology with spatial curvature and dark energy-dark matter interaction

NASA Astrophysics Data System (ADS)

We consider a late closed universe of which scale factor is a power function of time using observational data from combined WMAP5+BAO+SN Ia dataset and WMAP5 dataset. The WMAP5 data give power-law exponent, ?=1.01 agreeing with the previous study of H( z) data while combined data gives ?=0.985. Considering a scalar field dark energy and dust fluid evolving in the power-law universe, we find field potential, field solution and equation of state parameters. Decaying from dark matter into dark energy is allowed in addition to the non-interaction case. Time scale characterizing domination of the kinematic expansion terms over the dust and curvature terms in the scalar field potential are found to be approximately 5.3 to 5.5 Gyr. The interaction affects in slightly lowering the height of scalar potential and slightly shifting potential curves rightwards to later time. Mass potential function of the interacting Lagrangian term is found to be exponentially decay function.

Gumjudpai, Burin; Thepsuriya, Kiattisak

2012-12-01

288

Entropy and the Cosmic Ray Particle Energy Distribution Power Law Exponent

We consider the hypothesis that cosmic rays are emitted from the surfaces of neutron stars by a process of evaporation from an internal nuclear liquid to a dilute external gas which constitutes the "vacuum". On this basis, we find an inverse power in the energy distribution with a power law exponent of 2.701178 in excellent agreement with the experimental value of 2.7. The heat of nuclear matter evaporation via the entropy allows for the computation of the exponent. The evaporation model employed is based on the entropy considerations of Landau and Fermi that have been applied to the liquid drop model of evaporation in a heavy nucleus excited by a collision. This model provides a new means of obtaining power law distributions for cosmic ray energy distributions and, remarkably, an actual value for the exponent which is in agreement with experiment and explains the otherwise puzzling smoothness of the cosmic ray energy distribution over a wide range of energies without discontinuities due to contributions from different sources required by current models.

A. Widom; J. Swain; Y. N. Srivastava

2014-10-05

289

Full investigation on the dynamics of power-law kinetic quintessence

NASA Astrophysics Data System (ADS)

We give a full investigation on the dynamics of power-law kinetic quintessence L(X ,?)=V(?)(-X+X2) by considering the potential related parameter ?(=VV/''V'2) as a function of another potential parameter ?(=V/'?V3/2), which correspondingly extends the analysis of the dynamical system of our Universe from two dimensional to three dimensional. In addition to the critical points found in previous papers, we find a new de Sitter- like dominant attractor (cp6) and give its stable condition using the center manifold theorem. For the dark energy dominant solution (cp6 and cp7), it could be distinguished from canonical quintessence and tachyon models since the sound speed cs2=0 or cs2?1. For the scaling solution (cp8), it is very interesting that the sound speed cs2=1/5, while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on the cold dark matter power spectrum and the cosmic microwave background both at early time, when this scalar field is an early dark energy with ?? being non-negligible at high redshift, and at late time, when it drives the accelerating expansion. We still do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future.

Fang, Wei; Tu, Hong; Li, Ying; Huang, Jiasheng; Shu, Chenggang

2014-06-01

290

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

Saichev, A; Sornette, D

2010-01-01

291

Laboratory constraints on chameleon dark energy and power-law fields

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.

Jason H. Steffen; Amol Upadhye; Al Baumbaugh; Aaron S. Chou; Peter O. Mazur; Ray Tomlin; Amanda Weltman; William Wester

2010-10-05

292

Laboratory constraints on chameleon dark energy and power-law fields

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.

Steffen, Jason H.; /Fermilab; Upadhye, Amol; /KICP, Chicago; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; /Fermilab; Weltman, Amanda; /Cape Town U.; Wester, William; /Fermilab

2010-10-01

293

On global minimizers of repulsive-attractive power-law interaction energies.

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

Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong

2014-11-13

294

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

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 an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.

2002-01-01

295

Anisotropic Power-law Inflation: A counter example to the cosmic no-hair conjecture

It is widely believed that anisotropy in the expansion of the universe will decay exponentially fast during inflation. This is often referred to as the cosmic no-hair conjecture. However, we find a counter example to the cosmic no-hair conjecture in the context of supergravity. As a demonstration, we present an exact anisotropic power-law inflationary solution which is an attractor in the phase space. We emphasize that anisotropic inflation is quite generic in the presence of anisotropic sources which couple with an inflaton.

Jiro Soda

2014-10-31

296

Precision of quantization of the hall conductivity in a finite-size sample: Power law

A microscopic calculation of the conductivity in the integer quantum Hall effect (IQHE) mode is carried out. The precision of quantization is analyzed for finite-size samples. The precision of quantization shows a power-law dependence on the sample size. A new scaling parameter describing this dependence is introduced. It is also demonstrated that the precision of quantization linearly depends on the ratio between the amplitude of the disorder potential and the cyclotron energy. The data obtained are compared with the results of magnetotransport measurements in mesoscopic samples.

Greshnov, A. A.; Kolesnikova, E. N.; Zegrya, G. G. [Russian Academy of Sciences, Ioffe Physicotechnical Institute (Russian Federation)], E-mail: zegrya@mail.ioffe.ru

2006-01-15

297

Power-law rheology and mechano-sensing in a cytoskeleton model with forced protein unfolding

We describe a model of cytoskeletal mechanics based on the force-induced conformational change of protein cross-links in a stressed polymer network. Slow deformation of simulated networks containing cross-links that undergo repeated, serial domain unfolding leads to an unusual state--with many cross-links accumulating near the critical force for further unfolding. Thermal activation of these links gives rise to power-law rheology resembling the previously unexplained mechanical response of living cells. Moreover, we hypothesize that such protein cross-links function as biochemical mechano-sensors of cytoskeletal deformation.

Brenton D. Hoffman; Gladys Massiera; John C. Crocker

2006-03-18

298

Jell-O Optics: Edibly Exploring Snell's Law and Optical Power

NASA Astrophysics Data System (ADS)

This presentation details a laboratory exercise and/or demonstration of refraction with an inexpensive, simple set-up: a pan of Jell-O, protractors, and laser pointers. This activity is presented from the perspective of an optical sciences graduate student who has spent the school year team-teaching high school math and physics (through Academic Decathlon). The goal is to present some of the fundamentals of optics with an enjoyable and affordable approach. The concepts include Snell's law, index of refraction, and optical power/focal length as they relate to the curvature of a lens.

Hendryx, Jennifer; Reynolds, Mathias

2012-03-01

299

Power-law tail of the velocity distribution in granular gases

NASA Astrophysics Data System (ADS)

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 ? 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 ^- ?. The simulation results for the exponent ? are in good agreement with the theoretical predictions of Ref. [1]. [1] E. Ben-Naim and J. Machta, Phys. Rev. Lett. 94, 138001 (2005).

Kang, Wenfeng; Ben-Naim, Eli; Machta, Jon

2007-03-01

300

On global minimizers of repulsive–attractive power-law interaction energies

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

Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong

2014-01-01

301

Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

NASA Astrophysics Data System (ADS)

We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a ?-3/2 power spectrum. This is successfully applied to the totally asymmetric simple exclusion process with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and the discreteness of the system is not effective.

Takesue, Shinji; Mitsudo, Tetsuya; Hayakawa, Hisao

2003-07-01

302

Non-commutative power-law inflation: mode equation and spectra index

NASA Astrophysics Data System (ADS)

Following an elegant approach that merges the effects of the stringy spacetime uncertainty relation into primordial perturbations suggested by Brandenberger and Ho, we show the mode equation up to the first order of non-commutative parameter. A new approximation is provided to calculate the mode functions analytically in the non-commutative power-law inflation models. It turns out that non-commutativity of spacetime can provide small corrections to the power spectrum of primordial fluctuations as the first-year results of WMAP indicate. Moreover, using the WMAP data, we obtain the value of expansion parameter, non-commutative parameter and find the approximation is viable. In addition, we determined the string scale ls ? 2.0 ×10-29 cm.

Liu, Dao-jun; Li, Xin-zhou

2004-10-01

303

Validation of a power-law noise model for simulating small-scale breast tissue

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. PMID:23938858

Reiser, I.; Edwards, A.; Nishikawa, R. M.

2013-01-01

304

Statistical properties of the energy in time-dependent homogeneous power law potentials

We study 1D Hamilton systems with homogeneous power law potential and their statistical behaviour, assuming the microcanonical distribution of the initial conditions and describing its change under monotonically increasing time-dependent function $a(t)$ (prefactor of the potential). Using the nonlinear WKB-like method by Papamikos and Robnik {\\em J. Phys. A: Math. Theor. {\\bf 44} (2012) 315102} and following a previous work by Papamikos G and Robnik M {\\em J. Phys. A: Math. Theor. {\\bf 45} (2011) 015206} we specifically analyze the mean energy, the variance and the adiabatic invariant (action) of the systems for large time $t\\rightarrow\\infty$ and we show that the mean energy and variance increase as powers of $a(t)$, while the action oscillates and finally remains constant. By means of a number of detailed case studies we show that the theoretical prediction is excellent which demonstrates the usefulness of the method in such applications.

Dimitris Andresas; Marko Robnik

2014-05-22

305

Validation of a power-law noise model for simulating small-scale breast tissue

NASA Astrophysics Data System (ADS)

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.

Reiser, I.; Edwards, A.; Nishikawa, R. M.

2013-09-01

306

Highly optimized tolerance and power laws in dense and sparse resource regimes

Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\\geq l)\\sim l^{-\\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\\alpha= 1+ 1/d $. In this paper we describe and analyze a third model, the cuts m...

Manning, M; Doyle, J

2005-01-01

307

The time-domain behavior of power-law noises. [of many geophysical phenomena

NASA Technical Reports Server (NTRS)

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).

Agnew, Duncan C.

1992-01-01

308

Semiclassical trace formula for the two-dimensional radial power-law potentials.

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 ?=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. PMID:23848757

Magner, A G; Vlasenko, A A; Arita, K

2013-06-01

309

The power-law expansion universe and the late-time behavior

Using the SNe Ia data we determine the three parameters in the power-law expanding universe model with time-dependent power \\cite{W}. Inputting $H_0$ and $t_0$, then we find the $\\dot{a}-t$ evolution curve with $m=5.0$ and $q_0=-0.90$ can fit very well to that from SNe observation data. The model predicts the transition redshift $z\\simeq0.38$. The dark energy deduced from this model have phantom property but the universe doesn't encounter the Big Rip singularity. Assuming that this model with the three parameters is valid for the future universe, then we predict that the total energy density of the universe is decreasing and will soon reach its minimum.

Yi-Huan Wei

2004-11-17

310

Background: Sample size calculations are an important tool for planning epidemiological studies. Large sample sizes are often required in Mendelian randomization investigations. Methods and results: Resources are provided for investigators to perform sample size and power calculations for Mendelian randomization with a binary outcome. We initially provide formulae for the continuous outcome case, and then analogous formulae for the binary outcome case. The formulae are valid for a single instrumental variable, which may be a single genetic variant or an allele score comprising multiple variants. Graphs are provided to give the required sample size for 80% power for given values of the causal effect of the risk factor on the outcome and of the squared correlation between the risk factor and instrumental variable. R code and an online calculator tool are made available for calculating the sample size needed for a chosen power level given these parameters, as well as the power given the chosen sample size and these parameters. Conclusions: The sample size required for a given power of Mendelian randomization investigation depends greatly on the proportion of variance in the risk factor explained by the instrumental variable. The inclusion of multiple variants into an allele score to explain more of the variance in the risk factor will improve power, however care must be taken not to introduce bias by the inclusion of invalid variants. PMID:24608958

Burgess, Stephen

2014-01-01

311

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

NASA Astrophysics Data System (ADS)

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 ?t and change in spectral index for scalar perturbation ?st to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ?CDM 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 ? and 8.1 ? 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.

Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun

2015-01-01

312

So You Think the Crab is Described by a Power-Law Spectrum

NASA Technical Reports Server (NTRS)

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.

Weisskopf, Martin C.

2008-01-01

313

Taylor's Power Law was fit to Tylenchulus semipenetrans population data obtained from individual trees in a survey of 50 Florida citrus orchards (geographic survey) and to data from individual trees within a single orchard collected at regular intervals for 2 years (temporal survey). No significant differences were detected between slope or intercept values when log variance was regressed against log mean for the geographic and temporal data sets. The geographic survey was divided into two subsets of data according to the perceived size of patches of T. semipenetrans. Subsets consisted of orchards which appeared to have numerous small patches of trees infected by the nematode (small patch) and orchards in which most of the trees were infected (large patch). The slope value for the orchards with smaller patches of nematodes was different (P Power Law fit to the survey data. PMID:19287677

Duncan, L W; Ferguson, J J; Dunn, R A; Noling, J W

1989-10-01

314

Bose-Einstein condensation in dark power-law laser traps

We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order $\\ell$ 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 quasi-homogeneous 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 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.

Amine Jaouadi; Naceur Gaaloul; Bruno Viaris De Lesegno; Mourad Telmini; Laurence Pruvost; Eric Charron

2009-09-28

315

NASA Astrophysics Data System (ADS)

In predictive engineering for polymer processes, the proper prediction of material microstructure from known processing conditions and constituent material properties is a critical step forward properly predicting bulk properties in the finished composite. Operating within the context of long-fiber thermoplastics (LFT, length > 15mm) this investigation concentrates on the influence of the power law index on the final fiber length distribution within the injection molded part. To realize this, the Autodesk Simulation Moldflow Insight Scandium 2013 software has been used. In this software, a fiber breakage algorithm is available from this release on. Using virtual material data with realistic viscosity levels allows to separate the influence of the power law index on the fiber breakage from the other material and process parameters. Applying standard settings for the fiber breakage parameters results in an obvious influence on the fiber length distribution through the thickness of the part and also as function of position in the part. Finally, the influence of the shear rate constant within the fiber breakage model has been investigated illustrating the possibility to fit the virtual fiber length distribution to the possible experimentally available data.

Desplentere, Frederik; Six, Wim; Bonte, Hilde; Debrabandere, Eric

2013-04-01

316

Effective power-law dependence of Lyapunov exponents on the central mass in galaxies

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation $L\\propto m^p$ between the mean Lyapunov exponent $L$ of stellar orbits chaotically scattered by a supermassive black hole in the center of a galaxy and the mass parameter $m$, i.e. ratio of the mass of the black hole over the mass of the galaxy. The exponent $p$ is found numerically to obtain values in the range $p \\approx 0.3$--$0.5$. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the black hole's sphere of influence. We thus predict $p=2/3-q$ with $q\\approx 0.1$--$0.2$. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power law scaling of $L$ with $m$ holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show...

