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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

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

3

Power laws, Pareto distributions and Zipf's law

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For

Mej Newman

2005-01-01

4

NASA Astrophysics Data System (ADS)

Stellar mass black holes in certain types of binary systems accrete matter from their companion stars through rotating, turbulent flows known as accretion disks. These disks are observed by space X-ray missions to have a number of distinct spectral/variability states, the most mysterious one being the very high/steep power law state that generally occurs at very high luminosities. This state is particularly interesting as it exhibits unique quasi-periodic oscillations observed in the X-rays that, if understood, might help us directly measure the properties of the black hole spacetime. Radiation pressure is an important physical process at such high luminosities, and modifies the character of the accretion disk in a number of unique ways. One of the ways that it does this is that it enables turbulent speeds in the disk to exceed thermal speeds of electrons, thereby introducing a completely new radiation process - turbulent Comptonization. This radiation process is promising for explaining the unique spectral characteristics of the very high/steep power law state. We will test this hypothesis by making detailed calculations of the emergent radiation spectrum from numerical simulation data of the turbulence in local patches of the disk at high levels of radiation pressure. These will be the first detailed theoretical calculations of turbulent Comptonization, which should be an important process for modeling NASA data from high luminosity black hole accretion. We hope that this will shed light on the nature of the mysterious very high/steep power law state. The research will form the basis of the PhD thesis of a graduate student, in line with NASA's educational and training objectives.

Blaes, Omer

5

Zipf's law, power laws, and maximum entropy

Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to economics to linguistics to zoology, and even warfare. A recent model of random group formation [RGF] attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present article I argue that the cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.

Visser, Matt

2012-01-01

6

Zipf's law, power laws, and maximum entropy

Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation [RGF] attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present article I argue that the cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.

Matt Visser

2013-04-07

7

Power Laws are Disguised Boltzmann Laws

NASA Astrophysics Data System (ADS)

Using a previously introduced model on generalized Lotka-Volterra dynamics together with some recent results for the solution of generalized Langevin equations, we derive analytically the equilibrium mean field solution for the probability distribution of wealth and show that it has two characteristic regimes. For large values of wealth, it takes the form of a Pareto style power law. For small values of wealth, w<=wm, the distribution function tends sharply to zero. The origin of this law lies in the random multiplicative process built into the model. Whilst such results have been known since the time of Gibrat, the present framework allows for a stable power law in an arbitrary and irregular global dynamics, so long as the market is ``fair'', i.e., there is no net advantage to any particular group or individual. We further show that the dynamics of relative wealth is independent of the specific nature of the agent interactions and exhibits a universal character even though the total wealth may follow an arbitrary and complicated dynamics. In developing the theory, we draw parallels with conventional thermodynamics and derive for the system some new relations for the ``thermodynamics'' associated with the Generalized Lotka-Volterra type of stochastic dynamics. The power law that arises in the distribution function is identified with new additional logarithmic terms in the familiar Boltzmann distribution function for the system. These are a direct consequence of the multiplicative stochastic dynamics and are absent for the usual additive stochastic processes.

Richmond, Peter; Solomon, Sorin

8

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

9

Binary-flashing geothermal power plants

Binary-flashing units utilize new types of geothermal power cycles, which may be used with resources of relatively low temperatures (less than 150 C) where other cycles result in very low efficiencies. The thermodynamic cycles for the binary-flashing units are combinations of the geothermal binary and flashing cycles. They have most of the advantages of these two conventionally used cycles, but

Z. Yuan; E. E. Michaelides

1993-01-01

10

Power Laws in Firm Productivity

NASA Astrophysics Data System (ADS)

We estimate firm productivity for about 3.2 million firms from30 countries. We find that the distribution of firm productivity in each country, which is measured by total factor productivity (TFP), has a power law upper tail. However, the power law exponent of a TFP distribution in a country tends to be greater than that of a sales distribution in that country, indicating that the upper tail of a TFP distribution is less heavy compared to that of a sales distribution. We also find that the power law exponent of a TFP distribution tends to be greater than the power law exponents associated with the number of workers or tangible fixed assets. Given the idea that the sales of a firm is determined by the amount of various inputs employed by the firm (i.e., ``production function'' in the terminology of economics), these results suggest that the heavy tail of a sales distribution in a country comes not from the tail of a TFP distribution, but from the tail of the distribution of the number of workers or tangible fixed assets.

Mizuno, T.; Ishikawa, A.; Fujimoto, S.; Watanabe, T.

11

Power colours: simple X-ray binary variability comparison

NASA Astrophysics Data System (ADS)

We demonstrate a new method of variability classification using observations of black hole X-ray binaries. Using `power colours' - ratios of integrated power in different Fourier frequency bands - we can clearly differentiate different canonical black hole states as the objects evolve during outburst. We analyse (˜2400) Rossi X-ray Timing Explorer observations of 12 transient low-mass black hole X-ray binaries and find that the path taken around the power colour-colour diagram as the sources evolve is highly consistent from object to object. We discuss how the consistency observed in the power colour-colour diagram between different objects allows for easy state classification based on only a few observations, and show how the power-spectral shapes can be simply classified using a single parameter, the power-spectral `hue'. To illustrate the benefits of our simple model-independent approach, we show that the persistent high-mass X-ray binary Cyg X-1 shows very similar power-spectral evolution to the transient black hole sources, with the main difference being caused by a combination of a lack of quasi-periodic oscillations and an excess of low-frequency power-law noise in the Cyg X-1 power spectra during the transitional state. We also compare the transient objects to the neutron star atoll source Aquila X-1, demonstrating that it traces a different path in the power colour-colour plot. Thus, power colours could be an effective method to classify newly discovered X-ray binaries.

Heil, L. M.; Uttley, P.; Klein-Wolt, M.

2015-04-01

12

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

13

The Expressive Power of Binary Submodular Functions

We investigate whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This question has been considered within several different contexts in computer science, including computer vision, artificial intelligence, and pseudo-Boolean optimisation. Using a connection between the expressive power of valued constraints and certain algebraic properties of functions,

Stanislav Zivný; David A. Cohen; Peter G. Jeavons

2009-01-01

14

Small sample estimation for Taylor's power law

An analysis of counts of sample size N=2 arising from a survey of the grass Bromus commutatus identified several factors which might seriously affect the estimation of parameters of Taylor's power law for such small sample sizes. The small sample estimation of Taylor's power law was studied by simulation. For each of five small sample sizes, N=2, 3, 5, 15

S. J. Clark; J. N. Perry

1994-01-01

15

First law of mechanics for black hole binaries with spins

NASA Astrophysics Data System (ADS)

We use the canonical Hamiltonian formalism to generalize to spinning point particles the first law of mechanics established for binary systems of nonspinning point masses moving on circular orbits [A. Le Tiec, L. Blanchet, and B. F. Whiting, Phys. Rev. D 85, 064039 (2012)PRVDAQ1550-7998]. We find that the redshift observable of each particle is related in a very simple manner to the canonical Hamiltonian and, more generally, to a class of Fokker-type Hamiltonians. Our results are valid through linear order in the spin of each particle, but hold also for quadratic couplings between the spins of different particles. The knowledge of spin effects in the Hamiltonian allows us to compute spin-orbit terms in the redshift variable through 2.5PN order, for circular orbits and spins aligned or anti-aligned with the orbital angular momentum. To describe extended bodies such as black holes, we supplement the first law for spinning point-particle binaries with some “constitutive relations” that can be used for diagnosis of spin measurements in quasi-equilibrium initial data.

Blanchet, Luc; Buonanno, Alessandra; Le Tiec, Alexandre

2013-01-01

16

The Expressive Power of Binary Submodular Functions

We investigate whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a\\u000a possibly larger set of variables. This question has been considered within several different contexts in computer science,\\u000a including computer vision, artificial intelligence, and pseudo-Boolean optimisation. Using a connection between the expressive\\u000a power of valued constraints and certain algebraic properties of functions,

Stanislav Zivný; David A. Cohen; Peter G. Jeavons

2009-01-01

17

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

18

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

19

Injection molding of power-law polymer

NSDL National Science Digital Library

A polymer in injected with a constant pressure gradient between two parallel plates. The progression of the polymer front is modeled for a power law fluid (typical of a polymer) and compared to results for a Newtonian fluid.

Krane, Matthew J. M.

2008-10-25

20

Power-Law Distributions in Empirical Data

Power-law distributions occur in many situations of scientific interest and\\u000ahave significant consequences for our understanding of natural and man-made\\u000aphenomena. Unfortunately, the detection and characterization of power laws is\\u000acomplicated by the large fluctuations that occur in the tail of the\\u000adistribution -- the part of the distribution representing large but rare events\\u000a-- and by the difficulty of

Aaron Clauset; Cosma Rohilla Shalizi; Mark E. J. Newman

2009-01-01

21

Advanced Binary Geothermal Power Plants Limits Of Performance

The Heat Cycle Research Program is currently investigating the potential improvements to power cycles uti 1 izing 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

C. J. Bliem; G. L. Mines

1990-01-01

22

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

23

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

24

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

25

Relativity, nonextensivity, and extended power law distributions.

A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory. PMID:16383791

Silva, R; Lima, J A S

2005-11-01

26

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

27

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

28

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

29

Fractal power law in literary English

NASA Astrophysics Data System (ADS)

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.

Gonçalves, L. L.; Gonçalves, L. B.

2006-02-01

30

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

31

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

32

Neutrino processes with power law dispersion relations

We compute various processes involving neutrinos in the initial and/or final state and we assume that neutrinos have energy momentum relation with a general power law $E^2 =p^2+ \\xi_n p^n$ correction due to Lorentz invariance violation. We find that for $n>2$ the bounds on $\\xi_n$ from direct time of flight measurement are much more stringent than from constraining the neutrino Cerenkov decay process.

Subhendra Mohanty; Soumya Rao

2012-05-11

33

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 the nouns may change, but the underlying questions are similar in many

34

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

2012-04-02

35

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

36

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

37

Power-law spatial dispersion from fractional Liouville equation

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)] [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

2013-10-15

38

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

39

Long-term power-law fluctuation in Internet traffic

Power-law fluctuation in observed Internet packet flow are discussed. The data is obtained by a multi router traffic grapher (MRTG) system for 9 months. The internet packet flow is analyzed using the detrended fluctuation analysis. By extracting the average daily trend, the data shows clear power-law fluctuations. The exponents of the fluctuation for the incoming and outgoing flow are almost unity. Internet traffic can be understood as a daily periodic flow with power-law fluctuations.

Shin-ichi Tadaki

2007-06-11

40

Equipment of the binary-cycle geothermal power unit at the Pauzhet geothermal power station

NASA Astrophysics Data System (ADS)

The equipment of and technological processes in the pilot industrial model of the domestically produced binary-cycle geothermal power unit operating on the discharge separate at the Pauzhet geothermal power station are considered. The development principles, the design and operational features, and the data on selecting the metal in manufacturing the main equipment of the 2.5-MW binary power unit of the geothermal power station are described.

Tomarov, G. V.; Nikol'skii, A. I.; Semenov, V. N.; Shipkov, A. A.

2014-06-01

41

Small power systems for law enforcement applications

NASA Astrophysics Data System (ADS)

Recent events have increased interest in the use of sensors by law enforcement and homeland defense related organizations. Autonomous sensors such as those under development for the Unattended Ground Sensor (UGS) program are suitable for some of these applications. The operational lifetime of a UGS depends on the power consumption of the package and the space allocated for batteries. We survey and assess options for powering these devices ina long-term scenario. These alternatives are in various stages of development, and range from conventional batteries and solar cells that are ready for deployment and are now commercially available; to technologies developed for other applications (e.g., power for deep-space probes, man portable power for soldiers, or for sensors in oil drilling bore holes) that would need to be adapted to UGS's; to new and often speculative concepts that are in the laboratory or are still on the drawing board. Ideally, unattended ground sensors do not require servicing, re- energizing or refueling; and are capable of autonomous operation for weeks or even years. Further, UGS's may need to be used covertly, which restricts schemes that would provide a detectable signature. Reliability, ruggedness, cost, weight, size, camouflaging, use of toxic materials and other safety or disposal aspects, restrictions on their deployment (e.g., whether UGS's can be dropped form the air or whether they need to be uprighted or favorably oriented), storage and inventorying considerations, temperature ranges of operation, and complexity of associated electronics are also important issues. In this paper, we will limit the discussion to systems where operating power does not exceed 5 watts since larger systems are commercially available. Some subjectivity in comparisons is perhaps inevitable, but despite the disparate physics upon which these devices are based, a few common criteria can be invoked for discussing their suitability for energy storage and powering UGS's. Metrics can be developed to assess and compare options, but since most of the options are in very different stages of development, one is sometimes forced to use performance specifications that are predicted, rather than demonstrated. Thus, in some cases the comparisons are tentative or speculative.

Sims, Paul E.; Mauk, Michael G.; Sulima, Oleg V.

2002-08-01

42

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

43

Two samples test for discrete power-law distributions

Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn from the same power-law distribution.

Bessi, Alessandro

2015-01-01

44

Power-Colours: Simple X-ray Binary Variability Comparison

We demonstrate a new method of variability classification using observations of black hole X-ray binaries. Using `power colours' -- ratios of integrated power in different Fourier frequency bands -- we can clearly differentiate different canonical black hole states as the objects evolve during outburst. We analyse (~ 2400) Rossi X-ray Timing Explorer observations of 12 transient low mass black hole X-ray binaries and find that the path taken around the power colour-colour diagram as the sources evolve is highly consistent from object to object. We discuss how the consistency observed in the power colour-colour diagram between different objects allows for easy state classification based on only a few observations, and show how the power-spectral shapes can be simply classified using a single parameter, the power-spectral `hue'. To illustrate the benefits of our simple model-independent approach, we show that the persistent high mass X-ray binary Cyg X-1 shows very similar power-spectral evolution to the transi...

Heil, L M; Klein-Wolt, M

2014-01-01

45

Power law exponents characterizing human DNA

NASA Astrophysics Data System (ADS)

The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc(S) of size S present long tails Pnc(S)˜S-1-?nc , with exponents ?nc ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments Pc(S) in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.

Provata, A.; Oikonomou, Th.

2007-05-01

46

Power law models of stock indices

NASA Astrophysics Data System (ADS)

Viewing the stock market as a self-organized system, Sornette and Johansen introduced physics-based models to study the dynamics of stock market crashes from the perspective of complex systems. This involved modeling stock market Indices using a mathematical power law exhibiting log-periodicity as the system approaches a market crash, which acts like a critical point in a thermodynamic system. In this dissertation, I aim to investigate stock indices to determine whether or not they exhibit log-periodic oscillations, according to the models proposed by Sornette, as they approach a crash. In addition to analyzing stock market crashes in the frequency domain using the discrete Fourier transform and the Lomb-Scargle periodogram, I perform a detailed analysis of the stock market crash models through parameter estimation and model testing. I find that the probability landscapes have a complex topography and that there is very little evidence that these phase transition-based models accurately describe stock market crashes.

Tse, Man Kit

47

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

48

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 ?(on/off) ? 1.6, especially if ?(on) ? ?(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. PMID:24655179

Amecke, Nicole; Heber, André; Cichos, Frank

2014-03-21

49

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

50

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

51

Evolution of power law distributions in science and society

NASA Astrophysics Data System (ADS)

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.

Jeon, Young-Pyo; McCoy, Benjamin J.

2005-09-01

52

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

53

Power-Law Entropic Corrections to Newton's Law and Friedmann Equations

A possible source of black hole entropy could be the entanglement of quantum fields in and out the horizon. The entanglement entropy of the ground state obeys the area law. However, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. Inspired by the power-law corrections to entropy and adopting the viewpoint that gravity emerges as an entropic force, we derive modified Newton's law of gravitation as well as the corrections to Friedmann equations. In a different approach, we obtained power-law corrected Friedmann equation by starting from the first law of thermodynamics at apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a power-law corrected relation. Our study shows a consistency between the obtained results of these two approaches. We also examine the time evolution of the total entropy including the power-law corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon and show that the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.

Ahmad Sheykhi; Seyed Hossein Hendi

2011-08-07

54

Shifted powers in binary recurrence sequences

NASA Astrophysics Data System (ADS)

Let $u_k$ be a Lucas sequence. A standard technique for determining the perfect powers in the sequence $u_k$ combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approach is the fact that the equation $u_k=x^n$ can be translated into a ternary equation of the form $a y^2=b x^{2n}+c$ (with $a$, $b$, $c \\in \\mathbb{Z}$) for which Frey curves are available. In this paper we consider shifted powers in Lucas sequences, and consequently equations of the form $u_k=x^n+c$ which do not typically correspond to ternary equations with rational unknowns. However, they do, under certain hypotheses, lead to ternary equations with unknowns in totally real fields, allowing us to employ Frey curves over those fields instead of Frey curves defined over $\\mathbb{Q}$. We illustrate this approach by showing that the quaternary Diophantine equation $x^{2n} \\pm 6 x^n+1=8 y^2$ has no solutions in positive integers $x$, $y$, $n$ with $x$, $n>1$.

Bennett, Michael A.; Dahmen, Sander R.; Mignotte, Maurice; Siksek, Samir

2015-03-01

55

Power-law inflation from the rolling tachyon

Modeling the potential by an inverse square law in terms of the tachyon field [V(T)=betaT-2] we find an exact solution for a spatially flat isotropic universe. We show that for beta>2(3)\\/3 the model undergoes power-law inflation. A way to construct other exact solutions is specified and exemplified.

Alexander Feinstein; F ´ õsica Teorica

2002-01-01

56

Power Law Discounting for N-Gram Language Models

We present an approximation to the Bayesian hierarchical Pitman-Yor process language model which maintains the power law distribution over word tokens, while not requiring a computationally expensive approximate inference process. This approximation...

Huang, Songfang; Renals, Steve

2010-01-01

57

The applicability of power-law frequency statistics to floods

Many natural hazards satisfy power-law (fractal) frequency-size statistics to a good approximation for medium and large events. Examples include earthquakes, volcanic eruptions, asteroid impacts, landslides, and forest fires. A major question is whether this is also true for floods. A number of authors have argued in favor of the applicability of power-law statistics to floods. We discuss these arguments and

Bruce D. Malamud; Donald L. Turcotte

2006-01-01

58

The evolution of the power law k-essence cosmology

NASA Astrophysics Data System (ADS)

We investigate the evolution of the power law k-essence field in FRWL spacetime. The autonomous dynamical system and critical points are obtained. The corresponding cosmological parameters, such as ? ? and w ? , are calculated at these critical points. We find it is possible to achieve an equation of state crossing through -1 for k-essence field. The results we obtained indicate that the power law k-essence dark energy model can be compatible with observations.