Delis, N; Kalapotharakos, C

2015-01-01

317

Absence of power-law scaling in the dendritic crystal growth of ammonium chloride

NASA Astrophysics Data System (ADS)

We report measurements of the dendritic crystal growth of NH4Cl from supersaturated aqueous solution at small supersaturations, with a goal of understanding the origin of the sidebranching structure. The early detection of sidebranches requires measurements of small deviations from the smooth steady state shape, but that underlying shape is not precisely known at the intermediate distances relevant for sidebranch measurements. We find that no simple power law describes the average crystal shape, the average sidebranch amplitude, or the average sidebranch envelope. Instead, the effective power law exponents appear to increase steadily as a function of distance from the dendritic tip. Comparisons of the amplitude of sidebranches with that predicted by models of noise-driven sidebranching require careful measurements of materials parameters such as the capillary length. Previous published estimates for this material varied by over a factor of 20. We report new measurements of the capillary length and find d0= 0.224 ±0.005;nm. Based on those new measurements, we find that the amplitude of the sidebranches in this system is larger than expected from numerical models.

Dougherty, Andrew

2013-03-01

318

NASA Astrophysics Data System (ADS)

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.

Hong, S. Lee; Bodfish, James W.; Newell, Karl M.

2006-03-01

319

Power law approximations of movement network data for modeling infectious disease spread.

Globalization and increased mobility of individuals enable person-to-person transmitted infectious diseases to spread faster to distant places around the world, making good models for the spread increasingly important. We study the spatiotemporal pattern of spread in the remotely located and sparsely populated region of North Norway in various models with fixed, seasonal, and random effects. The models are applied to influenza A counts using data from positive microbiology laboratory tests as proxy for the underlying disease incidence. Human travel patterns with local air, road, and sea traffic data are incorporated as well as power law approximations thereof, both with quasi-Poisson regression and based on the adjacency structure of the relevant municipalities. We investigate model extensions using information about the proportion of positive laboratory tests, data on immigration from outside North Norway and by connecting population to the movement network. Furthermore, we perform two separate analyses for nonadults and adults as children are an important driver for influenza A. Comparisons of one-step-ahead predictions generally yield better or comparable results using power law approximations. PMID:24843881

Geilhufe, Marc; Held, Leonhard; Skrøvseth, Stein Olav; Simonsen, Gunnar S; Godtliebsen, Fred

2014-05-01

320

Underestimating extreme events in power-law behavior due to machine-dependent cutoffs.

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. PMID:25493726

Radicchi, Filippo

2014-11-01

321

Full Investigation on the Dynamics of Power-Law Kinetic Quintessence

We give a full investigation on the dynamics of power-law kinetic quintessence $L(X, \\phi)=V(\\phi)(-X+X^2)$ by considering the potential related parameter $\\Gamma$($=\\frac{V V''}{V'^2}$) as a function of another potential parameter $\\lambda$($=\\frac{V'}{\\kappa V^{3/2}}$), which correspondingly extends the analysis of the dynamical system of our universe from two-dimension to three-dimension. Beside the critical points found in previous papers, we find a new de-Sitter-like dominant attractor(\\textit{cp$6$}) and give its stable condition using the center manifold theorem. For the dark energy dominant solution(\\textit{cp$6$} and \\textit{cp$7$}), it could be distinguished from canonical quintessence and tachyon models since the sound speed $c_s^2=0$ or $c_s^2\\ll 1$. For the scaling solution (\\textit{cp$8$}), it is very interesting that the sound speed $c_s^2=1/5$ while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on cold dark matter...

Fang, Wei; Li, Ying; Huang, Jiasheng; Shu, Chenggang

2014-01-01

322

Bose-Einstein condensation in dark power-law laser traps

We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order l allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a 'finger' or of a 'hockey puck' in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.

Jaouadi, A. [Universite Paris-Sud, Institut des Sciences Moleculaires d'Orsay (ISMO), F-91405 Orsay (France); CNRS, Orsay, F-91405 France (France); Laboratoire de Spectroscopie Atomique, Moleculaire et Applications (LSAMA), Department of Physics, Faculty of Science of Tunis, University of Tunis El Manar, T-2092 Tunis (Tunisia); Gaaloul, N. [Institut fuer Quantenoptik, Welfengarten 1, Gottfried Wilhelm Leibniz Universitaet, D-30167 Hannover (Germany); Viaris de Lesegno, B.; Pruvost, L. [CNRS, Laboratoire Aime Cotton (LAC), F-91405 Orsay (France); Universite Paris-Sud, Orsay, F-91405 France (France); Telmini, M. [Laboratoire de Spectroscopie Atomique, Moleculaire et Applications (LSAMA), Department of Physics, Faculty of Science of Tunis, University of Tunis El Manar, T-2092 Tunis (Tunisia); Charron, E. [Universite Paris-Sud, Institut des Sciences Moleculaires d'Orsay (ISMO), F-91405 Orsay (France); CNRS, Orsay, F-91405 (France)

2010-08-15

323

NASA Technical Reports Server (NTRS)

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.

Howell, Leonard W.

2002-01-01

324

ENERGY-DEPENDENT POWER SPECTRAL STATES AND ORIGIN OF APERIODIC VARIABILITY IN BLACK HOLE BINARIES

We found that the black hole candidate MAXI J1659-152 showed distinct power spectra, i.e., power-law noise (PLN) versus band-limited noise (BLN) plus quasi-periodic oscillations (QPOs) below and above about 2 keV, respectively, in observations with Swift and the Rossi X-ray Timing Explorer during the 2010 outburst, indicating a high energy cutoff of the PLN and a low energy cutoff of the BLN and QPOs around 2 keV. The emergence of the PLN and the fading of the BLN and QPOs initially took place below 2 keV when the source entered the hard intermediate state and settled in the soft state three weeks later. The evolution was accompanied by the emergence of the disk spectral component and decreases in the amplitudes of variability in the soft and hard X-ray bands. Our results indicate that the PLN is associated with an optically thick disk in both hard and intermediate states, and the power spectral state is independent of the X-ray energy spectral state in a broadband view. We suggest that in the hard or intermediate state, the BLN and QPOs emerge from the innermost hot flow subjected to Comptonization, while the PLN originates from the optically thick disk farther out. The energy cutoffs of the PLN and the BLN or QPOs then follow the temperature of the seed photons from the inner edge of the optically thick disk, while the high frequency cutoff of the PLN follows the orbital frequency of the inner edge of the optically thick disk as well.

Yu Wenfei; Zhang Wenda, E-mail: wenfei@shao.ac.cn [Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030 (China)

2013-06-20

325

An interacting binary system powers precessing outflows of an evolved star.

Stars are generally spherical, yet their gaseous envelopes often appear nonspherical when ejected near the end of their lives. This quirk is most notable during the planetary nebula phase, when these envelopes become ionized. Interactions among stars in a binary system are suspected to cause the asymmetry. In particular, a precessing accretion disk around a companion is believed to launch point-symmetric jets, as seen in the prototype Fleming 1. Our finding of a post-common-envelope binary nucleus in Fleming 1 confirms that this scenario is highly favorable. Similar binary interactions are therefore likely to explain these kinds of outflows in a large variety of systems. PMID:23139326

Boffin, Henri M J; Miszalski, Brent; Rauch, Thomas; Jones, David; Corradi, Romano L M; Napiwotzki, Ralf; Day-Jones, Avril C; Köppen, Joachim

2012-11-01

326

Issues in ad hoc networks: scaling laws, media access control, and power control

NASA Astrophysics Data System (ADS)

We present a brief account of three problems in wireless networks. First, on the problem of scalability, we show that under a certain model of interference, a network with n nodes can only provide a per-node throughput of order square-root of n bits/sec. However, an experimental investigation with IEEE 802.11 technology yielded the considerably worse power law of n raised to -1.68. We then present a new media access control protocol for ad hoc networks, called SEEDEX. It attempts to make reservations without explicitly doing so for each and every packet. Nodes use random schedule, and can inform each other about their schedules merely by exchanging the seeds of their pseudo random number generators. Last we turn to the problem of power control in ad hoc networks. We present a new protocol called COMPOW, which is designed to find the lowest power level at which the entire network is connected. We provide the theoretical justification for it, and a solution of the architectural issues involved. Using a notion of parallel modularity at the network layer, this protocol provides a joint solution for both the routing and power control problems. It has been implemented in the Linux kernel.

Kumar, Panganamala R.

2001-07-01

327

Diagnostic Power of Broad Emission Line Profiles in Searches for Binary Supermassive Black Holes.

NASA Astrophysics Data System (ADS)

Motivated by advances in observational searches for sub-parsec supermassive black hole binaries (SBHBs) made in the past few years we develop a semi-analytic model to describe the spectral emission line signatures of these systems. The goal of this work is to test one of the leading models of binary accretion flows in the literature: SBHB in a circumbinary disk. In this context, we model SBHB accretion flows as a set of three accretion disks: two mini-disks that are gravitationally bound to the individual black holes and a circumbinary disk that forms a common envelope about a gravitationally bound binary. We find that emission line profiles tend to have different statistical properties depending on the semi-major axis, mass ratio, eccentricity of the binary, and the alignment of the triple-disk system, and can in principle be used to infer the statistical distribution of these parameters.

Nguyen, Khai; Bogdanovic, Tamara

2015-01-01

328

We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes ('aftershocks'). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake ('productivity' or 'fertility'), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities {mu} is characterized by a power law {approx}1/{mu}{sup 1+{gamma}} and the bare Omori law for the memory of previous triggering mothers decays slowly as {approx}1/t{sup 1+{theta}}, with 0<{theta}<1 relevant for earthquakes. Using the tool of generating probability functions and a quasistatic approximation which is shown to be exact asymptotically for large durations, we show that the density distribution of total aftershock lifetimes scales as {approx}1/t{sup 1+{theta}}{sup sol{gamma}} when the average branching ratio is critical (n=1). The coefficient 1<{gamma}=b/{alpha}<2 quantifies the interplay between the exponent b{approx_equal}1 of the Gutenberg-Richter magnitude distribution {approx}10{sup -bm} and the increase {approx}10{sup {alpha}}{sup m} of the number of aftershocks with mainshock magnitude m (productivity), with 0.5<{alpha}<1. The renormalization of the bare Omori decay law {approx}1/t{sup 1+{theta}} into {approx}1/t{sup 1+{theta}}{sup sol{gamma}} stems from the nonlinear amplification due to the heavy-tailed distribution of fertilities and the critical nature of the branching cascade process. In the subcritical case n<1, the crossover from {approx}1/t{sup 1+{theta}}{sup sol{gamma}} at early times to {approx}1/t{sup 1+{theta}} at longer times is described. More generally, our results apply to any stochastic branching process with a power-law distribution of offspring per parent and a long memory.

Saichev, A. [Mathematical Department, Nizhny Novgorod State University, Gagarin prospekt 23, Nizhny Novgorod, 603950 (Russian Federation); Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA (United States); Sornette, D. [Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095 (United States); Department of Earth and Space Sciences, University of California, Los Angeles, California 90095 (United States); Laboratoire de Physique de la Matiere Condensee, CNRS UMR 6622 and Universite de Nice-Sophia Antipolis, 06108 Nice Cedex 2 (France)

2004-10-01

329

NASA Astrophysics Data System (ADS)

We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (“productivity” or “fertility”), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities ? is characterized by a power law ˜1/?1+? and the bare Omori law for the memory of previous triggering mothers decays slowly as ˜1/t1+? , with 0law ˜1/t1+? into ˜1/t1+?/? stems from the nonlinear amplification due to the heavy-tailed distribution of fertilities and the critical nature of the branching cascade process. In the subcritical case n<1 , the crossover from ˜1/t1+?/? at early times to ˜1/t1+? at longer times is described. More generally, our results apply to any stochastic branching process with a power-law distribution of offspring per parent and a long memory.

Saichev, A.; Sornette, D.

2004-10-01

330

Full Investigation on the Dynamics of Power-Law Kinetic Quintessence

We give a full investigation on the dynamics of power-law kinetic quintessence $L(X, \\phi)=V(\\phi)(-X+X^2)$ by considering the potential related parameter $\\Gamma$($=\\frac{V V''}{V'^2}$) as a function of another potential parameter $\\lambda$($=\\frac{V'}{\\kappa V^{3/2}}$), which correspondingly extends the analysis of the dynamical system of our universe from two-dimension to three-dimension. Beside the critical points found in previous papers, we find a new de-Sitter-like dominant attractor(\\textit{cp$6$}) and give its stable condition using the center manifold theorem. For the dark energy dominant solution(\\textit{cp$6$} and \\textit{cp$7$}), it could be distinguished from canonical quintessence and tachyon models since the sound speed $c_s^2=0$ or $c_s^2\\ll 1$. For the scaling solution (\\textit{cp$8$}), it is very interesting that the sound speed $c_s^2=1/5$ while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on cold dark matter power spectrum and cosmic microwave background both at early time when this scalar field is an early dark energy with $\\Omega_\\phi$ being non-negligible at high redshift and at late time when it drives the accelerating expansion. We even do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future.

Wei Fang; Hong Tu; Ying Li; Jiasheng Huang; Chenggang Shu

2014-06-01

331

Wavelet-based analysis and power law classification of C/NOFS high-resolution electron density data

NASA Astrophysics Data System (ADS)

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.

Rino, C. L.; Carrano, C. S.; Roddy, Patrick

2014-08-01

332

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

NASA Astrophysics Data System (ADS)

Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.

Deluca, Anna; Corral, Álvaro

2013-12-01

333

On the power spectra of the wind-fed X-ray binary pulsar GX 301 - 2

NASA Technical Reports Server (NTRS)

A phenomenological model of accretion which is applied to the wind-fed X-ray binary pulsar GX 301 - 2 is developed, assuming that the accretion onto the neutron star does not occur from a continuous flux of plasma, but from blobs of matter which are threaded by the magnetic field lines onto the magnetic polar caps of the neutron star. These 'lumps' are produced at the magnetospheric limit by magnetohydrodynamical instability, introducing a 'noise' in the accretion process, due to the discontinuity in the flux of matter onto the neutron star. This model is able to describe the change of slope observed in the continuum component of the power spectra of the X-ray binary pulsar GX 301 - 2, in the frequency range 0.01 - 0.1 Hz. The physical properties of the infalling blobs derived in the model are in agreement with the constraints imposed by observations.

Orlandini, Mauro; Morfill, G. E.

1992-01-01

334

From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies

NASA Astrophysics Data System (ADS)

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-larger accumulations. There is no characteristic length or time scale in the partial melting process or its products. Smallest melt segregations and >km-scale plotuns form the end members of a continuous chain of mergers of magma batches.

Soesoo, Alvar; Bons, Paul D.

2014-12-01

335

Listing triangles in expected linear time on a class of power law graphs.

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 in the range that is relevant for the degree distribution of the World-Wide Web.

Nordman, Daniel J. (Iowa State University, Ames, Iowa); Wilson, Alyson G. (Iowa State University, Ames, Iowa); Phillips, Cynthia Ann; Berry, Jonathan W.

2010-07-01

336

Power-law Maxwell rheologies and the interaction between tectonic and seismic deformations

NASA Astrophysics Data System (ADS)

In a lithosphere where dislocation creep dominates the steady-state flow and the viscosity is stress-dependent, the equilibrium between tectonic stress and strain rate is broken after an earthquake due to the sudden coseismic stress change. The imbalance between tectonic stress and strain rate manifests itself during the post-seismic phase and, when seismic stress is comparable or smaller than tectonic stress, it affects post-seismic deformation via an effective anisotropy along the principal axes of the tectonic stress tensor. This issue is herein discussed within the framework of post-seismic models based on power-law Maxwell rheologies and, in the limit case of seismic stress much smaller than tectonic stress, we obtain a first-order approximation of the rheology which results into a linear anisotropic Maxwell model and we find that the effective anisotropy is associated to a two-modal relaxation characterized by the Maxwell time and the Maxwell time divided by the power-law index. Thus, as far as the steady-state flow within the lithosphere is dominated by dislocation creep, linear isotropic viscoelastic rheologies, like Newtonian Maxwell and Burgers models, represent a severe oversimplification which does not account for the physics of post-seismic deformation. This new physics is discussed characterizing the stress state of the ductile layers of the lithosphere before and after the earthquake for normal, inverse and strike mechanisms and for a variety of continental seismogenic zones and thermal models. We show that the first-order approximation of the power-law Maxwell rheology is valid for a quite wide range of small and moderate earthquakes. The most restrictive upper bounds of the seismic magnitude (which hold for the hottest thermal model here considered, with lithospheric thickness of H = 80 km and surface heat flux of Q = 70 mW m-2) occur for normal and inverse earthquakes and are 5.6 or 6.3 for a lower crust of wet diorite or felsic granulite, and 6.5 for a mantle of wet olivine. The upper bounds increase by about 0.3-0.4 for strike earthquakes and by more than 1.0 for the cold thermal model (H = 200 km and Q = 50 mW m-2).

Cambiotti, G.; Rigamonti, S.; Splendore, R.; Marotta, A. M.; Sabadini, R.

2014-09-01

337

A growth model for directed complex networks with power-law shape in the out-degree distribution.

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

Esquivel-Gómez, J; Stevens-Navarro, E; Pineda-Rico, U; Acosta-Elias, J

2015-01-01

338

A growth model for directed complex networks with power-law shape in the out-degree distribution

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

Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.

2015-01-01

339

A growth model for directed complex networks with power-law shape in the out-degree distribution

NASA Astrophysics Data System (ADS)

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.

Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.

2015-01-01

340

Pattern formation and Turing instability in an activator-inhibitor system with power-law coupling

NASA Astrophysics Data System (ADS)

We investigate activator-inhibitor systems in two spatial dimensions with a non-local coupling, for which the interaction strength decreases with the lattice distance as a power-law. By varying a single parameter we can pass from a local (Laplacian) to a global (all-to-all) coupling type. We derived, from a linear stability analysis of the Fourier spatial modes, a set of conditions for the occurrence of a Turing instability, by which a spatially homogeneous pattern can become unstable. In nonlinear systems the growth of these modes is limited and pattern formation is possible. We have studied some qualitative features of the patterns formed in non-local coupled activator-inhibitor systems described by the Meinhardt-Gierer equations.

dos S. Silva, F. A.; Viana, R. L.; Lopes, S. R.

2015-02-01

341

Slow synaptic dynamics in a network: From exponential to power-law forgetting

NASA Astrophysics Data System (ADS)

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.

Luck, J. M.; Mehta, A.

2014-09-01

342

Slow synaptic dynamics in a network: from exponential to power-law forgetting.

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. PMID:25314475

Luck, J M; Mehta, A

2014-09-01

343

The nature of the hard X-ray power-law tail in M87

Spatially-resolved spectroscopy of the elliptical galaxy M87 with the MECS instrument on board BeppoSAX demonstrates that the hard X-ray power-law tail, originally discovered by ASCA (Matsumoto et al 1996; Allen et al. 1999), originates in the innermost 2'. Our results are consistent with it being produced in an Accretion Dominated Flow, although a substantial jet contribution cannot be ruled out. An origin from a Seyfert-like nucleus is disfavored by our data. As a by-product of this result, we present an analysis of the thermal emission coming from the center of the Virgo cluster, which exhibits a strong positive radial temperature gradient, along with a radial decrease of the iron abundance.

M. Guainazzi; S. Molendi

1999-10-14

344

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical system

To study a chaotic itinerant motion among varieties of ordered states, we propose a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line, and a Markov chain with a transition probability matrix. To investigate the stability of attractor ruins in the model, we analyze the residence time distribution of orbits at attractor ruins. We show that the residence time distribution averaged by all attractor ruins is given by the superposition of (truncated) power-law distributions, if a basin of attraction for each attractor ruin has zero measure. To make sure of this result, we carry out a computer simulation for models showing chaotic itinerancy. We also discuss the fact that chaotic itinerancy does not occur in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.

Jun Namikawa

2005-02-23

345

Extreme power law in a driven many-particle system without threshold dynamics.

We study a one-dimensional system of spatially extended particles, which are attached to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by Gaussian noise and to have dissipative, energy-conserving, or antidissipative (pinball-like) interactions, when the particle density exceeds a critical threshold. While each particle in separation shows a well-behaved behavior characterized by a Gaussian velocity distribution, the interaction of particles at high densities can cause an avalanchelike momentum and energy transfer, which can generate extreme (steep) power laws without a well-defined variance and mean value. Specifically, the velocity variance increases dramatically towards the free boundaries of the driven many-particle system. The model might also have some relevance for better understanding of crowd disasters. Our results suggest that these are most likely caused by passive momentum transfers, not by active pushing. PMID:25375483

Mani, Roman; Böttcher, Lucas; Herrmann, Hans J; Helbing, Dirk

2014-10-01

346

NASA Astrophysics Data System (ADS)

It is well established that the distribution of social ties (degree) of an individual in a social network follows a power-law. How this heavy-tailed distribution arises in practice, however, has not been conclusively demonstrated. Mechanisms of ``preferential-attachment'' and optimization are often cited as the origin of heavy-tailed degree distributions. Our data indicate that there is a different cause for these phenomena. For different social networks we find an intrinsic relationship degree and activity (number of posts, edits etc): The degree distribution is entirely random except for its mean value which depends deterministically on the volume of the users' activity. This suggests that heavy-tailed degree distribution is a consequence of the intrinsic activity of users. More importantly, human activity deterministically affects the mean success at establishing links in a social network, and the specific degree of a given user is otherwise random following a ``maximum entropy attachment'' model.

Muchnik, Lev; Pei, Sen; Parra, Lucas; Reis, Saulo; Andrade, José., Jr.; Havlin, Shlomo; Makse, Hernan

2013-03-01

347

Scalar Field Probes of Power-Law Space-Time Singularities

We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.

Matthias Blau; Denis Frank; Sebastian Weiss

2006-03-01

348

Power law signature of media exposure in human response waiting time distributions.

We study the humanitarian response to the destruction brought by the tsunami generated by the Sumatra earthquake of December 26, 2004, as measured by donations, and find that it decays in time as a power law ?1/t? with ?=2.5 ± 0.1 . This behavior is suggested to be the rare outcome of a priority queuing process in which individuals execute tasks at a rate slightly faster than the rate at which new tasks arise. We believe this to be an empirical evidence documenting the recently predicted [G. Grinstein and R. Linsker, Phys. Rev. E 77, 012101 (2008)] regime, and provide additional independent evidence that suggests that this "highly attentive regime" arises as a result of the intense focus placed on this donation "task" by the media. PMID:20866291

Crane, Riley; Schweitzer, Frank; Sornette, Didier

2010-05-01

349

Power law signature of media exposure in human response waiting time distributions

NASA Astrophysics Data System (ADS)

We study the humanitarian response to the destruction brought by the tsunami generated by the Sumatra earthquake of December 26, 2004, as measured by donations, and find that it decays in time as a power law ˜1/t? with ?=2.5±0.1 . This behavior is suggested to be the rare outcome of a priority queuing process in which individuals execute tasks at a rate slightly faster than the rate at which new tasks arise. We believe this to be an empirical evidence documenting the recently predicted [G. Grinstein and R. Linsker, Phys. Rev. E 77, 012101 (2008)] regime, and provide additional independent evidence that suggests that this “highly attentive regime” arises as a result of the intense focus placed on this donation “task” by the media.

Crane, Riley; Schweitzer, Frank; Sornette, Didier

2010-05-01

350

On the similarity solutions of magnetohydrodynamic flows of power-law fluids over a stretching sheet

NASA Astrophysics Data System (ADS)

A rigorous mathematical analysis is given for a magnetohydrodynamics boundary layer problem, which arises in the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting power-law fluid along a stretching flat sheet in the presence of an exterior magnetic field orthogonal to the flow. In the self-similar case, the problem is transformed into a third-order nonlinear ordinary differential equation with certain boundary conditions, which is proved to be equivalent to a singular initial value problem for an integro-differential equation of first order. With the aid of the singular initial value problem, the uniqueness and existence results for (generalized) normal solutions are established and some properties of these solutions are explored.

Zhang, Zhongxin; Wang, Junyu

2007-06-01

351

A study of dynamic contact angles of shear-thickening power-law fluids

NASA Astrophysics Data System (ADS)

We study the dynamic wetting of shear-thickening power-law fluids in a liquid-solid-gas contact system. In the previous model based on hydrodynamic analysis, microscopic effects near the contact line are neglected. In this work, we adopt two different physical models, slip boundary model and molecular force model, to incorporate microscopic effects and relieve the stress singularity at the moving contact line in hydrodynamics analysis. The two models, which are mathematically equivalent for Newtonian fluids, lead to different results on the dependence of the liquid's dynamic contact angle on its moving speed in both complete wetting and partial wetting cases. By comparing with experiments, we find that the slip boundary model matches the experiments better than the previous model and the molecular force model.

Wang, Yu; Zhu, Ke-Qin

2014-05-01

352

NASA Technical Reports Server (NTRS)

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.

Beltrametti, M.

1980-01-01

353

NASA Astrophysics Data System (ADS)

We study a dome structure (10x10x10 cu km) at an intermediate scale between laboratory analyses and tectonic processes. Local gas extraction induced about 1000 events within the dome (1.0 is less than or equal to M(sub 1) is less than or equal to 4.2) recorded by a local network during 19 years (1974-1992). Two types of autosimilarity coefficients (b value and correlation dimension) are analyzed in three-dimensional (3-D) space. The hypocenter distribution shows a fractal pattern characterized by the noninteger value of the correlation dimension. Moreover the frequency-magnitude relation of the events obeys a power law. The existence of these two parameters shows that the spatial distribution of the earthquakes induced by the Lacq gas extraction is governed by a nonrandom behavior. We observe no temporal correlation between the temporal behavior of the b value (slope of frequency-magnitude relation) and D (correlation dimension). Three-dimensional fractal analysis of induced earthquakes allows us to define two distinct classes of events separated by a critical distance of 500 m. The first class (r is greater than 500 m) shows a diffuse seismicity. This diffuse class of earthquakes (M(sub 1) is less than 3.0) follows the frequency-magnitude relation. The low number of events prevent us from analyzing whether there is a fractal or random behavior. The second class (r less than 500 m) defines nests of seismicity and attests a bifractal character (r less than 500 m, D(sub 1) is approximately equal to 2.4; r is greater than 500 m, D(sub 2) is approximately equal to 1.3). The difference of one unit between the fractal dimension of the seismicity within the nests (D(sub 1)) and the fractal dimension of the nests distribution (D(sub 2)) suggests an influence of the geological dome structure on the spatial development of seismic nests. Moreover, a slope break above M(sub 1) = 3.0 (G-R relation) is observed on this second class (1.0 is less than or equal to M(sub 1) is less than or equal to 4.2). The slope break of both the b value and the fractal dimension at a common threshold (M(sub 1) is approximately equal to 3.0 is equivalent to a 500-m fracture size) suggests a critical distance for the brittle behavior of the uppermost crust as proposed for tectonic earthquakes by Scholz (1991). Such a critical distance correlates in our study with the maximum thickness of local seismogenic layers (brittle calcareous layer versus ductile marly layer). On this basis we propose that (1) the finite extension of the earthquake power law is driven by the local setting and therefore is also a scale dependent process, (2) the geomechanical link between fractal behavior and fracture size, i.e., a physical mapping of the power law behavior, must also be found in the boundary values of the autosimilarity processes (slope breaks) rather than in the values of the power law exponents.

Volant, Philippe; Grasso, Jean-Robert

1994-11-01

354

Modelling of semi-solid processing using a modified temperature-dependent power-law model

NASA Astrophysics Data System (ADS)

A fairly simple one-phase rheological model has been implemented into a commercial fluid flow finite element software to simulate mould filling during the semi-solid processing (thixoforming) of aluminium alloys. This model is of purely viscous nature. Its temperature-dependent viscosity is a power-law function of the shear rate with a shear rate cut-off. The constitutive parameters of this model were determined for a rheocast A356 alloy. For that purpose, simulation results were compared with instrumented thixoforming experiments performed on a production-scale injection machine. The selected configuration was that of a transient flow near a bifurcation, i.e. obstruction of an established Poiseuille-type flow by a shaft placed at the centre of a tube. Using these parameters, the model was then further validated by comparing the simulation of an axisymmetric reservoir mould filling with the shape of solidified shells obtained after interrupted injection experiments.