Yang, Rongjia; Chen, Bohai; Li, Jun; Qi, Jingzhao

2015-04-01

59

Optical monitoring for power law fluids during spin coating.

Optical monitoring is applied, in situ and in real time, to non-newtonian, power law fluids in the spin coating process. An analytical exact solution is presented for thickness evolution that well fits to most measurement data. As result, typical rheological parameters are obtained for several CMC (carboximetilcelullose) concentrations and rotation speeds. Optical monitoring thus precisely indicates applicability of the model to power law fluids under spin coating. PMID:22330554

Jardim, P L G; Michels, A F; Horowitz, F

2012-01-30

60

Soliton solutions with power-law nonlinearity in inhomogeneous media

NASA Astrophysics Data System (ADS)

We construct the relation between the variable coefficient nonlinear Schrödinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schrödinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.

Dai, Chao-Qing; Yu, Fang-Bo

2013-04-01

61

Power spectra of sinusoidal amplitude-modulated binary signals

NASA Technical Reports Server (NTRS)

Power spectra for binary phase-shift keyed (PSK) and frequency-shift keyed (FSK) signals with combined sinusoidal amplitude modulation by the bit rate clock are presented. Such signal formats have application in 'burst' communication systems wherein reliable bit synchronization is provided with relative receiver simplicity. Effects of the clock amplitude modulation index and phase are considered, and corresponding power spectra are illustrated. Further, effects of the clock parameters on the rate of spectral rolloff are given and compared with those of conventional PSK and FSK spectra.

Gee, T. H.; Geist, J. M.

1976-01-01

62

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

63

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

64

Raft River 5MW power plant: A small binary power plant

The Raft River 5MW power plant is a binary cycle pilot plant. The system uses isobutane in a dual boiling cycle. This cycle was selected because the well field and temperatures were not well known at the time of cycle selection, and therefore, a boiling cycle was desirable. The dual boiling features provides about 15 to 20% more power and

J. F. Whitbeck; E. G. Dibello; L. F. Walrath

1982-01-01

65

Leakage Current: Moore's Law Meets Static Power

Abstract: for some time. Figure 1shows total chip dynamic and static power consumptiontrends based on 2002 statistics normalizedto the 2001 International Technology Roadmapfor Semiconductors.The ITRS projects adecrease in dynamic power per device over time.However, if we assume a doubling of on-chipdevices every two years, total dynamic power willincrease on a per-chip basis. Packaging and coolingcosts as well as the limited

Nam Sung Kim; Todd M. Austin; David Blaauw; Trevor N. Mudge; Krisztián Flautner; Jie S. Hu; Mary Jane Irwin; Mahmut T. Kandemir; Narayanan Vijaykrishnan

2003-01-01

66

Henry's law, surface tension, and surface adsorption in dilute binary mixtures

NASA Astrophysics Data System (ADS)

Equilibrium properties of dilute binary fluid mixtures are studied in two-phase states on the basis of a Helmholtz free energy including the gradient free energy. The solute partitioning between gas and liquid (Henry's law) and the surface tension change ?? are discussed. A derivation of the Gibbs law ?? =-T? is given with ? being the surface adsorption. Calculated quantities include the derivatives dTc/dX and dpc/dX of the critical temperature and pressure with respect to the solute molar fraction X and the temperature-derivative (??/?T)cx,p of the surface tension at fixed pressure p on the coexistence surface. Here (??/?T)cx,p can be both positive and negative, depending on the solute molecular size and the solute-solvent interaction, and diverges on the azeptropic line. Explicit expressions are given for all these quantities in the van der Waals model.

Onuki, Akira

2009-03-01

67

The Distance-Decay Function of Geographical Gravity Model: Power Law or Exponential Law?

The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be explained with the ideas from Euclidean geometry. This results in what is called dimension dilemma. In particular, the gravity model based on power law could not be derived from general principles by traditional ways. Consequently, a negative exponential function substituted for the inverse power function to serve for a distance-decay function for the gravity model. However, the exponential-based gravity model goes against the first law of geography. This paper is devoted to solve these kinds of problems by mathematical reasoning and empirical analysis. First, it can be proved that the distance exponent of the gravity model is essentially a fractal dimension. Thus the dimensional dilemma of the power-based gravity model can be resolved using the concepts from fractal geometry. Second, the exponential fun...

Chen, Yanguang

2015-01-01

68

APPROXIMATING POWER OF THE UNCONDITIONAL TEST FOR CORRELATED BINARY PAIRS.

We provide a simple and good approximation of power of the unconditional test for two correlated binary variables. Suissa and Shuster (1991) described the exact unconditional test. The most commonly used statistical test in this setting, McNemar's test, is exact conditional on the sum of the discordant pairs. Although asymptotically the conditional and unconditional versions coincide, a long-standing debate surrounds the choice between them. Several power approximations have been studied for both methods (Miettinen, 1968; Bennett and Underwood, 1970; Connett, Smith, and McHugh, 1987; Connor, 1987; Suissa and Shuster, 1991; Lachenbruch, 1992; Lachin, 1992). For the unconditional approach most existing power approximations use the Gaussian distribution, while the accurate ("exact") method is computationally burdensome. A new approximation uses the F statistic corresponding to a paired-data T test computed from the difference scores of the binary outcomes. Enumeration of all possible 2 × 2 tables for small sample sizes allowed evaluation of both test size and power. The new approximation compares favorably to others due to the combination of ease of use and accuracy. PMID:24465078

Selicato, Grace R; Muller, Keith E

1998-01-01

69

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

70

Testing power-law cosmology with galaxy clusters

Power-law cosmologies, in which the cosmological scale factor evolves as a power law in the age, $a \\propto t^{\\alpha}$ with $\\alpha \\ga 1$, regardless of the matter content or cosmological epoch, is comfortably concordant with a host of cosmological observations.} {In this article, we use recent measurements of the X-ray gas mass fractions in clusters of galaxies to constrain the $\\alpha$ parameter with curvature $k = \\pm1, 0$. We find that the best fit happens for an open scenario with the power index $\\alpha = 1.14 \\pm 0.05$, though the flat and closed model can not be rule out at very high confidence level.} {Our results are in agreement with other recent analyses and show that the X-ray gas mass fraction measurements in clusters of galaxies provide a complementary test to the power law cosmology.

Zong-Hong Zhu; Ming Hu; J. S. Alcaniz; Yu-Xing Liu

2007-12-21

71

A law of mixtures for transport properties in binary particulate composites

A connected-grain model was developed earlier to explain mechanical and thermal properties of porous ceramics and sedimentary rocks. We have now generalized this model for binary particulate composites, based on simulation of a connected-grain structure of individual components of the composites by randomly selecting individual grains and shrinking them. Repetition of this procedure results in a structure of a binary particulate composite that contains channels of individual components, through which transport occurs. We developed a generalized law of mixtures in which transport properties are expressed as scaling relationships that depend on the shrinking parameter expressed as an exponent. This parameter provides the skewness of the distribution of the grains. The model is compared with various transport properties of binary composites reported in the literature. In addition, the model is tested on YBa{sub 2}Cu{sub 3}O{sub x} superconductors and Ag composites that were fabricated in our laboratory and tested for electrical conductivity and elastic modulus. This test demonstrates how the model predicts two entirely different transport properties through their common microstructure and grain-size distribution. {copyright} {ital 1998 American Institute of Physics.}

Duncan, K.L.; Lodenquai, J.F. [Physics Department, University of the West Indies, Mona, Kingston 7 (Jamaica)] [Physics Department, University of the West Indies, Mona, Kingston 7 (Jamaica); Wagh, A.S.; Goretta, K.C. [Energy Technology Division, Argonne National Laboratory, Argonne, Illinois 60439-4838 (United States)] [Energy Technology Division, Argonne National Laboratory, Argonne, Illinois 60439-4838 (United States)

1998-09-01

72

Power-law creep behavior of a semiflexible chain

NASA Astrophysics Data System (ADS)

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell’s viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain’s creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain’s end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain’s stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Majumdar, Arnab; Suki, Béla; Rosenblatt, Noah; Alencar, Adriano M.; Stamenovi?, Dimitrije

2008-10-01

73

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

74

There is More than a Power Law in Zipf

NASA Astrophysics Data System (ADS)

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf's Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto's or Benford's, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf's law for the largest cities. This pathology is reflected in the fact that Zipf's Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call `coherence' and it corresponds to a `screening' between various elements of the set. We show how it should be accounted for when fitting Zipf's Law.

Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano

2012-11-01

75

8Four-thirds power law for knots and links

. The symmetric ener- gy3 is given by S(K)=(|dx r||dy r|)/ 2 K K If K is the centre curve of a radiating tube, T-radiation of the tube. A natural 4/3 power law relates rope length to measures based on inverse-square laws (including is sharp. Consider the Hopf link of two tori in its natural geo- metrical position. Fill each torus with N

Buck, Greg

76

Testing power-law cross-correlations: rescaled covariance test

NASA Astrophysics Data System (ADS)

We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range cross-correlated processes. Utilizing a heteroskedasticity and auto-correlation robust estimator of the long-term covariance, we develop a test with desirable statistical properties which is well able to distinguish between short- and long-range cross-correlations. Such test should be used as a starting point in the analysis of long-range cross-correlations prior to an estimation of bivariate long-term memory parameters. As an application, we show that the relationship between volatility and traded volume, and volatility and returns in the financial markets can be labeled as the power-law cross-correlated one.

Kristoufek, Ladislav

2013-10-01

77

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

78

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

79

The applicability of power-law frequency statistics to floods

NASA Astrophysics Data System (ADS)

Many natural hazards satisfy power-law (fractal) frequency-size statistics to a good approximation for medium and large events. Examples include earthquakes, volcanic eruptions, asteroid impacts, landslides, and forest fires. A major question is whether this is also true for floods. A number of authors have argued in favor of the applicability of power-law statistics to floods. We discuss these arguments and consider a number of examples, using both instrumental records and paleoflood studies. In our analyses we consider both annual and partial-duration flood series. We argue that use of annual floods for statistical considerations strongly biases the flood-frequency estimates, as in some years, the annual flood will be much smaller than a number of 'statistically independent' floods (partial-duration floods) in other years. We examine six USGS hydrologic stations with drainage areas from 41 to 95,300 km 2, representing very different climatic regions and hydrologic conditions, and with periods of records ranging from 74 to 110 water years. Excellent power-law fits to each partial-duration series are found taking Q˜ T?, with Q the discharge associated with the recurrence interval T, and the power-law exponent ? ranging from 0.27 to 0.90. We also consider paleoflood estimates for Axehandle Alcove on the Colorado River and Bonza Alcove on the Paria River, and find that that power-law extrapolations based on instrumental partial-duration series for stations in each of these two areas is within a half order of magnitude when compared to their respective paleoflood estimates. Finally, we consider an alternative approach to extreme streamflows that has been proposed, examining the cumulative probability distribution of instrumental daily mean streamflows. We show that this distribution is in good agreement with the power-law correlation found using the partial-duration series.

Malamud, Bruce D.; Turcotte, Donald L.

2006-05-01

80

The power law relationship for landslide fatality data

NASA Astrophysics Data System (ADS)

In recent years there has been considerable interest in the nature of the power law relationship in landslide area and volume datsets. In other hazards, similar fat-tailed power law distributions have been observed for loss data. For example, both earthquake fatality datasets for large events (Knopoff and Sornette 1995) and for flood losses (Pisarenko 1998) have been shown to display power law distributions. Data from very large rockslope failures also suggests that fat tailed power law distributions may describe the occurrence of fatalities associated with these events (Evans et al. 2006). However, there has been a lack of rigorous analysis of the statistical distributions for fatality datasets for all landslide events, which is unfortunate given the potential use of this data to examine potential losses from forecast events. This paper examines nine years of rainfall induced landslide data from the Durham Fatal Landslide database, which provides records losses of life from landslides on a global basis. It is demonstrated that the landslide fatality data exhibits a clear fat tailed power law distribution. A roll-over is noted for events with small numbers of fatalities (i.e. one or two deaths per event), suggesting under-sampling in that part of the distribution. Examination of this roll-over for the data for individual years suggests that its magnitude is becoming smaller, which in turn implies that the quality of the dataset may be improving with time. An examination is made of the power law distribution for different geographical areas; it is suggested that differences in the scaling of the dataset may be related to a combination of the physical conditions associated with the landslides themselves (e.g. topography, climate, geology and land cover) and the social setting (e.g. population density, household size and wealth).

Petley, D. N.

2011-12-01

81

Fractional-power-law level statistics due to dynamical tunneling.

For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power law of the level-spacing distribution P(s) over a wide range of small spacings s. Going beyond Berry-Robnik statistics, we take into account that dynamical tunneling rates between the regular and the chaotic region vary over many orders of magnitude. This results in a prediction of P(s) which excellently describes the spectral data of the standard map. Moreover, we show that the power-law exponent is proportional to the effective Planck constant h(eff). PMID:21405229

Bäcker, Arnd; Ketzmerick, Roland; Löck, Steffen; Mertig, Normann

2011-01-14

82

Power-law cosmologies in minimal and maximal gauged supergravity

In this paper we search for accelerating power-law solutions and ekpyrotic solutions within minimal and maximal four dimensional supergravity theories. We focus on the STU model for N=1 and on the new CSO(p,q,r) theories, which were recently obtained exploiting electromagnetic duality, for N=8. In the minimal case we find some new ekpyrotic solutions, while in the maximal case we find some new generic power-law solutions. We do not find any new accelerating solutions for these models.

J. Blåbäck; A. Borghese; S. S. Haque

2013-03-13

83

Power-law phenomena in adhesive de-bonding

NASA Astrophysics Data System (ADS)

Acoustic emission (AE) was recorded during the peeling of pressure-sensitive adhesive (PSA) tapes from their surfaces. The viscous and non-linear behavior of PSA tapes produces significant energy dissipation in the form of adhesive fibril formation, elongation and final failure within the peel zone. AE generated during the peeling process corresponds to the final de-bonding event, in which elastic energy is rapidly released to the substrate. The recording and analyzing of AE generated during peeling is used here in a novel application for characterizing microscopic de-bonding events. Present results indicate that the distribution of AE event magnitudes have the form of power-laws and the power spectral densities have the form of flicker noise. Both power-law dependencies and flicker noise are recognized as consequences of SOC in homogeneous systems. A significant feature of power-law dependencies is the absence of any characteristic length or time scales. The present results, however, indicate that the interface is not homogeneous and that pre-existing surface conditions cause non-uniform adhesive bonding. This is heavily supported by the literature regarding the nature of engineering surfaces. Consequentially, Mandelbrot's fractal concepts were applied to characterize the heterogeneous adhesive interface, and to investigate the relation of interfacial structure with the power-law features of the PSA de-bonding process. It is concluded that fractally distributed variations in adhesive bond strengths at the PSA-glass interface produce the observed hyperbolic distributions in AE events. All the formalism of SOC: applies under this alternative explanation of PSA de-bonding phenomena because of the observed hyperbolic distributions of the AE data. It may be that the explanation based on an underlying fractal structure may be a more general explanation to power law and flicker noise phenomena than the SOC model for heterogeneous systems.

Kendall, Gay

84

Reciprocity and the Emergence of Power Laws in Social Networks

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local

Michael Schnegg

2006-01-01

85

Shock wave shape on power law leading edges

Computations using the Direct Simulation Monte Carlo method are presented for hypersonic flow on power law shaped leading edges. The primary aim of this paper is to examine the geometry effect of such leading edges on the shock wave structure. The sensitivity of the shock wave shape and shock standoff distance to shape variations of such leading edges is calculated

W. F. N. Santos

2005-01-01

86

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

87

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

88

Constraints on cosmological parameters in power-law cosmology

NASA Astrophysics Data System (ADS)

In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H0 (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ?CDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H0 average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ?CDM model as q ? ?1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.

Rani, Sarita; Altaibayeva, A.; Shahalam, M.; Singh, J. K.; Myrzakulov, R.

2015-03-01

89

John Yoo's War Powers: The Law Review and the World

John Yoo’s 1996 The Continuation of Politics by Other Means: The Original Understanding of War Powers is surely among the most consequential articles ever to appear in the California Law Review. Five years after its publication, Yoo became the principal theorist of the Bush administration's War on Terrorism policies. His expansive theory of presidential primacy became the legal basis for

Janet Cooper Alexander

2012-01-01

90

Life cycle assessment of geothermal binary power plants using enhanced low-temperature reservoirs

Geothermal binary power plants that use low-temperature heat sources have gained increasing interest in the recent years due to political efforts to reduce greenhouse gas emissions and the consumption of finite energy resources. The construction of such plants requires large amounts of energy and material. Hence, the question arises if geothermal binary power plants are also environmentally promising from a

Stephanie Frick; Martin Kaltschmitt; Gerd Schröder

2010-01-01

91

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

92

Second law analysis of a conventional steam power plant

NASA Astrophysics Data System (ADS)

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.

1993-11-01

93

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

94

Swings between accretion and rotation power in binary millisecond pulsars

NASA Astrophysics Data System (ADS)

Neutron stars in low mass X-ray binaries can be spun-up to millisecond rotational periods by accreting the matter transferred by a companion star. When the rate of mass transfer decreases at the end of this Gyr-long X-ray bright phase, a radio pulsar powered by the rotation of the neutron star magnetic field turns on. Recently, the evolutionary link between these two classes of sources was finally proven by the XMM-Newton discovery of an accreting millisecond X-ray pulsar, previously seen as a rotation-powered radio pulsar. This source is the prototype of a new class of transitional systems that can alternate between accretion and rotation-powered states in response to variations of the rate of mass in-flow, on time scales as short as a couple of weeks. Observations of this and other similar systems indicate that transitions to the accretion phase not only involve bright X-ray outbursts, but also a fainter intermediate X-ray state, possibly caused by centrifugal inhibition of the matter in-fall. I will review the main observed properties, as well as prospects of finding more sources of this newly established class.

Papitto, A.

2014-07-01

95

Deviation from Power Law Behavior in Landslide Phenomenon

NASA Astrophysics Data System (ADS)

Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law behavior in landslide phenomenon. Figure shows that a rollover of landslide size distribution in the small size end is produced as the probability for V/S (the failure volume to failure surface ratio of landslide) exceeding the mechanical threshold applied to the power law distribution of landslide volume.

Li, L.; Lan, H.; Wu, Y.

2013-12-01

96

There is More than a Power Law in Zipf

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law. PMID:23139862

Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano

2012-01-01

97

Power-law behavior of power spectra in low Prandtl number Rayleigh-Bénard convection.