Orgéas, L.; Gabathuler, J.-P.; Imwinkelried, Th.; Paradies, Ch.; Rappaz, M.

2003-07-01

355

Power-law rheology and the dynamical heterogeneity in a sheared granular material

Rheology of a granular material at the jamming density is investigated using molecular dynamics simulation. It is found that shear stress exhibits power-law dependence on shear rate with a nontrivial exponent. Due to the criticality of the jamming transition point, finite-size effect is observed in smaller systems at lower shear rates. Finite-size scaling indicates the correlation length algebraically diverges in the zero shear rate limit. It is also found that the dynamical susceptibility monotonically decreases with time so that the dynamical heterogeneity is detected by a two-point correlation function. Several exponents that describe rheology, the correlation length, and the amplitude of the dynamical susceptibility are estimated.

Takahiro Hatano

2008-11-09

356

NASA Technical Reports Server (NTRS)

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.

Choi, Sung R.; Gyekenyesi, John P.

2002-01-01

357

On syntheses of the X-ray background with power-law sources

NASA Technical Reports Server (NTRS)

The conditions under which the combined emission from power law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit sleeper spectra at higher energies.

Dezotti, G.; Boldt, E. A.; Cavaliere, A.; Danese, L.; Franceschini, A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.

1981-01-01

358

Power-law scaling of asymmetries in viscous flow with PT-symmetric inflow and outflow

In recent years, open systems with balanced loss and gain, that are invariant under the combined parity and time-reversal ($\\mathcal{PT}$) operations, have been studied via asymmetries of their solutions. They represent systems as diverse as coupled optical waveguides and electrical or mechanical oscillators. We numerically investigate the asymmetries of incompressible viscous flow in two and three dimensions with "balanced" inflow-outflow ($\\mathcal{PT}$-symmetric) configurations. By introducing configuration-dependent classes of asymmetry functions in velocity, kinetic energy density, and vorticity fields, we find that the flow asymmetries exhibit power-law scaling with a single exponent in the laminar regime with the Reynolds number ranging over four decades. We show that such single-exponent scaling is expected for small Reynolds numbers, although its robustness at large values of Reynolds numbers is unexpected. Our results imply that $\\mathcal{PT}$-symmetric inflow-outflow configurations provide a hitherto unexplored avenue to tune flow properties.

Huidan; Yu; Xi Chen; Yousheng Xu; Yogesh N. Joglekar

2014-10-13

359

Collision-dependent power law scalings in two dimensional gyrokinetic turbulence

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.

Cerri, S. S., E-mail: silvio.sergio.cerri@ipp.mpg.de; Bañón Navarro, A.; Told, D. [Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, D-85748 Garching (Germany); Jenko, F. [Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, D-85748 Garching (Germany); Max-Planck/Princeton Center for Plasma Physics (Germany)

2014-08-15

360

NASA Technical Reports Server (NTRS)

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.

Howell, Leonard W.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

361

NASA Astrophysics Data System (ADS)

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poisson’s index ?=0.17±0.01 , which does not depend neither the paper kind and sheet sizes (thickness, edge length) nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poisson’s ratio ?e=0.33±0.01 . This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

Balankin, Alexander S.; Ochoa, Didier Samayoa; León, Ernesto Pineda; de Oca, Rolando Cortes Montes; Rangel, Antonio Horta; Cruz, Miguel Ángel Martínez

2008-03-01

362

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poissons index nu = 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes, nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poissons ratio nu_e = 0.33 pm 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

Alexander S. Balankin; Didier Samayoa Ochoa; Ernesto Pineda Leon; Rolando Cortes Montes de Oca; Antonio Horta Rangel; Miguel Angel Martinez Cruz

2008-08-24

363

NASA Astrophysics Data System (ADS)

The effects of power-law plasticity (yield strength and strain hardening exponent) on the plastic strain distribution underneath a Vickers indenter was systematically investigated by recourse to three-dimensional finite element analysis, motivated by the experimental macro- and micro-indentation on heat-treated Al-Zn-Mg alloy. For meaningful comparison between simulated and experimental results, the experimental heat treatment was carefully designed such that Al alloy achieve similar yield strength with different strain hardening exponent, and vice versa. On the other hand, full 3D simulation of Vickers indentation was conducted to capture subsurface strain distribution. Subtle differences and similarities were discussed based on the strain field shape, size and magnitude for the isolated effect of yield strength and strain hardening exponent.

Chollacoop, Nuwong; Ramamurty, Upadrasta

364

The unipolar induction DC circuit model, originally developed by Goldreich & Lynden-Bell for the Jupiter-Io system, has been applied to different types of binary systems in recent years. We show that there exists an upper limit to the magnetic interaction torque and energy dissipation rate in such model. This arises because when the resistance of the circuit is too small, the large current flow severely twists the magnetic flux tube connecting the two binary components, leading to breakdown of the circuit. Applying this limit, we find that in coalescing neutron star binaries, magnetic interactions produce negligible correction to the phase evolution of the gravitational waveform, even for magnetar-like field strengths. However, energy dissipation in the binary magnetosphere may still give rise to electromagnetic radiation prior to the final merger. For ultra-compact white dwarf binaries, we find that DC circuit does not provide adequate energy dissipation to explain the observed X-ray luminosities of several sources. For exoplanetary systems containing close-in Jupiters or super-Earths, magnetic torque and dissipation are negligible, except possibly during the early T Tauri phase, when the stellar magnetic field is stronger than 10^3G.

Dong Lai

2012-06-17

365

NASA Astrophysics Data System (ADS)

The unipolar induction DC circuit model, originally developed by Goldreich and Lynden-Bell for the Jupiter-Io system, has been applied to different types of binary systems in recent years. We show that there exists an upper limit to the magnetic interaction torque and energy dissipation rate in such a model. This arises because when the resistance of the circuit is too small, the large current flow severely twists the magnetic flux tube connecting the two binary components, leading to the breakdown of the circuit. Applying this limit, we find that in coalescing neutron star binaries, magnetic interactions produce negligible correction to the phase evolution of the gravitational waveform, even for magnetar-like field strengths. However, energy dissipation in the binary magnetosphere may still give rise to electromagnetic radiation prior to the final merger. For ultracompact white dwarf binaries, we find that unipolar induction does not provide adequate energy dissipation to explain the observed X-ray luminosities of several sources. For exoplanetary systems containing close-in Jupiters or super-Earths, the magnetic torque and energy dissipation induced by the orbital motion are negligible, except possibly during the early T Tauri phase, when the stellar magnetic field is stronger than 103 G.

Lai, Dong

2012-09-01

366

The unipolar induction DC circuit model, originally developed by Goldreich and Lynden-Bell for the Jupiter-Io system, has been applied to different types of binary systems in recent years. We show that there exists an upper limit to the magnetic interaction torque and energy dissipation rate in such a model. This arises because when the resistance of the circuit is too small, the large current flow severely twists the magnetic flux tube connecting the two binary components, leading to the breakdown of the circuit. Applying this limit, we find that in coalescing neutron star binaries, magnetic interactions produce negligible correction to the phase evolution of the gravitational waveform, even for magnetar-like field strengths. However, energy dissipation in the binary magnetosphere may still give rise to electromagnetic radiation prior to the final merger. For ultracompact white dwarf binaries, we find that unipolar induction does not provide adequate energy dissipation to explain the observed X-ray luminosities of several sources. For exoplanetary systems containing close-in Jupiters or super-Earths, the magnetic torque and energy dissipation induced by the orbital motion are negligible, except possibly during the early T Tauri phase, when the stellar magnetic field is stronger than 10{sup 3} G.

Lai Dong [Department of Astronomy, Cornell University, Ithaca, NY 14850 (United States)

2012-09-20

367

Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and <0.39 in radius, respectively). Thus, the power law relationship is conserved in Xenopus and C. elegans, while the absolute powers in C. elegans were different from that in Xenopus. Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic C. elegans cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures. PMID:25674063

Arata, Yukinobu; Takagi, Hiroaki; Sako, Yasushi; Sawa, Hitoshi

2015-01-01

368

369

Code of Federal Regulations, 2012 CFR

...2012-07-01 false Duties and powers of administrative...Hearings § 102.35 Duties and powers of administrative... (a) It shall be the duty of the administrative...and affirmations; (2) To grant applications...C. 557; (11) To call, examine, and...

2012-07-01

370

Evidence for two hard X-ray components in double power-law fits to the 1980 June 7 flare

NASA Technical Reports Server (NTRS)

The June 7, 1980 flare at 0312 UT was analyzed with double power-law fits on the basis of SMM hard X-ray burst spectrometer data. The flare is found to consist of seven peaks of characteristic time scale of about 8 sec followed by seven valleys which may contain significant peak components because of overlap. It is suggested that the possibility of thermal spectra for the peaks is unlikely. An investigation of the double power-law parameters through the third and fourth peaks revealed a hysteresis effect in the fourth peak. The present results have been interpreted in terms of a trap plus precipitation model.

Smith, Dean F.; Orwig, Larry E.

1988-01-01

371

A simple marriage model for the power-law behaviour in the frequency distributions of family names

NASA Astrophysics Data System (ADS)

In many countries, the frequency distributions of family names are found to decay as a power law with an exponent ranging from 1.0 to 2.2. In this work, we propose a simple marriage model which can reproduce this power-law behaviour. Our model, based on the evolution of families, consists of the growth of big families and the formation of new families. Preliminary results from the model show that the name distributions are in good agreement with empirical data from Taiwan and Norway.

Wu, Hao-Yun; Chou, Chung-I.; Tseng, Jie-Jun

2011-01-01

372

NASA Astrophysics Data System (ADS)

In several high-energy astrophysical sites, shocks are assumed to produce a power-law distribution of accelerated charged particles (e.g., electrons, protons) and to generate mild to strong magnetic fields, which favours synchrotron emission. For such environments and conditions, we have performed and present here four practical formulas, with different levels of accuracy, for fitting the synchrotron spectral power radiated by a pure power-law particle distribution, with isotropic pitch angle distribution. The first three ones can be useful compared to the fourth one, because of their simplicity, in the case of particle distribution with no high-energy cutoff. However, the fourth formula, the more accurate one, can be of great interest for astrophysical applications (even though it is more complicated) for the more general case of a power-law distribution with high-energy sharp cutoff. The latter is derived for index p within the range, 1 < p < 6, with maximum relative error of less than 0.5 per cent in the case of infinite energy range and of less than 8.2 per cent in the more general case of particle energy with sharp cutoff. The latter is expressed in terms of parameters as functions of index p. These parameters have been fitted with adopting the Levenberg-Marquardt algorithm in log-log scale. According to these formulas, initially derived for the total spectral power, we have then derived (1) the degree of polarization, (2) cooling spectra for a broken power-law distribution and (3) synchrotron self-absorption spectra for both the broken and non-broken power-law distributions. The proposed expressions are relevant for non-thermal astrophysical sources in the sense that by using them one avoids usually complicated and long CPU time calculations, without performing any integration.

Fouka, M.; Ouichaoui, S.

2014-08-01

373

Cascade model of gamma-ray bursts: Power-law and annihilation-line components

NASA Technical Reports Server (NTRS)

If, in a neutron star magnetosphere, an electron is accelerated to an energy of 10 to the 11th or 12th power eV by an electric field parallel to the magnetic field, motion of the electron along the curved field line leads to a cascade of gamma rays and electron-positron pairs. This process is believed to occur in radio pulsars and gamma ray burst sources. Results are presented from numerical simulations of the radiation and photon annihilation pair production processes, using a computer code previously developed for the study of radio pulsars. A range of values of initial energy of a primary electron was considered along with initial injection position, and magnetic dipole moment of the neutron star. The resulting spectra was found to exhibit complex forms that are typically power law over a substantial range of photon energy, and typically include a dip in the spectrum near the electron gyro-frequency at the injection point. The results of a number of models are compared with data for the 5 Mar., 1979 gamma ray burst. A good fit was found to the gamma ray part of the spectrum, including the equivalent width of the annihilation line.

Harding, A. K.; Sturrock, P. A.; Daugherty, J. K.

1988-01-01

374

A Recommended Procedure for Estimating the Cosmic Ray Spectral Parameter of a Simple Power Law

NASA Technical Reports Server (NTRS)

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.

Howell, Leonard W.; Rose, M. Franklin (Technical Monitor)

2000-01-01

375

Critical properties of homogeneous binary trees

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

P. Silvi; V. Giovannetti; S. Montangero; M. Rizzi; J. I. Cirac; R. Fazio

2010-09-10

376

The phase-integral approximation devised by Froeman and Froeman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform-approximation methods.

Rojas, Clara; Villalba, Victor M. [Centro de Fisica IVIC Apdo 21827, Caracas 1020A (Venezuela)

2007-03-15

377

Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges

Summary The classical solution of the steady-state creep problem for a pressurized thick-walled cylinder is based on the power law\\u000a constitutive equation. Several heat resistant steels show, however, the linear dependence of the creep rate on the applied\\u000a stress within a certain stress range. In this paper we apply an extended constitutive equation which includes both the linear\\u000a and the power

Holm Altenbach; Y. Gorash; K. Naumenko

2008-01-01

378

Several time domain fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long range probe-ion direct correlation function and ion-ion dynamic structure factor. Although the power law decay is reminiscent of Debye-Falkenhagen effect yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small w...

Bagchi, Biman

2014-01-01

379

NASA Astrophysics Data System (ADS)

behavior in streams is a complex and dynamic function of both source material supply and event-driven transport. While the primary controls on turbidity behavior across time and space are still not fully understood, recent increases in the availability of high temporal resolution, colocated stream turbidity, and discharge data provide an opportunity for more detailed analysis. Here we examine methods to quantitatively characterize event responses by modeling the shape of turbidity-discharge hysteresis loops. A total of 1559 events from 20 gages in the Mid-Atlantic region of the U.S. were modeled using both previously reported models and new models combining elements of existing models. The results suggest that a more general power law-based model, utilizing both a discharge rate of change term and a "supply" term, allows characterization of a wide range of simple and complex events. Additionally, this study explores a decorrelation approach to address the strong correlation frequently observed between the power law model coefficient (a) and exponent (b), with the goal of exposing the underlying behavior of each parameter individually. An examination of seasonal parameter behavior suggests that this approach may facilitate greater physically based interpretation of the power law coefficient. The power law parameter decorrelation strategy and the loop models examined here provide a step toward the larger goal of understanding the physical controls on turbidity-discharge hysteretic behavior.