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics. PMID:11580703

Paul, M R; Cross, M C; Fischer, P F; Greenside, H S

2001-10-01

98

Power-law distribution in Japanese racetrack betting

Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds $P_o(x)$ indicates a clear power law $P_o(x)\\propto 1/x$, where $x$ represents the final odds. This power law can be explained on the basis of the assumption that that every bettor bets his money on the horse that appears to be the strongest in a race.

Ichinomiya, T

2006-01-01

99

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

100

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

101

The Bretherton problem in a power-law fluid

NASA Astrophysics Data System (ADS)

Understanding the movement of drops and bubbles in microchannels is increasingly important in the design and operation of microfluidic devices that involve two-phase flows. Thus, Bretherton's analysis of the motion of long bubbles in tubes [F P Bretherton, J Fluid Mech, 10:166-188 (1961)] and the associated profile of the wetting film around it are relevant. In this work, Bretherton's problem is revisited in the case where the wetting film between the bubble interface and the capillary wall is non-Newtonian and described by the power-law constitutive relation. Using the standard lubrication analysis, the equation for the thickness of the wetting film as a function of axial distance is derived and integrated to find the film thickness. The film thickness and pressure drop across the entire bubble are found to scale with the capillary number as Ca^2/3, with a proportionality factor that depends on the power-law index.

Nadim, Ali; Borhan, Ali

2003-11-01

102

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

103

Quasi-power laws in multiparticle production processes

We review the ubiquitous presence in multiparticle production processes of quasi-power law distributions (i.e., distributions following pure power laws for large values of the argument but remaining finite, usually exponential, for small values). Special emphasis is placed on the conjecture that this reflects the presence in the produced hadronic systems of some intrinsic fluctuations. If described by parameter q they form, together with the scale parameter $T$ ("temperature"), basis of Tsallis distribution, ${f(X)\\sim [1 - (1-q)X/T]^{1/(1-q)}}$, frequently used to describe the relevant distributions (the X being usually a transverse momentum). We discuss the origin of such quasi-power law behavior based on our experience with the description of multiparticle production processes. In particular, we discuss Tsallis distribution with complex nonextensivity parameter q and argue that it is needed to describe log-oscillations as apparently observed in recent data on large momentum distributions in very high energy p-p collisions.

Grzegorz Wilk; Zbigniew W?odarczyk

2015-03-30

104

Power law scaling in Universal Extra Dimension scenarios

We study the power law running of gauge, Yukawa and quartic scalar couplings in the universal extra dimension scenario where the extra dimension is accessed by all the standard model fields. After compactifying on an $S_1 /Z_2$ orbifold, we compute one-loop contributions of the relevant Kaluza-Klein (KK) towers to the above couplings up to a cutoff scale $\\Lambda$. Beyond the scale of inverse radius, once the KK states are excited, these couplings exhibit power law dependence on $\\Lambda$. As a result of faster running, the gauge couplings tend to unify at a relatively low scale, and we choose our cutoff also around that scale. For example, for a radius $R \\sim 1 TeV^{-1}$, the cutoff is around 30 TeV. We then examine the consequences of power law running on the triviality and vacuum stability bounds on the Higgs mass. We also comment that the supersymmetric extension of the scenario requires $R^{-1}$ to be larger than $\\sim 10^{10}$ GeV in order that the gauge couplings remain perturbative up to the scale where they tend to unify.

Gautam Bhattacharyya; Anindya Datta; Swarup Kumar Majee; Amitava Raychaudhuri

2006-11-14

105

Development of Jet Noise Power Spectral Laws Using SHJAR Data

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. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.

Khavaran, Abbas; Bridges, James

2009-01-01

106

NASA Astrophysics Data System (ADS)

The paper presents an analysis of two-dimensional zero pressure gradient (ZPG) turbulent boundary layers (TBL) with regard to the application of power laws. Only TBL with low Reynolds number 300 < Re?2 < 6200 are taken into account. It is found that a certain region of the mean velocity profile can be described with a power law of the formu +=C Pow{*}y +a. This power law region is not a priori identical with the overlap region. An algorithm for the determination of the wall skin friction using the power law is proposed. The method was applied with good result to ZPG TBL and to adverse pressure gradient (APG) TBL. To bridge the gap between the wall and the power law region an approach for the turbulent viscosity is suggested.

Buschmann, Matthias

2000-03-01

107

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

108

1 Experimental verification of the usefulness of the nth power law MOSFET model under hot In this paper the usefulness of the nth power law MOSFET model under Hot Carrier Injection (HCI) wearout has analyzed under different HCI conditions and the nth power law MOSFET model has been extracted for each

Paris-Sud XI, Université de

109

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.

110

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

111

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

112

Non-equilibrium thermodynamics of dark energy on the power-law entropy corrected apparent horizon

We investigate the Friedmann-Robertson-Walker (FRW) universe (containing dark energy) as a non-equilibrium (irreversible) thermodynamical system by considering the power-law correction to the horizon entropy. By taking power-law entropy area law which appear in dealing with the entanglement of quantum fields in and out the horizon, we determine the power-law entropy corrected apparent horizon of the FRW universe.

M. Umar Farooq; Mubasher Jamil

2011-11-24

113

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

114

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

115

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

116

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

117

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

118

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

119

Inverse Power Law distribution and failure initiation of subaerial landslides

NASA Astrophysics Data System (ADS)

Landslides are sometimes considered together with other natural hazards, such as earthquakes and fires, as a cascading avalanche or self-organized critical process, where the disturbance initiates in one or a few locations and propagates to the entire region. This view stems from numerous studies of subaerial landslides that show an inverse power law size distribution. Inverse power law distributions are the result of additive avalanche processes, in which the final size cannot be predicted at the onset of the disturbance. However, the observation of a large number of small separate subaerial landslides being triggered by a single earthquake, such as the 1994 Northridge earthquake, is incompatible with a cascading hypothesis and suggests instead that failure occurs simultaneously in many locations within the area affected by ground shaking. Unlike submarine landslides, which are found on large uniformly dipping slopes, a single large landslide scarp cannot form on land because of the heterogeneous morphology and short slope distances of tectonically-active subaerial regions. However, for a given earthquake magnitude, the total area affected by subaerial landslides is shown to be comparable to the affected area calculated by slope stability analysis for submarine landslides and is thus predictable. We show a statistical similarity between morphological attributes of the affected area and area distribution of the landslides from the Northridge earthquake, which suggests that area distribution of subaerial landslides may be determined by the morphology of the affected area, not by the initiation process.

ten Brink, U. S.; Barkan, R.; Andrews, B. D.; Chaytor, J. D.

2009-12-01

120

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 wherein gamma and zeta function regulation is employed. The key reason for the surprising accuracy of the ideal boson and ideal fermion cases resides in the asymptotic freedom or equivalently the Feynman "parton" structure of the ultra-high energy tails of spectral functions.

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

2015-02-07

121

An inverse method for rheometry of power-law fluids

NASA Astrophysics Data System (ADS)

This paper is concerned with the determination of the constitutive viscous parameters of dilute solutions of xanthan gum by means of an inverse method used in conjunction with finite element modeling of the governing system of partial differential equations. At low concentrations xanthan gum behaves as a shear-thinning, power-law non-Newtonian fluid. Finite element modeling is used to simulate the pressure-driven flow of xanthan gum solutions in a microchannel T-junction. As the flow is forced to turn the corner of the T-junction a range of shear rates, and hence viscosities, is produced. It is shown that the statistical properties of the velocity field are sensitive to the constitutive parameters of the power-law model. The inverse method is shown to be stable and accurate, with measurement error in the velocity field translating to small errors in the rheological parameter estimation. Due to the particular structure of the inverse map, the error propagation is substantially less than the estimate from the Hadamard criterion.

Hemaka Bandulasena, H. C.; Zimmerman, William B.; Rees, Julia M.

2011-12-01

122

Limit Laws for the Randic Index of Random Binary Tree Models

We investigate the Randic index of random binary trees under two standard probability models: the one induced by random permutations and the Catalan (uniform). In both cases the mean and variance are computed by recurrence methods and shown to be asymptotically linear in the size of the tree. The recursive nature of binary search trees lends itself in a natural

Qunqiang Feng; Hosam M. Mahmoud; Alois Panholzer

2006-01-01

123

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 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

124

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

125

Deviations from uniform power law scaling in nonstationary time series

NASA Technical Reports Server (NTRS)

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.

Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.

1997-01-01

126

Molecular clouds have power-law probability distribution functions

NASA Astrophysics Data System (ADS)

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 Herschel/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 AK ? 0.1 and 0.2 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 AK ? 0.1 mag, limiting our ability to investigate more complex models for the shape of the cloud PDF.

Lombardi, Marco; Alves, João; Lada, Charles J.

2015-04-01

127

Unexpected power-law stress relaxation of entangled ring polymers.

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. PMID:18953345

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

2008-12-01

128

An effective quintessence field with a power-law potential

NASA Astrophysics Data System (ADS)

In this paper, we consider an effective quintessence scalar field with a power-law potential interacting with a P b = ?q? 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.