Mather, Amanda L.; Johnson, Richard L.

2014-10-01

380

Geophys. J. Int. (2000) 142, 151161 A damage mechanics model for power-law creep and earthquake

of relatively constant strain rate, with a power-law rheology, as observed in laboratory creep test data of accelerating creep results in theto carry out a static load, or `creep', test; that is, holding a eventual RAS #12;152 I. G. Main by stress intensity reduction at the crack tip as the crack grows. Costin (1987

381

Single and Double Power Laws for Cyber-Crimes Richard E Overill and Jantje A M Silomon

Single and Double Power Laws for Cyber-Crimes Richard E Overill and Jantje A M Silomon Department are interpreted in terms of the modus operandi of cyber-criminals as revealed in the CSI survey data. In particular, a distinction between opportunistic cyber-crime and serious organized cyber-crime is found

Overill, Richard E.

382

The particle size distribution (PSD) is commonly used in studies of sediment fluxes, phytoplankton dynamics, and optical scattering from particulates, but little is known about the spatial and temporal variability of this parameter. Here, we analyze in situ laser diffraction measurements of the PSD from a variety of estuarine and open ocean systems. The power law or “Junge-type” distribution provided

C. J. Buonassissi; H. M. Dierssen

2010-01-01

383

This paper investigates convection heat and mass transfer flow in an electrically conducting power law fluid past a vertical porous plate in presence of a transverse magnetic field, thermal radiation, and thermal diffusion. The non–linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method and the resulting similarity equations are solved numerically

B. I. Olajuwon

2010-01-01

384

A formula is developed to compute the maximum amount of work which can be extracted from a given combined mass of warm and cold ocean water (a quantity called the exergy of the ocean thermal resource). The second law efficiencies of various proposed ocean thermal energy conversion power cycles are compared to determine which best utilizes the exergy of the

D. H. Johnson

1982-01-01

385

The variation of the wind profile power-law exponent with respect to changes in surface roughness and atmospheric stability is depicted using the formulation of Nickerson and Smiley for specifying the vertical variations of the horizontal wind. The theoretical estimates of the po...

386

The XMM deep survey in the CDF-S. VI. Obscured AGN selected as infrared power-law galaxies

NASA Astrophysics Data System (ADS)

Context. Accretion onto supermassive black holes is believed to occur mostly in obscured active galactic nuclei (AGN). Such objects are proving rather elusive in surveys of distant galaxies, including those at X-ray energies. Aims: Our main goal is to determine whether the revised IRAC criteria of Donley et al. (2012, ApJ, 748, 142; objects with an infrared (IR) power-law spectral shape), are effective at selecting X-ray type-2 AGN (i.e., absorbed NH > 1022 cm-2). Methods: We present the results from the X-ray spectral analysis of 147 AGN selected by cross-correlating the highest spectral quality ultra-deep XMM-Newton and the Spitzer/IRAC catalogues in the Chandra Deep Field South. Consequently it is biased towards sources with high S/N X-ray spectra. In order to measure the amount of intrinsic absorption in these sources, we adopt a simple X-ray spectral model that includes a power-law modified by intrinsic absorption at the redshift of each source and a possible soft X-ray component. Results: We find 21/147 sources to be heavily absorbed but the uncertainties in their obscuring column densities do not allow us to confirm their Compton-Thick nature without resorting to additional criteria. Although IR power-law galaxies are less numerous in our sample than IR non-power-law galaxies (60 versus 87 respectively), we find that the fraction of absorbed (NHintr > 1022 cm-2) AGN is significantly higher (at about 3 sigma level) for IR-power-law sources (~2/3) than for those sources that do not meet this IR selection criteria (~1/2). This behaviour is particularly notable at low luminosities, but it appears to be present, although with a marginal significance, at all luminosities. Conclusions: We therefore conclude that the IR power-law method is efficient in finding X-ray-absorbed sources. We would then expect that the long-sought dominant population of absorbed AGN is abundant among IR power-law spectral shape sources not detected in X-rays.

Castelló-Mor, N.; Carrera, F. J.; Alonso-Herrero, A.; Mateos, S.; Barcons, X.; Ranalli, P.; Pérez-González, P. G.; Comastri, A.; Vignali, C.; Georgantopoulos, I.

2013-08-01

387

NASA Technical Reports Server (NTRS)

Recent observations indicate that the eclipsing pulsar binary PSR B1957+20 undergoes alternating epochs of orbital period increase and decrease. We apply a model developed to explain orbital period changes of alternating sign in other binaries to the PSR B1957+20 system and find that it fits the pulsars observations well. The novel feature of the PSR B1957+20 system is that the energy flow in the companion needed to power the orbital period change mechanism can be supplied by tidal dissipation, making the companion the first identified tidally powered star. The flow of energy in the companion drives magnetic activity, which underlies the observed orbital period variations. The magnetic activity and the wind driven by the pulsar irradiation results in a torque on the spin of the companion. This torque holds the companion out of synchronous rotation, causing tidal dissipation of energy. We propose that the progenitor had a approximately 2 hr orbital period and a companion mass of 0.1-0.2 solar mass, and the system is evolving to longer orbital periods by mass and angular momentum loss on a timescale of 10(exp 8) yr.

Applegate, James H.; Shaham, Jacob

1994-01-01

388

Scalable Solvers for Optimal Control of a Power-Law Fluid

NASA Astrophysics Data System (ADS)

Inverse problems such as determining internal fields or basal boundary conditions quickly become very large when applied to large glaciers or ice sheets. Millions of degrees of freedom are required to resolve critical flow features in a three dimensional ice sheet model. Traditional inverse methods involve forming and factoring a linearized inverse operator which is a dense matrix. The memory needed to store a single 106 × 106 matrix is 8 terabytes and the CPU cost to factor such a matrix is impractical. Instead, we pose the inverse problem as PDE-constrained optimization and apply fully iterative methods. For our problems, the design and state spaces are mesh-dependent, so we seek a method which scales linearly with respect to both spaces. The recently developed Lagrange-Newton-Krylov-Schur (LNKS) method applies the well-established Newton-Krylov machinery directly to the first-order optimality condition. Unlike reduced space quasi-Newton methods, the Newton iteration displays mesh-independent quadratic convergence and the Krylov iteration will also exhibit mesh-independent convergence if an optimal preconditioner is available. Obtaining an optimal preconditioner is difficult since the Jacobian matrix has saddle point structure and is very poorly conditioned, but Schur complement preconditioning is effective and frequently optimal. Since the incompressible flow constraint also has saddle point structure, we require two levels of Schur complement preconditioning, providing a vast array of choices. For a power-law fluid, globalization by continuation in the exponent is natural but reduced space alternatives are available when the preconditioning matrix is expensive to form. We present a computational study of LNKS and reduced space methods in the context of a novel p-version finite element method which applies the full-order Jacobian matrix-free and assembles a much sparser preconditioning matrix using low-order finite elements. We devote special attention to the design of Schur complement preconditioners which are robust with respect to strength of the power-law nonlinearity since these are critical for efficient forward modeling as well.

Brown, J.

2008-12-01

389

Atmospheric correction of ocean color imagery: Use of Junge power-law size distribution

NASA Astrophysics Data System (ADS)

In this study, a new atmospheric correction algorithm capable of simultaneously retrieving aerosol and ocean optical parameters under the presence of both highly- and weakly-absorbing aerosols has been developed. It is suggested that the radiative properties of realistic aerosols can be well simulated with those resulting from the Junge power-law aerosol models. The use of the latter makes it possible to vary the atmospheric radiative properties continuously through a variation of the aerosol parameters. The atmosphere is assumed to consist of two, plane parallel and horizontally homogeneous, layers with the Fresnel reflecting bottom boundary. The radiative properties of the ocean water are assumed to be those of Case 1 waters. A system of non-linear equations is constructed for the radiances detected by a multi-band remote sensor and, is subsequently solved using non- linear optimization procedures. The algorithm's performance has been studied with simulated test data. It is shown that the aerosol single scattering albedo (?0) and the pigment concentration (C) can be excellently retrieved to within 6% and 10% respectively even under the presence of the instrument calibration errors. However, because of significant differences in the scattering phase functions for the test and power-law distributions, large error is possible in the estimate of the aerosol optical thickness. The positive results for the pigment concentration C suggest that the detailed shape of the aerosol scattering phase function is not needed for the atmospheric correction of ocean color sensors. The relevant parameters are the single scattering albedo and the relative spectral variation of the optical depth. The vertical distribution of aerosols and a spectral variation of the aerosol's refractive index have adverse effects on the accuracy of retrievals. Fortunately, these cases are easily identifiable in the course of non-linear optimization procedure as long as the data ``fit'' objective function SLSQ becomes relatively large, i.e., 5-6%, in contrast to less than 1% in other test cases. The algorithm was incorporated into the SeaWiFS image processing system SeaDAS. The results demonstrate that the algorithm's performance is superior to the NASA Standard Atmospheric Correction algorithm. A significant advantage of the new approach is that realistic multicomponent aerosol models are not required for the retrieval of C.

Chomko, Roman M.

1999-12-01

390

This report describes both the theoretical development and the experimental evaluation of a novel, robust methodology for the time-optimal adjustment of a reactor's neutronic power under conditions of closed-loop digital control. Central to the approach are the MIT-SNL Period-Generated Minimum Time Control Laws' which determine the rate at which reactivity should be changed in order to cause a reactor's neutronic power to conform to a specified trajectory. Using these laws, reactor power can be safely raised by five to seven orders of magnitude in a few seconds. The MIT-SNL laws were developed to facilitate rapid increases of neutronic power on spacecraft reactors operating in an SDI environment. However, these laws are generic and have other applications including the rapid recovery of research and test reactors subsequent to an unanticipated shutdown, power increases following the achievement of criticality on commercial reactors, power adjustments on commercial reactors so as to minimize thermal stress, and automated startups. The work reported here was performed by the Massachusetts Institute of Technology under contract to the Sandia National Laboratories. Support was also provided by the US Department of Energy's Division of University and Industry Programs. The work described in this report is significant in that a novel solution to the problem of time-optimal control of neutronic power was identified, in that a rigorous description of a reactor's dynamics was derived in that the rate of change of reactivity was recognized as the proper control signal, and in that extensive experimental trials were conducted of these newly developed concepts on actual nuclear reactors. 43 refs., 118 figs., 11 tabs.

Bernard, J.A. (Massachusetts Inst. of Tech., Cambridge, MA (USA). Nuclear Reactor Lab.)

1989-09-01

391

propose the use of power laws to describe the topology of the Internet at the autonomous system (AS of the Internet at the autonomous system (AS) level. First, we show that the topology can be described efficiently topology with correlation coefficient above 99% for the degree-based power law. In addition, we study

Faloutsos, Petros

392

Unsteady gravity-driven slender rivulets of a power-law fluid Y. M. Yatim, S. K. Wilson, B. R. Duffy

rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle to the horizontal for the steady gravity-driven spreading of a rivulet of a power-law fluid down an inclined plane which predicts, where x denotes a coordinate measured down the plane and t denotes time. Numerical and asymptotic

Mottram, Nigel

393

A Hard X-ray Power-Law Cutoff in Cen X-4

NASA Astrophysics Data System (ADS)

The LMXB Cen X-4 is the brightest and closest quiescent neutron star (NS) transient. Previous 0.5-10 keV observations in quiescence identified two spectral components: soft thermal emission from the NS atmosphere and a hard power-law tail of unknown origin. We report on a simultaneous observation of Cen X-4 with XMM-Newton (35 ks) and NuSTAR (116 ks) in 2013 January, providing the first sensitive measurement of the hard X-ray spectrum of a quiescent NS/LMXB transient. We clearly detect a cutoff the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. Comptonization is ruled out on physical grounds, while synchrotron shock emission from a pulsar wind is possible but unlikely. The spectrum is well fit by an 18 keV thermal bremsstrahlung model, which can be understood if only a small fraction of the accretion flow eventually reaches the NS. We argue that most of the flow is centrifugally inhibited by the propeller effect. The soft spectrum is consistent with NS atmosphere emission in the presence of extremely weak accretion. We discuss the implications of these results for the X-ray spectra expected from quiescent neutron stars and black holes in LMXB transients.

Chakrabarty, D.; Tomsick, J.; Grefenstette, B.; Psaltis, D.; Barret, D.; Fuerst, F.; Harrison, F.; Nowak, M.; Rana, V.; Stern, D.

2014-07-01

394

Effects of power law primordial magnetic field on big bang nucleosynthesis

Big bang nucleosynthesis (BBN) is affected by the energy density of a primordial magnetic field (PMF). For an easy derivation of constraints on models for PMF generations, we assume a PMF with a power law (PL) distribution in wave number defined with a field strength, a PL index, and maximum and minimum scales at a generation epoch. We then show a relation between PL-PMF parameters and the scale invariant (SI) strength of PMF for the first time. We perform a BBN calculation including PMF effects, and show abundances as a function of baryon to photon ratio $\\eta$. The SI strength of the PMF is constrained from observational constraints on abundances of $^4$He and D. The minimum abundance of $^7$Li/H as a function of $\\eta$ slightly moves to a higher $^7$Li/H value at a larger $\\eta$ value when a PMF exists during BBN. We then discuss degeneracies between the PL-PMF parameters in the PMF effect. In addition, we assume a general case in which both the existence and the dissipation of PMF are possible. It is then found that an upper limit on the SI strength of the PMF can be derived from a constraint on $^4$He abundance, and that a lower limit on the allowed $^7$Li abundance is significantly higher than those observed in metal-poor stars.

Dai G. Yamazaki; Motohiko Kusakabe

2012-12-12

395

A unified econophysics explanation for the power-law exponents of stock market activity

NASA Astrophysics Data System (ADS)

We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.

Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, Eugene

2007-08-01

396

Cosmological Evolution of Einstein-Aether Models with Power-law-like Potential

The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the present work, we study the cosmological evolution of Einstein-Aether models with power-law-like potential, by using the method of dynamical system. In the case without matter, there are two attractors which correspond to an inflationary universe in the early epoch, or a de Sitter universe in the late time. In the case with matter but there is no interaction between dark energy and matter, there are only two de Sitter attractors, and no scaling attractor exists. So, it is difficult to alleviate the cosmological coincidence problem. Therefore, we then allow the interaction between dark energy and matter. In this case, several scaling attractors can exist under some complicated conditions, and hence the cosmological coincidence problem could be alleviated.

Hao Wei; Xiao-Peng Yan; Ya-Nan Zhou

2014-04-15

397

Power Law and Logarithmic Ricci Dark Energy Models in Ho?ava-Lifshitz Cosmology

NASA Astrophysics Data System (ADS)

In this work, we studied the Power Law and the Logarithmic Entropy Corrected versions of the Ricci Dark Energy (RDE) model in a spatially non-flat universe and in the framework of Ho?ava-Lifshitz cosmology. For the two cases containing non-interacting and interacting RDE and Dark Matter (DM), we obtained the exact differential equation that determines the evolutionary form of the RDE energy density. Moreover, we obtained the expressions of the deceleration parameter q and, using a parametrization of the equation of state (EoS) parameter ? D given by the relation ? D (z) = ? 0+? 1 z, we derived the expressions of both ? 0 and ? 1. We interestingly found that the expression of ? 0 is the same for both non-interacting and interacting case. The expression of ? 1 for the interacting case has strong dependence from the interacting parameter b 2. The parameters derived in this work are done in small redshift approximation and for low redshift expansion of the EoS parameter.

Pasqua, Antonio; Chattopadhyay, Surajit; Khurshudyan, Martiros; Myrzakulov, Ratbay; Hakobyan, Margarit; Movsisyan, Artashes

2014-08-01

398

A stable and robust calibration scheme of the log-periodic power law model

NASA Astrophysics Data System (ADS)

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time tc, defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.

Filimonov, V.; Sornette, D.

2013-09-01

399

Pressure effects on electroosmotic flow of power-law fluids in rectangular microchannels

NASA Astrophysics Data System (ADS)

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids.

Vakili, Mohammad Ali; Sadeghi, Arman; Saidi, Mohammad Hassan

2014-08-01

400

Can log-periodic power law structures arise from random fluctuations?

NASA Astrophysics Data System (ADS)

Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable LPPL structures. To this end, we first estimate the stochastic process underlying the DAX log-returns during the period from mid-1997 until end-2003. The employed data set contains about 3.93?106 intraday DAX quotes at a sampling rate of 15 s. Our results indicate that the DAX log-returns can be described as a Markov process. As a consequence, a Langevin equation is derived. Based on this model equation, we run extensive simulations in order to generate 100 synthetic DAX trajectories each covering 3000 trading days. We find LPPL behavior in ten artificial time series. Moreover, we can establish a link between LPPL patterns and ensuing bubble bursts in seven synthetic 600-week windows. However, the LPPL components in most synthetic trajectories differ fundamentally from those LPPL structures that have previously been detected in real financial time series. Summarized, this paper demonstrates that LPPL structures are not necessarily the signature of imitative behavior among investors but can also stem from noise, even though the likelihood of this is extremely low. Thus, our findings confirm with high statistical confidence that the LPPL structures in the DAX development are rooted deeper than only in the random fluctuations of the German stock market.

Wosnitza, Jan Henrik; Leker, Jens

2014-05-01

401

Apparent power-law distributions in animal movements can arise from intraspecific interactions.

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight. PMID:25519992

Breed, Greg A; Severns, Paul M; Edwards, Andrew M

2015-02-01

402

NASA Astrophysics Data System (ADS)

We study the multidimensional aggregation equation {u_t+div(uv)=0, v=-nabla K*u} with initial data in {fancyscript{P}_2left(mathbb R^dright)\\cap Lp left(mathbb R^dright)}. We prove that with biological relevant potential K( x) = | x|, the equation is ill-posed in the critical Lebesgue space {L_{d/(d-1)}left(mathbb R^dright)} in the sense that there exists initial data in {fancyscript{P}_2left(mathbb R^dright)\\cap L_{d/(d-1)}left(mathbb R^dright)} such that the unique measure-valued solution leaves {L_{d/(d-1)}left(mathbb R^dright)} immediately. We also extend this result to more general power-law kernels K( x) = | x| ? , 0 < ? < 2 for p = p s := d/( d + ? - 2), and prove a conjecture in Bertozzi et al. (Comm Pure Appl Math 64(1):45-83, 2010) about instantaneous mass concentration for initial data in {fancyscript{P}_2left(mathbb R^dright)\\cap Lpleft(mathbb R^dright)} with p < p s . Finally, we characterize all the "first kind" radially symmetric similarity solutions in dimension greater than two.

Dong, Hongjie

2011-06-01

403

Measurement of power-law creep parameters by instrumented indentation methods

NASA Astrophysics Data System (ADS)

New experimental methods are developed to measure the uniaxial power-law creep parameters ? and n in the relation ??=?? (?? is the creep strain rate and ? is the creep stress) from indentation data obtained with a conical or pyramidal indenter. The methods are based on an analysis of Bower et al., which relates the indentation creep rate to the uniaxial creep parameters based on simple assumptions about the constitutive behavior (Bower et al., 1993). Using finite element simulations to establish the influences of finite indenter geometry and transients caused by elasticity, the proposed methods are explored experimentally using amorphous selenium as a model material. This material is well suited for the study because it creeps at temperatures slightly above ambient in a load-history independent fashion with a stress exponent close to unity. Indentation creep tests were conducted with a Berkovich indenter using three different loading methods. With a few notable exceptions, the values of both ? and n derived from the indentation data are generally in good agreement with those measured in uniaxial compression tests, thus demonstrating the validity of the approach.

Su, Caijun; Herbert, Erik G.; Sohn, Sangjoon; LaManna, James A.; Oliver, Warren C.; Pharr, George M.

2013-02-01

404

Exact, E = 0, classical and quantum solutions for general power-law oscillators

NASA Technical Reports Server (NTRS)

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.

Nieto, Michael Martin; Daboul, Jamil

1995-01-01

405

Effect of streaming current on helical flows of power law fluids

NASA Astrophysics Data System (ADS)

We highlight the implications of electrokinetic effects on the axially pressure driven flow of a shear-thinning fluid in the gap between two concentric cylinders rotating with a relative angular velocity. Such helical flows are important from a practical perspective, as these may lead to a non-trivial alteration in the axial volume flow rate, owing to a combined interplay of the kinematics, electro-hydrodynamics, and the flow rheology. In particular, our results demonstrate the consequences of the establishment of an induced electrical potential, also known as streaming potential, on the volumetric transport, for shear thinning fluids. Our results demonstrate that an increment in the relative rotational speed induces more electrokinetic resistance into the flow. The flow rate initially decreases with increment in the relative angular speed till it reaches a minima for a given power law index, beyond which it again increases. The analytical and numerical results presented in this work bear significant consequences in the design of novel microfluidic systems governed by electrokinetic effects.

Bandopadhyay, Aditya; Goswami, Prakash; Chakraborty, Suman

2014-12-01

406

Extended Power-Law Decays in BATSE Gamma-Ray Bursts: Signatures of External Shocks?

NASA Astrophysics Data System (ADS)

We present a temporal and spectral analysis of a subset of BATSE GRBs with smooth extended emission tails to search for signatures of the ``early high-energy'' afterglow, i.e., the onset of the afterglow emission that initially peaks in gamma-rays and subsequently evolves into X-Ray, optical, and radio emission according to the internal/external shock model. From our sample of 40 GRBs we find that the temporal decays are best described with a power-law ~ t?, rather than an exponential, with a mean index ~ -2. Spectral analysis shows that ~ 20% of these events are consistent with a fast-cooling synchrotron spectrum for an adiabatic blast wave; three of which are consistent with the blast wave evolution of a jet, with Fv ~ t-p. This behavior suggests that, in some cases, the emission may originate from a narrow jet, possibly consisting of ``nuggets'' whose angular size are less than 1/?, where ? is the bulk Lorentz factor.

Giblin, Timothy W.; Connaughton, Valerie; van Paradijs, Jan; Preece, Robert D.; Briggs, Michael S.; Kouveliotou, Chryssa; Wijers, Ralph A. M. J.; Fishman, Gerald J.

2003-04-01

407

Energies E(N) of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials vary in a convoluted fashion with the particle totalities N. Accurate rigorous upper bounds to these energies, which are amenable to detailed mathematical analysis, are found to comprise terms with smooth, oscillatory, and fluctuating dependences on N. The smooth energy component is obtained as a power series in N(-2/3) with the first two terms corresponding to the bulk and Madelung energies. The oscillatory component possesses the large-N asymptotics given by a product of N(1/(? + 1)), where ? is the power-law exponent, and a function periodic in N(1/3). The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy E(Th)(n) on n, also scales like N(1/(? + 1)). PMID:24050343

Cioslowski, Jerzy; Albin, Joanna

2013-09-14

408

The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in -symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of -symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in -symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the cell. PMID:24983624

Dai, Chao-Qing; Wang, Yan

2014-01-01

409

Scale-free relaxation of a wave packet in a quantum well with power-law tails

NASA Astrophysics Data System (ADS)

We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: a quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ˜x-2 and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.

Miccichè, Salvatore; Buchleitner, Andreas; Lillo, Fabrizio; Mantegna, Rosario N.; Paul, Tobias; Wimberger, Sandro

2013-03-01

410

NASA Astrophysics Data System (ADS)

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.

Shalashilin, Dmitrii V.; Beddard, Godfrey S.; Paci, Emanuele; Glowacki, David R.

2012-10-01

411

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. PMID:23126740

Shalashilin, Dmitrii V; Beddard, Godfrey S; Paci, Emanuele; Glowacki, David R

2012-10-28

412

Application of power laws to low Reynolds number boundary layers on smooth and rough surfaces

Scaling laws for the overlap region of near-wall turbulent flows are of particular interest to turbulence researchers and engineers. For the mean flow at sufficiently high Reynolds numbers, the classical boundary layer theory proposes a logarithmic law for the overlap region. On the other hand, at low Reynolds numbers, refined measurements and direct numerical simulation results indicate that the log

D. J. Bergstrom; M. F. Tachie; R. Balachandar

2001-01-01

413

The origin of tablet boudinage: Results from experiments using power-law rock analogs

NASA Astrophysics Data System (ADS)

We used power-law viscous plasticine ( n = ca. 7) as a rock analog to simulate boudinage of rocks undergoing dislocation creep and brittle fracture. A competent plasticine layer, oriented perpendicular to the main shortening direction, Z, underwent bulk pure flattening inside a less competent plasticine matrix. Computer tomographic analyses of the deformed samples revealed that boudinage results from an initial phase of viscous necking followed by tensile failure along the previously formed necks. The resulting boudins display a polygonal shape in plan-view and are referred to as 'tablet boudins' (in contrast to the square to rectangular shaped chocolate-tablet boudins). The ratio between the plan-view long and short axis, R, ranges from 1.2 to 2.6. The polygonal, non-isometric shape of the tablet boudins can be explained by the strong interaction of concentric and radial tensile fractures. With increasing layer thickness, Hi, the mean diameter of the boudin tablets, Wa, increases, while the number of boudins, N, decreases. Progressive finite strain results in a higher number of the boudins and a smaller mean diameter. The thickness of the boudins, Hf, is almost the same as the initial layer thickness, Hi, while the aspect ratio ( Wd = Wa / Hf) decreases with layer thickness and finite strain. The mean Wd values obtained from all experiments span from ca. 4 to ca. 11. Tablet boudins, described in the present paper, have yet not been described from natural outcrops. The reasons might be that pure flattening strain is not common in nature, and the characterization and evaluation of tablet boudins requires geometrical analysis in three dimensions, which is a difficult task when such structures occur in nature.

Zulauf, J.; Zulauf, G.; Kraus, R.; Gutiérrez-Alonso, G.; Zanella, F.

2011-10-01

414

The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

NASA Astrophysics Data System (ADS)

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.

Borodich, Feodor M.; Galanov, Boris A.; Suarez-Alvarez, Maria M.

2014-08-01

415

The End of the MACHO Era: Limits on Halo Dark Matter from Stellar Halo Wide Binaries

We simulate the evolution of halo wide binaries in the presence of MAssive Compact Halo Objects (MACHOs) and compare our results to the sample of wide binaries of Chaname & Gould (2003). The observed distribution is well fit by a single power law for angular separation, 3.5" 43Msun at the standard local halo density rho_H. This all but removes the last permitted window for a full MACHO halo for masses M > 10^{-7.5}Msun.

Jaiyul Yoo; Julio Chaname; Andrew Gould

2003-10-08

416

NASA Astrophysics Data System (ADS)

We study experimentally, the conductance as a function of porosity for a two dimensional disordered porous media far from the percolation treshold. We used photolithography and electron beam lithography to fabricate a "swiss cheese'' two dimensional porous media. We obtain a power law dependence for the conductance as a function of the porosity in the high porosity region. The exponent is found to be the ratio of two characteristic scales. One of them is not affected by the shape of the obstacles and is equal to the area of the system divided by the area of a single obstacle. The other one is expected to be sensitive to transport properties. The exponent of the power law varies with the size of the system. A simple empirical relation is found for the exponent as a function of the ratio of the area of the system over the area of a single obstacle.

Sánchez, Iván; Reyes, Leonardo; Donoso, Arnaldo; Paredes, Ricardo; Gutiérrez, Gustavo

2003-03-01

417

NASA Astrophysics Data System (ADS)

Mixed traffic without signal control is complicated. This paper proposes a pedestrian-vehicle cellular automata (CA) model to study the characteristics of the mixed traffic. The model includes two sub models. One is the pedestrian model, in which the heterogeneity is taken into consideration. The other is the vehicle model, in which a safely running mode and a normally running mode are introduced. Simulation results show that (1) the traffic flow experiences four phases, that is, free flow, pedestrians-free flow, vehicles-free flow and jams, (2) pedestrians cross the crosswalk in groups and the sizes of the groups obey power law distribution, and (3) the heterogeneity of pedestrians acts an important role in the system. If the pedestrians are simultaneously homogeneous, the mixed traffic flow shows a “polarization” and these power-laws disappear under high arrival rates of vehicles and pedestrians.