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

2015-04-01

129

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

2014-10-28

130

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

131

Limit laws for the Randi? index of random binary tree models

We investigate the Randi? index of random binary trees under two standard probability models: the one induced by random permutations\\u000a and the Catalan (uniform). In both cases the mean and variance are computed by recurrence methods and shown to be asymptotically\\u000a linear in the size of the tree. The recursive nature of binary search trees lends itself in a natural

Qunqiang Feng; Hosam M. Mahmoud; Alois Panholzer

2008-01-01

132

Screw Expanders Increase Output and Decrease the Cost of Geothermal Binary Power Plant Systems

1. ABSTRACT A study has been carried out on the feasibility of using screw expanders, as an alternative to turbines, in three types of binary systems, suitable for recovering power from liquid dominated brines. The maximum power that one machine can generate is of the order of 1-3 MW per unit, depending on the type of system, and the brine

Ian K Smith; Nikola Stosic; Ahmed Kovacevic

133

Power-Law Template for Infrared 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 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ?(sup Beta)B(?, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.

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

2012-01-01

134

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

135

A Hard X-Ray Power-law Spectral Cutoff in Centaurus X-4

NASA Astrophysics Data System (ADS)

The low-mass X-ray binary (LMXB) Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1× 1033 D^2_kpc erg s-1, with sime60% in the thermal component. We clearly detect a cutoff of the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. We show that thermal Comptonization and synchrotron shock origins for the hard X-ray emission are ruled out on physical grounds. However, the hard X-ray spectrum is well fit by a thermal bremsstrahlung model with kTe = 18 keV, which can be understood as arising either in a hot layer above the neutron star atmosphere or in a radiatively inefficient accretion flow. The power-law cutoff energy may be set by the degree of Compton cooling of the bremsstrahlung electrons by thermal seed photons from the neutron star surface. Lower thermal luminosities should lead to higher (possibly undetectable) cutoff energies. We compare Cen X-4's behavior with PSR J1023+0038, IGR J18245-2452, and XSS J12270-4859, which have shown transitions between LMXB and radio pulsar modes at a similar X-ray luminosity.

Chakrabarty, Deepto; Tomsick, John A.; Grefenstette, Brian W.; Psaltis, Dimitrios; Bachetti, Matteo; Barret, Didier; Boggs, Steven E.; Christensen, Finn E.; Craig, William W.; Fürst, Felix; Hailey, Charles J.; Harrison, Fiona A.; Kaspi, Victoria M.; Miller, Jon M.; Nowak, Michael A.; Rana, Vikram; Stern, Daniel; Wik, Daniel R.; Wilms, Jörn; Zhang, William W.

2014-12-01

136

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

137

Conductivity scaling in supercritical percolation of nanoparticles--not a power law.

The power-law behavior widely observed in supercritical percolation systems of conductive nanoparticles may merely be a phenomenological approximation to the true scaling law not yet discovered. In this work, we derive a comprehensive yet simple scaling law and verify its extensive applicability to various experimental and numerical systems. In contrast to the power law which lacks theoretical backing, the new scaling law is explanatory and predictive, and thereby helpful to gain more new insights into percolation systems of conductive nanoparticles. PMID:25631331

Li, Jiantong; Östling, Mikael

2015-02-28

138

Gaussian-type light bullets in power-law nonlinear media with PT-symmetric potentials

NASA Astrophysics Data System (ADS)

The (3+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearities in two kinds of PT-symmetric potentials is investigated, and two kinds of Gaussian-type light bullet (LB) solutions are analytically derived. Based on these analytical solutions, the powers, power-flow densities and the phase switches are discussed. The linear stability analysis and the direct numerical simulation show that LB solutions are stable only when the imaginary parts of PT-symmetric potentials are below some thresholds in the focusing power-law nonlinear media, while they are always unstable in the defocusing power-law nonlinear media.

Chen, Yi-Xiang; Dai, Chao-Qing

2015-03-01

139

Raft River 5MW power plant: A small binary power plant

NASA Astrophysics Data System (ADS)

The Raft River 5MW power plant is a binary cycle pilot plant. The system uses isobutane in a dual boiling cycle. This cycle was selected because the well field and temperatures were not well known at the time of cycle selection, and therefore, a boiling cycle was desirable. The dual boiling features provides about 15 to 20% more power and makes the output less sensitive to changes in geothermal temperature changes than a single boiler system. The plant design was based upon a 290F geothermal fluid temperature at the inlet to the plant and has a gross nominal generator rating of 5MW; however, actual output will vary according to ambient wet bulb temperatures over a range from 4.4MW to 6.2MW with the actual plant inlet temperature of 278F being obtained. The plant is supplied by three production wells. Geothermal fluid boost pumps within the plant inlet provide the pressure necessary to overcome plant pressure drop and return the fluid to the two injection sites.

Whitbeck, J. F.; Dibello, E. G.; Walrath, L. F.

1982-06-01

140

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

141

Power laws and fractal behavior in nuclear stability, atomic weights and molecular weights

Power laws and fractal behavior in nuclear stability, atomic weights and molecular weights V. Paar for the description of the line of stability of atomic nuclei, and for the description of atomic weights and molecular, a power law dependence on molecular weights was found experimentally for the interactions between

Pavin, Nenad

142

Scale-invariant power law and fractality for molecular weights V. Paar a,*, N. Pavin a

Scale-invariant power law and fractality for molecular weights V. Paar a,*, N. Pavin a , A. Rubcic of molecular weights of chemical compounds. A scale-invariant power law for molecular weights is introduced rights reserved. 1. Introduction Concepts of atomic and molecular weights are fundamental to chemistry

Pavin, Nenad

143

Power-law tail probabilities of drainage areas in river basins

We examine the appearance of power-law behavior in rooted tree graphs in the context of river networks. It has long been observed that the tails of statistical distributions of upstream areas in river networks, measured above every link, obey a power-law relationship over a range of scales. We examine this behavior by considering a subset of all links, defined as

Seth Veitzer; Brent Troutman; Vijay Gupta

2003-01-01

144

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

145

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

146

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

147

Power-Law and Stable Distribution of BGP Paths Julien Clement and Kwan-Wu Chin

systems (ASs) appearing in path vectors follow a Power-Law relation- ship. Secondly, it shows that path works that have thus far only shown Power-Law relationships exhibited by ASs degree. Index Terms of thousands of autonomous systems (ASs) that use the Border Gateway Protocol (BGP) [8] to form peering

Chin, Kwan-Wu

148

Power-law creep behavior of a semiflexible chain Arnab Majumdar,1,2

in response to an externally applied stretching force. The property that links the power law to the prestress over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical

Alencar, Adriano Mesquita

149

Transport coefficients in Lorentz plasmas with the power-law kappa-distribution

Transport coefficients in Lorentz plasma with the power-law ?-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient, and thermal conductivity for the power-law ?-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the ?-parameter, and in the limit of the parameter ??? they are reduced to the standard forms for a Maxwellian distribution.

Jiulin, Du [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China)] [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China)

2013-09-15

150

Money, power, gas and the law: The `big` convergence

Nothing ever endures but change, and in the ever whirling wheel of change that is the energy economy and its regulation, massive flux is under way. The key ingredients in this mix--the gas and electric industries, the financial instruments and entities that back them, and the laws and regulations that control and guide them--are in a confluence moving at warp speed. Assets are being divested or monetized. Financial products--not only reserves--are the answer to managing supply risks. Spark spreads--the financial differential between the price of gas as a commodity and gas that has been transformed into electrons--are being traded. Electric restructuring is being patterned on the template of the gas experience. Electronic bulletin boards and trading systems are linking the industries in cyberspace. And the consolidation of these industries has led to the biggest mating game in the energy industries` history, all at a fast-forward pace. Federal and state legislators and regulators swim in the same tank as the voracious entities this article discusses. Faced with unimagined combinations of players, complicated market power questions swirl around the merger and acquisition marriages. And, as the markets push ahead with new ideas, the regulators attempt to shape the process with their own proposals to influence the market of the next millennium. This article discusses some of the major moves and certain key regulatory decisions regarding these landscape-altering initiatives.

Hollis, S.S. [Duane, Morris and Heckscher LLP, Washington, DC (United States)

1998-06-29

151

Statistical tests for power-law cross-correlated processes.

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. PMID:22304166

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

2011-12-01

152

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

153

Consistency relation in power law G-inflation

NASA Astrophysics Data System (ADS)

In the standard inflationary scenario based on a minimally coupled scalar field, canonical or non-canonical, the subluminal propagation of speed of scalar perturbations ensures the following consistency relation: r <= -8nT, where r is the tensor-to-scalar-ratio and nT is the spectral index for tensor perturbations. However, recently, it has been demonstrated that this consistency relation could be violated in Galilean inflation models even in the absence of superluminal propagation of scalar perturbations. It is therefore interesting to investigate whether the subluminal propagation of scalar field perturbations impose any bound on the ratio r/|nT| in G-inflation models. In this paper, we derive the consistency relation for a class of G-inflation models that lead to power law inflation. Within these class of models, it turns out that one can have r > -8nT or r <= -8nT depending on the model parameters. However, the subluminal propagation of speed of scalar field perturbations, as required by causality, restricts r <= -(32/3) nT.

Unnikrishnan, Sanil; Shankaranarayanan, S.

2014-07-01

154

Power Spectrum of Gravitational Waves from Unbound Compact Binaries

NASA Astrophysics Data System (ADS)

Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum and the position of the frequency peak. Here we derive them for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation, following the work of Capozziello et al. In particular, we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. Within numerical approximation our formula is in agreement with the two known limiting cases: for the eccentricity ? = 1, the parabolic case, whose spectrum was computed by Berry and Gair, and the large ? limit with the formula given by Turner.

De Vittori, L.; Jetzer, P.; Klein, A.