Xin, Xiuying; Jia, Ning; Zheng, Liang; Ma, Shoufeng

2014-07-01

418

NASA Astrophysics Data System (ADS)

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.

Brey, J. Javier; Ruiz-Montero, M. J.

2015-01-01

419

A unified approach to the power law and the critical state modeling of superconductors in 2D

NASA Astrophysics Data System (ADS)

Two main options exist for modeling the non-linearity of the superconductor: the power law and the critical state model. A vanishing electric field is predicted by the critical state model, which does not take into account relaxation phenomena. The power law model is to be used if flux creep is to be taken into account. However, detectable flux creep may not occur in many operating conditions. In these cases the critical state represents a more accurate modeling option. The existing numerical tools usually incorporate either the power law with a finite n-exponent or the critical state model, not both. A numerical model which incorporates both the power law and the critical state modeling of superconductors in 2D is developed in this paper. The same mathematical formulation and discretization method are used in both of the cases, and the same matrix equation is obtained. The difference between the two models only arises when the solution of the matrix equation is dealt with. The model is implemented by means of one unique computer code. The discretization can be made by means of both triangular and rectangular meshes. A circuit interpretation of the model is also introduced. The equivalence of the proposed method with the variational approach reported in the literature for dealing with the critical state is also discussed in the paper. The numerical results for some cases of practical interest are presented. The difference between the results obtained by means of the two models in terms of current distribution and ac loss is pointed out.

Morandi, Antonio; Fabbri, Massimo

2015-02-01

420

We show that the dependence of the charged particle multiplicity on the centre-of-mass energy of the collision is, in the String Percolation Model, driven by the same power law behavior in both proton-proton and nucleus- nucleus collisions. The observed different growths are a result of energy- momentum constraints that limit the number of formed strings at low en- ergy. Based on the very good description of the existing data, we provide predictions for future high energy LHC runs.

Irais Bautista; Jorge Dias de Deus; José Guilherme Milhano; Carlos Pajares

2012-04-06

421

Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heated square cylinder in the unsteady cross-flow regime has been studied numerically by solving the relevant momentum and thermal energy equations using a finite-volume method for the range of conditions 0.7 ? Pr ? 50, 60 ? Re ? 160, and 0.5 ? n ? 1.8. Over this range of Reynolds numbers, the flow is truly periodic for Newtonian and

Akhilesh K. Sahu; R. P. Chhabra; V. Eswaran

2009-01-01

422

Modeling of Water Main Failure Rates Using the Log-linear ROCOF and the Power Law Process

This paper presents applications of the log-linear ROCOF and the power law process to model the failure rate and estimate\\u000a the economically optimal replacement time of the individual pipes in a water distribution system. The performance of the two\\u000a failure rate models is examined using the maximized log-likelihoods for different modeling approaches in which the method\\u000a of observing failures differs.

H. Jun; B. J. Kim; G. C. Im

2008-01-01

423

NASA Astrophysics Data System (ADS)

This paper addresses the Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation with power law nonlinearity. First the soliton solution is obtained by the aid of traveling wave hypothesis and along with it the constraint conditions fall out naturally, in order for the soliton solution to exist. Subsequently, the bifurcation analysis of this equation is carried out and the fixed points are obtained. The phase portraits are also analyzed for the existence of other solutions.

Biswas, Anjan; Song, Ming

2013-07-01

424

Pseudo-random binary sequency phase modulation in high power Yb-doped fiber amplifiers

NASA Astrophysics Data System (ADS)

We present experimental and theoretical studies on the stimulated Brillouin scattering (SBS) threshold in fiber amplifiers seeded with a spectrally broadened single-frequency laser source. An electro-optic phase modulator is driven with various pseudo-random binary sequence (PRBS) patterns to highlight the unique characteristics of this linewidth broadening technique and its facility in SBS mitigation. Theoretical predictions show a variation in SBS suppression based on PRBS pattern and modulation frequency. These predictions are experimentally investigated in a kilowatt level monolithic fiber amplifier operating with near diffraction-limited beam quality. We also show Rayleigh scattering and other sources of back reflected light in phase modulated signals can seed the SBS process and significantly reduce the nonlinear threshold.

Robin, Craig; Dajani, Iyad; Zernigue, Clint; Flores, Angel; Pulford, Ben; Lanari, Ann; Naderi, Shadi

2013-03-01

425

NASA Astrophysics Data System (ADS)

Electromagnetic methods of geophysical exploration are a reflection of the spatio-temporal variability in ground conductivity, a macroscopic physical property that is a function of lithology, pore-scale surface chemistry, fracture networks, and the presence and distribution of fluids and partial melts. As such, the bulk electrical properties of some representative elementary volume within the subsurface derive from the macroscopic effect of charge buildup and current pathways across a range of length scales within. Quantifying this relationship between multiscale electrical properties and the observed geophysical data is a critical step toward meaningful geologic interpretation. Previously we presented evidence of near-surface electromagnetic data whose small scale fluctuations are both repeatable and fractally distributed -- an observation that supports the notion of a spatially hierarchical Earth. Bounded by the end member cases from homogenized isotropic and anisotropic media, we present numerical modeling results from textured and spatially-correlated, stochastic geologic media, demonstrating that the electromagnetic response is a power law distribution similar to that seen in the earlier observational data, rather than a smooth response polluted with Gaussian noise as is commonly assumed. Furthermore, we show that such power law behavior is dependent on correlation length within the medium and that the power law distribution of Earth conductivity can be estimated from that of the observed electromagnetic data.

Beskardes, G. D.; Weiss, C. J.; Everett, M. E.

2013-12-01

426

NASA Astrophysics Data System (ADS)

Morphodynamic models of coastal evolution require relatively simple parameterizations of sediment transport for application over larger scales. Calantoni and Thaxton (2008) [6] presented a transport parameterization for bimodal distributions of coarse quartz grains derived from detailed boundary layer simulations for sheet flow and near sheet flow conditions. The simulation results, valid over a range of wave forcing conditions and large- to small-grain diameter ratios, were successfully parameterized with a simple power law that allows for the prediction of the transport rates of each size fraction. Here, we have applied the simple power law to a two-dimensional cellular automaton to simulate sheet flow transport. Model results are validated with experiments performed in the small oscillating flow tunnel (S-OFT) at the Naval Research Laboratory at Stennis Space Center, MS, in which sheet flow transport was generated with a bed composed of a bimodal distribution of non-cohesive grains. The work presented suggests that, under the conditions specified, algorithms that incorporate the power law may correctly reproduce laboratory bed surface measurements of bimodal sheet flow transport while inherently incorporating vertical mixing by size.

Holway, Kevin; Thaxton, Christopher S.; Calantoni, Joseph

2012-11-01

427

Capillary force between a probe tip with a power-law profile and a surface or a nanoparticle

NASA Astrophysics Data System (ADS)

This paper presents a method to exactly calculate the capillary bridge profile and capillary force between a probe tip with a power-law profile and a surface or nanoparticle at various humidities. The shape of the probe tip is denoted by a power-law profile including a shape index, which is a general extension of the usual parabolids. The accuracy of the usual circular approximation of the capillary bridge is investigated, and it is found that great deviations may occur for capillary bridges and capillary forces at nanoscales, especially for the probe tip with a small shape index. The proportion of the capillary pressure force and the surface tension force which constitute the capillary force is also considered. The results show that the surface tension force can even be dominant at nanoscales. The influences of various parameters, including the shape index, equivalent radius of the tip, relative humidity, contact angles and separation distances, on the capillary force between a probe tip with a power-law profile and a surface or nanoparticle are studied. The rupture distances of the liquid bridges at condensation equilibrium and constant volume conditions are also compared.

Wang, Lefeng; Régnier, Stéphane

2015-01-01

428

Orientational dynamics in a liquid crystalline system near the isotropic-nematic (I-N) phase transition is studied using Molecular Dynamics simulations of the well-known Lebwohl-Lasher (LL) model. As the I-N transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate timescales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the I-N boundary. In the mean squared angular displacement at comparable timescales, we observe the emergence of a \\emph{subdiffusive regime} which is followed by a \\emph{superdiffusive regime} before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through \\emph{pronounced non-Gaussian behavior in orientational motion} particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.

Suman Chakrabarty; Dwaipayan Chakrabarti; Biman Bagchi

2006-03-14

429

The FWHM of local pulses and the corresponding power-law index of gamma-ray burst FRED pulses

The FWHM of gamma-ray burst (GRB) pulses is known to be related with energy by a power-law. We wonder if the power-law index $\\alpha$ is related with the corresponding local pulse width $FWHM_0$. Seven FRED (fast rise and exponential decay) pulse GRBs are employed to study this issue, where six of them were interpreted recently by the relativistic curvature effect (the Doppler effect of fireballs) and the corresponding local pulses were intensely studied. A regression analysis shows an anti-correlation between $log \\alpha$ and $log FWHM_0$ with a slope of $-0.37\\pm0.13$. This suggests that, for the class of the GRB pulses which are consequences of the curvature effect, the difference of the local pulse width might lead to the variation of the power law index, where the smaller the width the larger the value of $\\alpha$. Since the number of sources employed in this analysis is small, our result is only a preliminary one which needs to be confirmed by larger samples.

L. -W. Jia; Y. -P. Qin

2005-08-05

430

A central question in community ecology is how the number of trophic links relates to community species richness. For simple dynamical food-web models, link density (the ratio of links to species) is bounded from above as the number of species increases; but empirical data suggest that it increases without bounds. We found a new empirical upper bound on link density in large marine communities with emphasis on fish and squid, using novel methods that avoid known sources of bias in traditional approaches. Bounds are expressed in terms of the diet-partitioning function (DPF): the average number of resources contributing more than a fraction f to a consumer's diet, as a function of f. All observed DPF follow a functional form closely related to a power law, with power-law exponents independent of species richness at the measurement accuracy. Results imply universal upper bounds on link density across the oceans. However, the inherently scale-free nature of power-law diet partitioning suggests that the DPF itself is a better defined characterization of network structure than link density. PMID:21068048

Rossberg, Axel G.; Farnsworth, Keith D.; Satoh, Keisuke; Pinnegar, John K.

2011-01-01

431

This paper reports the design, analysis, evaluation and characterization of closed-loop clean renewable power generation systems. For the aforementioned multi-input\\/multi-output systems, we design proportional-integral and soft-switching sliding mode control laws to guarantee: (1) Efficient mechanical-to-electrical, electrical-to-electrical and electrical-to-chemical energy conversions; (2) Enabling windor hydro-energy harvesting capabilities; (3) Optimal dynamics, robustness and stability. The prototypes of portable high-energy-density power systems were

Trevor C. Smith; Sergey Edward Lyshevski

2011-01-01

432

14 CFR 406.109 - Administrative law judges-powers and limitations.

Code of Federal Regulations, 2011 CFR

...instruct the party to file with the FDMS, a copy of each document that is submitted to the administrative law judge that has not bee filed with FDMS, except the portions of those documents that contain confidential information. (2) The...

2011-01-01

434

We study power law inflation in the context of non-minimally coupled to the scalar curvature. We analyze the inflationary solutions under an exact analysis and also in the slow roll approximation. In both solutions, we consider the recent data from Planck and BICEP2 data to constraint the parameter in our model. We find that the slow roll approximation is disfavored in the presence of non-minimal couplings during the power law expansion of the Universe.

Sergio del Campo; Carlos Gonzalez; Ramon Herrera

2015-01-23

435

We study power law inflation in the context of non-minimally coupled to the scalar curvature. We analyze the inflationary solutions under an exact analysis and also in the slow roll approximation. In both solutions, we consider the recent data from Planck and BICEP2 data to constraint the parameter in our model. We find that the slow roll approximation is disfavored in the presence of non-minimal couplings during the power law expansion of the Universe.

del Campo, Sergio; Herrera, Ramon

2015-01-01

436

High School Forum: Boyle's/Hooke's/Towneley and Power's/Mariotte's Law.

ERIC Educational Resources Information Center

This column for high school teachers, written by high school teachers, discusses several interesting anecdotes related to the formulation of laws and the determination of constants. Science history is presented in a manner that can enliven classroom presentations and aid in understanding the principle itself. (Authur/SA)

Hawthorne, Robert M.; Herron, J. Dudley, Ed.

1979-01-01

437

NASA Astrophysics Data System (ADS)

The reaction of a hydroxyl radical with molecular hydrogen and the respiration in Camellia Japonica are used as examples for studying chemical reaction rate constants by the power-law transition state theory. In the first example, the rate constants are numerically obtained at different temperature and activation energies based on the Morse potential at the potential well and improved potential energy surface 5 (I5B) at the saddle point respectively, and the relationship between the rate constants and the power-law parameter is plotted as well. In the second one, especially, the power-law parameter presents an abrupt change at temperature 290 K around, which may be explained that the Camellia Japonica is the ombrophyte, and the activity of biological enzyme reaches the maximum at this temperature. This theory allows accordance with experimental values by a power-law parameter. It is found that the values of the power-law parameter in both examples deviate from 1 but not too much and lie in the 0-1 range and proved that power-law transition state theory shows a good agreement with experiments.

Zhou, Yanjun; Yin, Cangtao

2015-01-01

438

What if the power-law model did not apply for the prediction of very large rockfall events?