2013-01-01

155

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

156

Counting, symbols, positions, powers, choice, arithmetic, binary, translation, hex, addresses- noted { , , }U a b c= . Consider how it is possible to make a selection from U . Here are the possi- bilities ( ) {{},{ },{ },{ },{ , },{ , },{ , },{ , , }}.P U a b c a b a c b c a b c= The so-called empty

Linner, Anders

157

Performance and parametric investigation of a binary geothermal power plant by exergy

Exergy analysis of a 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 diagram, and compared to the energy diagram. The sites with greater exergy destructions include brine reinjection, heat exchanger and condenser losses. Exergetic

Mehmet Kanoglu; Ali Bolatturk

2008-01-01

158

Raft River binary-cycle geothermal pilot power plant final report

The design and performance of a 5-MW(e) binary-cycle pilot power plant that used a moderate-temperature hydrothermal resource, with isobutane as a working fluid, are examined. Operating problems experienced and solutions found are discussed and recommendations are made for improvements to future power plant designs. The plant and individual systems are analyzed for design specification versus actual performance figures.

Bliem, C.J.; Walrath, L.F.

1983-04-01

159

Energy dependence of power-spectral noise in X-ray binaries

NASA Astrophysics Data System (ADS)

Black hole and neutron star X-ray binaries show variability on time-scales ranging from milliseconds to years. In the last two decades a detailed phenomenological picture of short-term variability in low-mass X-ray binaries has emerged mainly based on RXTE observations that cover energies above 3 keV. This picture comprises periodic or quasi-periodic variability, seen as spikes or humps in power density spectra, that are superposed on broad noise components. The overall shape of the noise components as well as the occurrence of quasi-periodic oscillations is known to vary with the state of the X-ray binary. We are accomplishing a comprehensive study of archival XMM-Newton observations in timing or burst mode of more than ten black hole and more than thirty neutron star low-mass X-ray binaries to investigate the variability properties of these sources at softer energies where the thermal disk component starts to emerge.Here we present some results of the energy dependence of the noise component in power density spectra: a discussion of the energy dependence of the power spectral state that we found in the “plateau” state of GRS 1915+105 and the intermediate state of 4U 1630-47; the dependence of the break-frequency of the band-limited noise component as well as the quasi-periodic oscillations on the studied energy band in several X-ray binaries like GX 339-4 or Swift J1753.5-0127. We will discuss the implications of these findings for the picture of the accretion geometry in black hole X-ray binaries.

Stiele, Holger; Yu, Wenfei

2014-08-01

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

NASA Astrophysics Data System (ADS)

In considering the irreversible chemical reaction A+B\\to C+B in liquid solutions two many-particle approaches to the derivation of binary non-Markovian kinetic equations are compared: simple superposition decoupling and a method of extracting 'pair' channels from three-particle correlation evolution. It is shown that both methods provide an almost identical description of this reaction. However, in studies of reversible reactions in liquid solutions only the channel extraction method gives a correct physically clear description of the reaction though it consists of a sequence of steps: the development of integral encounter theory (IET), effective pairs approximation (EPA), modified encounter theory (MET), and the final regular form (RF) of kinetic equations. It is shown that the rate equations often encountered in the literature correspond to the independence of transient channels of 'scattering' in the bimolecular reversible reaction (A+B \\rightleftarrows C+ B ), while the independent transient channel of 'decay' in the reversible reaction A+B \\rightleftarrows C is defined solely by time integral convolution. In the general case transient channels in non-Markovian theory are not independent, and their interference manifests itself as a non-Markovian inhomogeneous source in binary non-Markovian kinetic equations in regular form. Based on the derived equations new universal kinetics (independent of models) of chemical equilibrium attainment have been obtained. It is shown that these kinetics can differ essentially from the kinetics corresponding to the kinetic law of mass action of formal chemical kinetics.

Doktorov, Alexander B.; Kipriyanov, Alexey A.

2007-02-01

162

Power-law tail probabilities of drainage areas in river basins.

We examine the appearance of power-law behavior in rooted tree graphs in the context of river networks. It has long been observed that the tails of statistical distributions of upstream areas in river networks, measured above every link, obey a power-law relationship over a range of scales. We examine this behavior by considering a subset of all links, defined as those links which drain complete Strahler basins, where the Strahler order defines a discrete measure of scale, for self-similar networks with both deterministic and random topologies. We find an excellent power-law structure in the tail probabilities for complete Strahler basin areas, over many ranges of scale. We show analytically that the tail probabilities converge to a power law under the assumptions of (1) simple scaling of the distributions of complete Strahler basin areas and (2) application of Horton's law of stream numbers. The convergence to a power law does not occur for all underlying distributions, but for a large class of statistical distributions which have specific limiting properties. For example, underlying distributions which are exponential and gamma distributed, while not power-law scaling, produce power laws in the tail probabilities when rescaled and sampled according to Horton's law of stream numbers. The power-law exponent is given by the expression phi=ln(R(b))/ln(R(A)), where R(b) is the bifurcation ratio and R(A) is the Horton area ratio. It is commonly observed that R(b) approximately equal R(A) in many river basins, implying that the tail probability exponent for complete Strahler basins is close to 1.0. PMID:12935216

Veitzer, Seth A; Troutman, Brent M; Gupta, Vijay K

2003-07-01

163

Predicting the CMB power spectrum for binary polyhedral spaces

The COBE and the first-year WMAP data both find the CMB quadrupole and octopole to be anomalously low. Here it is shown, that a finite, multi-connected universe may explain this anomaly, supporting earlier analyses [5][18]. A novel technique, pioneered by [16] is used to compute the spectrum and its variance up to k=102. Based on the properties of the Lie group of rotations of S^3 it is shown that the spectrum and its variance may be computed solely from the matrix elements of the group-averaging operator, for each of the manifolds S^3/I^*, S^3/O^* and S^3/T^*. Further, it is proved that the spectrum of the CMB may be calculated solely from the radial function, due to the symmetry properties of the Lie-algebra, which is rigorously proven. It is shown, that if the topology of the universe is S^3/I^* the uncertainty on the estimates for the total energy density of the universe may be reduced by an order of magnitude. Finally, the paper highlights how the unavailability of an explicit probability function for the observations, given the model, is a challenge for Monte-Carlo simulations of the binary polyhedral spaces which has to be addressed in future work.

Jesper Gundermann

2005-03-01

164

family power relations. Childrearing: Disciplining and Boundaryfamily and wanting to win her grandchildren?s affection, her mother-in-law inadvertently crosses the boundaryfamily and her power vis-à-vis her in-laws. Even though such boundaries

Shih, Kristy

2011-01-01

165

NASA Astrophysics Data System (ADS)

The technique of Padé approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more “microscopic” level.

Alderweireld, Thomas; Nuyts, Jean

2004-01-01

166

NASA Astrophysics Data System (ADS)

We start from Gibrat’s law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu

2014-03-01

167

Summary of investigations of the use of modified turbine inlet conditions in a binary power plant

Investigators at the Idaho National Engineering and Environmental Laboratory (INEEL) are developing technologies that will enhance the feasibility of generating electrical power from a hydrothermal resource. One of the concepts investigated is the use of modified inlet conditions in geothermal binary power plant turbines to increase the power generation. An inlet condition of interest allows the expanding vapor to enter the two-phase region, a mode of operation typically avoided because of concern that condensate would form and damage the turbine, degrading performance. INEEL investigators postulated that initially a supersaturated vapor would be supported, and that no turbine damage would occur. This paper summarizes the investigation of these expansions that began with testing of their condensation behavior, and culminated with the incorporation of these expansions into the operation of several commercial binary plant turbines.

G. L. Mines

2000-09-24

168

Summary of Investigations of the Use of Modified Turbine Inlet Conditions in a Binary Power Plant

Investigators at the Idaho National Engineering and Environmental Laboratory (INEEL) are developing technologies that will enhance the feasibility of generating electrical power from a hydrothermal resource. One of the concepts investigated is the use of modified inlet conditions in geothermal binary power plant turbines to increase the power generation. An inlet condition of interest allows the expanding vapor to enter the two-phase region, a mode of operation typically avoided because of concern that condensate would form and damage the turbine, degrading performance. INEEL investigators postulated that initially a supersaturated vapor would be supported, and that no turbine damage would occur. This paper summarizes the investigation of these expansions that began with testing of their condensation behavior, and culminated with the incorporation of these expansions into the operation of several commercial binary plant turbines.

Mines, Gregory Lee

2000-09-01

169

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

170

Liquid-metal binary cycles for stationary power

NASA Technical Reports Server (NTRS)

The use of topping cycles to increase electric power plant efficiency is discussed, with particular attention to mercury and alkali metal Rankine cycle systems that could be considered for topping cycle applications. An overview of this technology, possible system applications, the required development, and possible problem areas is presented.

Gutstein, M.; Furman, E. R.; Kaplan, G. M.

1975-01-01

171

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

172

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

173

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

174

Liouville-Type Theorems for Steady Flows of Degenerate Power Law Fluids in the Plane

NASA Astrophysics Data System (ADS)

We extend the Liouville-type theorems of Gilbarg and Weinberger and of Koch, Nadirashvili, Seregin and Sverák valid for the stationary variant of the classical Navier-Stokes equations in 2 D to the degenerate power law fluid model.