NASA Astrophysics Data System (ADS)

Extreme events are of primary importance for risk management in a variety of natural phenomena, and more particularly for landslides and rockfalls, because they might be associated with huge losses. Numerous research works have addressed this problem based on the same paradigm: if events exhibit the same statistical properties across a broad range of sizes, the probability of extreme events can be evaluated by extrapolating the frequency-size distribution. Considering landslides' areas or rockfalls' volumes, the frequency distribution has been found to be heavy-tailed and the well-known power law distribution has been proposed to model it. Yet, the vision of very large extreme event (catastrophic) frequency being an extrapolation of the power laws fitted on small and intermediate events has been challenged in various contexts, in particular by Sornette and co-authors, who proposed viewing such catastrophic events as "outliers" from the power-law model, i.e. they deviate by an abnormal large distance from the extrapolated prediction. In this study, we address such an issue considering a rockfall inventory, containing >8500 events spanning 8 orders of magnitudes of volume and collated from 2.5 years of high-accuracy repeated terrestrial laser scanning (TLS) surveys on a coastal chalk cliff in Normandy (France). This inventory contains a particularly large event of 70,949 m3 which occurred some time between February 1 and 7 April 2008. It is the second largest cliff failure reported in Normandy, and is larger than those collated in historical cliff failure inventories across various geological and geomorphological coastal settings. Is this event an outlier of the power-law volume-frequency distribution ? And if so, why? This largest event recorded appears to stand out of the rest of the sample. We use it to revisit the techniques to fit power-law distribution with robust techniques (robust weighted maximum likelihood estimator), rarely used in rockfall studies, and presenting the appealing feature to be less sensitive to the presence of outliers by assigning a weight within [0 ; 1] to each observation according to its representativeness. Through a bootstrap-based technique, we demonstrate the statistical significance (with p-value <1 %, i.e. not arising by chance) of the low weight assigned to the largest rockfall event i.e. of the deviation from the fractal set of the smaller events. Excluding gross volumetric error on our observation since we used a high-accuracy TLS, we discuss possible mechanisms and their implications for prediction, focusing on two main issues: 1. normal faults bounding the largest rockfall and along which the rupture occurred, which may suggest the hypothesis of a "characteristic" rockfall, i.e. presenting a characteristic scale of the same order of the fault length, as suggested for earthquakes; 2. possible log-periodic signature that decorates the pure power law and linked with the concept of Discrete Scale Invariance. This concept means that scale invariance is kept, but only for specific scales organized in a discrete hierarchy and with some fixed preferred scaling ratio. Such scaling ratio may itself be linked to pre-existing fracture networks.

Rohmer, J.; Dewez, T.

2012-04-01

439

NASA Astrophysics Data System (ADS)

The choice of which statistical distribution to fit to historical discharge data is critical when attempting to predict the most extreme flows. It has been shown that depending upon the distribution selected, the calculated return periods can vary dramatically. Cunnane (1985) discussed the factors affecting the choice of distribution for river flow series data, and was able to show that small differences in the Extreme Value Type 1 (Gumbel), Type 2, and Type 3 can lead to large differences in the predicted return period. Indeed this divergence increases as the return period becomes larger: a finding which has obvious implications for fluvial management. Despite this, in many studies which fit a frequency-magnitude distribution to fluvial discharge data, the choice of distribution appears driven by regional convention, or even by some other apparently arbitrary factor. Benson (1968) analysed data for ten US stations, and compared the fit using the log-normal, gamma, Gumbel, log-Gumbel, Hazen and log-Pearson type 3 distributions. On the basis of this study alone, the standard approach to flow frequency estimation in the USA became the fitting of a log-Pearson type 3 (LP3) distribution (US Water Resources Council, 1982). While several other countries have adopted a similar approach, usage of the LP3 distribution is not geographically universal. Hydrologists in the United Kingdom conventionally utilise a fitted generalised logistic distribution for flow frequency estimation (Robson and Reed, 1999) while Chinese hydrologists utilise the log-normal distribution (Singh, 2002). Choice of fitted distribution is obviously crucial, since selecting one distribution rather than another will change the estimated probabilities of future droughts and floods, particularly the largest and rarest events. Malamud et al. (1996) showed that a flood of equivalent size to that experienced on the Mississippi in 1993 has a recurrence interval on the order of 100 years when a power-law 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.

Eadie, Chris; Favis-Mortlock, David

2010-05-01

440

Evaluating Power and Type 1 Error in Large Pedigree Analyses of Binary Traits

Studying population isolates with large, complex pedigrees has many advantages for discovering genetic susceptibility loci; however, statistical analyses can be computationally challenging. Allelic association tests need to be corrected for relatedness among study participants, and linkage analyses require subdividing and simplifying the pedigree structures. We have extended GenomeSIMLA to simulate SNP data in complex pedigree structures based on an Amish pedigree to generate the same structure and distribution of sampled individuals. We evaluated type 1 error rates when no disease SNP was simulated and power when disease SNPs with recessive, additive, and dominant modes of inheritance and odds ratios of 1.1, 1.5, 2.0, and 5.0 were simulated. We generated subpedigrees with a maximum bit-size of 24 using PedCut and performed two-point and multipoint linkage using Merlin. We also ran MQLS on the subpedigrees and unified pedigree. We saw no inflation of type 1 error when running MQLS on either the whole pedigrees or the sub-pedigrees, and we saw low type 1 error for two-point and multipoint linkage. Power was reduced when running MQLS on the subpedigrees versus the whole pedigree, and power was low for two-point and multipoint linkage analyses of the subpedigrees. These data suggest that MQLS has appropriate type 1 error rates in our Amish pedigree structure, and while type 1 error does not seem to be affected when dividing the pedigree prior to linkage analysis, power to detect linkage is diminished when the pedigree is divided. PMID:23658753

Cummings, Anna C.; Torstenson, Eric; Davis, Mary F.; D’Aoust, Laura N.; Scott, William K.; Pericak-Vance, Margaret A.; Bush, William S.; Haines, Jonathan L.

2013-01-01

441

NASA Astrophysics Data System (ADS)

This study theoretically and experimentally explores the behaviour of axisymmetric gravity currents of Newtonian and power-law fluids in inhomogeneous porous media. Systematic heterogeneity along the vertical is represented by a power-law permeability variation governed by the parameter ?, mimicking trends in natural media. A self-similar solution describing (i) the rate of propagation and (ii) the profile of the current is derived by considering a current of volume proportional to time raised to a non-negative power ?. Four critical values of ? are determined: the first two affect the time dependency of the radius, height and average gradient of the current on flow behaviour index n and ?; the third one dictates if the current accelerates or decelerates; the fourth one governs the asymptotic validity of the thin current approximation. Experimental validation is performed using shear-thinning suspensions and Newtonian mixtures in constant- and variable-flux regimes. A stratified porous medium composed of four uniform strata of glass beads with different diameters is used for this purpose. The experimental results for the radius and profile of the current agree well with the self-similar solution except at the beginning of the process, due to the limitations of the 1-D assumption and to boundary effects near the injection zone. An uncertainty analysis indicates that the rheological fluid behaviour and the variation in permeability significantly affect the propagation of the current.

Di Federico, Vittorio; Longo, Sandro; Chiapponi, Luca; Archetti, Renata; Ciriello, Valentina

2014-08-01

442

High-potential Working Fluids for Next Generation Binary Cycle Geothermal Power Plants

A thermo-economic model has been built and validated for prediction of project economics of Enhanced Geothermal Projects. The thermo-economic model calculates and iteratively optimizes the LCOE (levelized cost of electricity) for a prospective EGS (Enhanced Geothermal) site. It takes into account the local subsurface temperature gradient, the cost of drilling and reservoir creation, stimulation and power plant configuration. It calculates and optimizes the power plant configuration vs. well depth. Thus outputs from the model include optimal well depth and power plant configuration for the lowest LCOE. The main focus of this final report was to experimentally validate the thermodynamic properties that formed the basis of the thermo-economic model built in Phase 2, and thus build confidence that the predictions of the model could be used reliably for process downselection and preliminary design at a given set of geothermal (and/or waste heat) boundary conditions. The fluid and cycle downselected was based on a new proprietary fluid from a vendor in a supercritical ORC cycle at a resource condition of 200?C inlet temperature. The team devised and executed a series of experiments to prove the suitability of the new fluid in realistic ORC cycle conditions. Furthermore, the team performed a preliminary design study for a MW-scale turbo expander that would be used for a supercritical ORC cycle with this new fluid. The following summarizes the main findings in the investigative campaign that was undertaken: 1. Chemical compatibility of the new fluid with common seal/gasket/Oring materials was found to be problematic. Neoprene, Viton, and silicone materials were found to be incompatible, suffering chemical decomposition, swelling and/or compression set issues. Of the materials tested, only TEFLON was found to be compatible under actual ORC temperature and pressure conditions. 2. Thermal stability of the new fluid at 200?C and 40 bar was found to be acceptable after 399 hours of exposure?only 3% of the initial charge degraded into by products. The main degradation products being an isomer and a dimer. 3. In a comparative experiment between R245fa and the new fluid under subcritical conditions, it was found that the new fluid operated at 1 bar lower than R245fa for the same power output, which was also predicted in the Aspen HSYSY model. As a drop-in replacement fluid for R245fa, this new fluid was found to be at least as good as R245fa in terms of performance and stability. Further optimization of the subcritical cycle may lead to a significant improvement in performance for the new fluid. 4. For supercritical conditions, the experiment found a good match between the measured and model predicted state point property data and duties from the energy balance. The largest percent differences occurred with densities and evaporator duty (see Figure 78). It is therefore reasonable to conclude that the state point model was experimentally validated with a realistic ORC system. 5. The team also undertook a preliminary turbo-expander design study for a supercritical ORC cycle with the new working fluid. Variants of radial and axial turbo expander geometries went through preliminary design and rough costing. It was found that at 15MWe or higher power rating, a multi-stage axial turbine is most suitable providing the best performance and cost. However, at lower power ratings in the 5MWe range, the expander technology to be chosen depends on the application of the power block. For EGS power blocks, it is most optimal to use multi-stage axial machines. In conclusion, the predictions of the LCOE model that showed a supercritical cycle based on the new fluid to be most advantageous for geothermal power production at a resource temperature of ~ 200C have been experimentally validated. It was found that the cycle based on the new fluid is lower in LCOE and higher in net power output (for the same boundary conditions). The project, therefore has found a new optimal configuration for low temperature geothermal power production in the form of a su

Zia, Jalal [GE Global Research; Sevincer, Edip; Chen, Huijuan; Hardy, Ajilli; Wickersham, Paul; Kalra, Chiranjeev; Laursen, Anna Lis; Vandeputte, Thomas

2013-06-29

443

PHYSICAL REVIEWS 8 VOLUME 37, NUMBER 13 1 MAY 1988 Power-law fading of the frnstration eS'ect in a periodic rectanlnlar snpercondncting neiwork with increasing aspect ratio Chia-Ren Hu and Raymond Lei Chen Department of Physics, Center.... This means that those cusps in the T,2/T, o vs @/@p curve asso- ciated with a larger integer denominator q fade away fas- ter than those associated with a smaller q, leaving a less CHIA-REN HU AND RAYMOND I.EI CHEN "jerky" T,q/T, o vs +/4p curve at larger...

Hu, Chia-Ren; CHEN, RL.

1988-01-01

444

NASA Astrophysics Data System (ADS)

A similarity solution of the steady magnetohydrodynamic (MHD) mixed convection boundary layer flow due to a stretching vertical heated sheet in a power law nanofluid with thermal radiation effect is theoretically studied. The governing system of partial differential equations is first transformed into a system of ordinary differential equations. The transformed equations are solved numerically using the shooting method. The influence of pertinent parameters such as the nanoparticle volume fraction parameter, the magnetic parameter, the buoyancy or mixed convection parameter and the radiation parameter on the flow and heat transfer characteristics is discussed. Comparisons with published results are also presented.

Aini Mat, Nor Azian; Arifin, Norihan Md.; Nazar, Roslinda; Ismail, Fudziah; Bachok, Norfifah

2013-09-01

445

NASA Astrophysics Data System (ADS)

While sophisticated numerical computational techniques can calculate the hyperpolarizabilities of complex molecules, it is not clear what scale invariant parameters determine a large nonlinear response. We investigate the first and second intrinsic hyperpolarizabilities of one-dimensional power-law potentials with a hybrid analytical semiclassical analysis of energy spectra and numerical calculations of eigenfunctions. By varying the exponent, we determine how key underlying properties drive the nonlinear response as the system smoothly varies from particle in a box, harmonic oscillator, point charge potential, to all multipolar Coulomb potentials. The role of the well-known pathology of the 1/x2 potential is also discussed.

Mossman, Sean M.; Kuzyk, Mark G.

2013-09-01

446

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. PMID:18986181

Digilov, Rafael M

2008-12-01

447

Second Law Analysis for Process and Energy Engineering: Use in a Steam/Power Cycle

exergy value per unit of heat CQuid have been used. e. Using fuel to heat the entering combustion air, which Is at ambient temperature. The foregoing observations are qualitative rather than quantitative, and even without quantification they can... not -- the 2nd law concept, exergy, does .- represent ?potentlal to cause change: Nevertheless, energy is an important scientific concept. It Is a key to the modelling of natural phenomena and systems. (By no means do we advocate replacing ?energy analysis...

Sama, D.; Sanhong, Q.

448

22 CFR 1423.19 - Duties and powers of the Administrative Law Judge.

Code of Federal Regulations, 2013 CFR

...Foreign Relations 2 2013-04-01 2009-04-01 true Duties and powers of the...PROCEEDINGS § 1423.19 Duties and powers of the... It shall be the duty of the Administrative...7(d); (f) Call, examine and cross-examine...1423.11(e) (2) and (3);...

2013-04-01

449

22 CFR 1423.19 - Duties and powers of the Administrative Law Judge.

Code of Federal Regulations, 2012 CFR

...Foreign Relations 2 2012-04-01 2009-04-01 true Duties and powers of the...PROCEEDINGS § 1423.19 Duties and powers of the... It shall be the duty of the Administrative...7(d); (f) Call, examine and cross-examine...1423.11(e) (2) and (3);...

2012-04-01

451

Optical Variability of Infrared Power Law-Selected Galaxies & X-ray Sources in the GOODS-South Field

We investigate the use of optical variability to identify and study Active Galactic Nuclei (AGN) in the GOODS-South field. A sample of 22 mid-infrared power law sources and 102 X-ray sources with optical counterparts in the HST ACS images were selected. Each object is classified with a variability significance value related to the standard deviation of its magnitude in five epochs separated by 45-day intervals. The variability significance is compared to the optical, mid-IR, and X-ray properties of the sources. We find that 26% of all AGN candidates (either X-ray- or mid-IR-selected) are optical variables. The fraction of optical variables increases to 51% when considering sources with soft X-ray band ratios. For the mid-IR AGN candidates which have multiwavelength SEDs, we find optical variability for 64% of those classified with SEDs like Broad Line AGNs. While mostly unobscured AGN appear to have the most significant optical variability, some of the more obscured AGNs are also observed as variables. In particular, we find two mid-IR power law-selected AGN candidates without X-ray emission that display optical variability, confirming their AGN nature.

Alison Klesman; Vicki Sarajedini

2007-05-07