Bildhauer, Michael; Fuchs, Martin; Zhang, Guo

2013-09-01

175

Assessing the power law distribution of TGFs Andrew B. Collier,1,2,3

field required for RREA is appreciably smaller than that for conventional dielectric breakdown. While with a power law model for the distribution of TGF intensities. Finally it was found that the matched TGFs were

Bergen, Universitetet i

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

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

178

Coupled Quintessence in a Power-Law Case and the Cosmic Coincidence Problem

The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study a coupled quintessence scenario in which the scalar field evolves in a power law potential and the mass of dark matter particles depends on a power law function of $\\phi$. It is shown that this scenario has a stable attractor solution and can thus provide a natural solution to the cosmic coincidence problem.

Xin Zhang

2005-09-27

179

The present work concerns a quantitative analysis of parameters that affect apparent blood viscosity at different low shear\\u000a rates, i.e, between 1 s?1 and, 100 s?1. Viscosity profile of a large number of blood samples from thromboembolic stroke cases and age and sex matched healthy controls\\u000a were studied which confirmed non-Newtonian power law behaviour of blood. The power law coefficients,n

Mohammad A. Hussain; Subir Kar; Ram R. Puniyani

1999-01-01

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

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

182

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

183

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

184

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

185

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

186

Taylor's power law of fluctuation scaling and the growth-rate theorem.

Taylor's law (TL), a widely verified empirical relationship in ecology, states that the variance of population density is approximately a power-law function of mean density. The growth-rate theorem (GR) states that, in a subdivided population, the rate of change of the overall growth rate is proportional to the variance of the subpopulations' growth rates. We show that continuous-time exponential change implies GR at every time and, asymptotically for large time, TL with power-law exponent 2. We also show why diverse population-dynamic models predict TL in the limit of large time by identifying simple features these models share: If the mean population density and the variance of population density are (exactly or asymptotically) non-constant exponential functions of a parameter (e.g., time), then the variance of density is (exactly or asymptotically) a power-law function of mean density. PMID:23689021

Cohen, Joel E

2013-09-01

187

Timing of continuous motor imagery: the two-thirds power law originates in trajectory planning.

The two-thirds power law, v = ??(-1/3), expresses a robust local relationship between the geometrical and temporal aspects of human movement, represented by curvature ? and speed v, with a piecewise constant ?. This law is equivalent to moving at a constant equi-affine speed and thus constitutes an important example of motor invariance. Whether this kinematic regularity reflects central planning or peripheral biomechanical effects has been strongly debated. Motor imagery, i.e., forming mental images of a motor action, allows unique access to the temporal structure of motor planning. Earlier studies have shown that imagined discrete movements obey Fitts's law and their durations are well correlated with those of actual movements. Hence, it is natural to examine whether the temporal properties of continuous imagined movements comply with the two-thirds power law. A novel experimental paradigm for recording sparse imagery data from a continuous cyclic tracing task was developed. Using the likelihood ratio test, we concluded that for most subjects the distributions of the marked positions describing the imagined trajectory were significantly better explained by the two-thirds power law than by a constant Euclidean speed or by two other power law models. With nonlinear regression, the ? parameter values in a generalized power law, v = ??(-?), were inferred from the marked position records. This resulted in highly variable yet mostly positive ? values. Our results imply that imagined trajectories do follow the two-thirds power law. Our findings therefore support the conclusion that the coupling between velocity and curvature originates in centrally represented motion planning. PMID:25609105

Karklinsky, Matan; Flash, Tamar

2015-04-01

188

Power-law fluctuations in phase-separated lipid membranes.

The spatial structure of three binary lipid mixtures, prepared as multilamellar vesicles, was studied by small-angle neutron scattering. In the fluid-gel coexistence region, large-scale concentration fluctuations appear which scatter like surface fractals for small acyl-chain mismatch and like mass fractals for large mismatch over about one decade of length. The transition is highly discontinuous: The fractal dimension of the boundary between the gel and fluid drops from 2.7 to 1.7, the gel fraction in the fluctuations drops from about 0.5 to 0.07, and the gel domains interlamellar correlation drops from strong to weak. We interpret the fluctuations as long-lived descendants of the incipient two-phase equilibrium state and the transition as due to changes in the gel rigidity and phase diagram. PMID:11970681

Winter, R; Gabke, A; Czeslik, C; Pfeifer, P

1999-12-01

189

Power-law fluctuations in phase-separated lipid membranes

NASA Astrophysics Data System (ADS)

The spatial structure of three binary lipid mixtures, prepared as multilamellar vesicles, was studied by small-angle neutron scattering. In the fluid-gel coexistence region, large-scale concentration fluctuations appear which scatter like surface fractals for small acyl-chain mismatch and like mass fractals for large mismatch over about one decade of length. The transition is highly discontinuous: The fractal dimension of the boundary between the gel and fluid drops from 2.7 to 1.7, the gel fraction in the fluctuations drops from about 0.5 to 0.07, and the gel domains interlamellar correlation drops from strong to weak. We interpret the fluctuations as long-lived descendants of the incipient two-phase equilibrium state and the transition as due to changes in the gel rigidity and phase diagram.

Winter, R.; Gabke, A.; Czeslik, C.; Pfeifer, P.

1999-12-01

190

ERIC Educational Resources Information Center

This interview study interrogates how cultural values of filial piety inform Chinese American daughters-in-law's understanding of their relationship and power dynamics with immigrant Chinese American mothers-in-law. Ideals of filial respect accord limited authority to mothers-in-law, who engage other mechanisms of power, such as their domestic…

Shih, Kristy Y.; Pyke, Karen

2010-01-01

191

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

192

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

193

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

Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science. PMID:12079523

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

2002-01-01

194

Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

NASA Astrophysics Data System (ADS)

The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.

Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.

195

Power-law decay of the view times of scientific courses on YouTube

NASA Astrophysics Data System (ADS)

The temporal power-law decay is one class of interesting decay processes, usually indicating a long-time correlation and benefiting for a system to perform functions in various time-scales. In this work, I collect the data of the view times versus lectures of some scientific courses on YouTube, according to some special principles. These data can reflect the dynamical property of the spontaneous learning behavior, influenced by the decay of learning interest. The view times versus lectures show an obviously power-law decay process. The power approximates to 1, a universal constant. This finding brings the learning process into the interesting power-law family. It will be of interest in the fields of the human dynamics, psychology and education.

Gao, Lingling

2012-11-01

196

Statistical evidence for power law temporal correlations in exploratory behaviour of rats.

Dynamics of exploratory behaviour of rats and home base establishment is investigated. Time series of instantaneous speed of rats was computed from their position during exploration. The probability distribution function (PDF) of the speed obeys a power law distribution with exponents ranging from 2.1 to 2.32. The PDF of the recurrence time of large speed also exhibits a power law, P(?) ~ ?(??) with ? from 1.56 to 2.30. The power spectrum of the speed is in general agreement with the 1/f spectrum reported earlier. These observations indicate that the acquisition of spatial information during exploration is self-organized with power law temporal correlations. This provides a possible explanation for the home base behaviour of rats during exploration. The exploratory behaviour of rats resembles other systems exhibiting self-organized criticality, e.g., earthquakes, solar flares etc. PMID:20688133

Yadav, Chetan K; Verma, Mahendra K; Ghosh, Subhendu

2010-01-01

197

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

198

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

199

A spatially variable power law tropospheric correction technique for InSAR data

NASA Astrophysics Data System (ADS)

Microwave signals traveling through the troposphere are subject to delays. These delays are mainly described by spatial and temporal variations in pressure, temperature, and relative humidity in the lower part of the troposphere, resulting in a spatially varying tropospheric signal in interferometric synthetic aperture radar (InSAR). Tropospheric correction techniques rely either on external data, often limited by spatial and temporal accuracy or can be estimated from the high-resolution interferometric phase itself. However, current phase-estimated correction techniques do not account for the spatial variability of the tropospheric properties and fail to capture tropospheric signals over larger regions. Here we propose and test a novel power law correction method that accounts for spatial variability in atmospheric properties and can be applied to interferograms containing topographically correlated deformation. The power law model has its reference fixed at the relative top of the troposphere and describes, through a power law relationship, how the phase delay varies with altitude. We find the power law model reduces tropospheric signals both locally (on average by ˜0.45 cm for each kilometer of elevation in Mexico) and the long-wavelength components, leading to an improved fit to independent Global Navigation Satellite Systems data. The power law model can be applied in presence of deformation, over a range of different time periods and in different atmospheric conditions, and thus permits the detection of smaller-magnitude crustal deformation signals with InSAR.

Bekaert, D. P. S.; Hooper, A.; Wright, T. J.

2015-02-01

200

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

201

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

NASA Astrophysics Data System (ADS)

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 & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: rLD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M. P.

2013-08-01

202

NASA Astrophysics Data System (ADS)

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. 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 (Busse's and Curtis Ness') with the radiometric law to yield "Bode's"-type laws governing planetary radio emission. Further analysis allows the reduction of variables to planetary mass and orbital distance. These generalized laws are then used to predict the power output of Neptune to be about 1.6×107W; with the intensity peaking at about 3 MHz.

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

1988-01-01

203

Alpha-power law MOSFET model and its applications to CMOS inverter delay and other formulas

An ?-power-law MOS model that includes the carrier velocity saturation effect, which becomes prominent in short-channel MOSFETs, is introduced. The model is an extension of Shockley's square-law MOS model in the saturation region. Since the model is simple, it can be used to handle MOSFET circuits analytically and can predict the circuit behavior in the submicrometer region. Using the model,

T. Sakurai; A. R. Newton

1990-01-01

204

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

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

2011-01-01

205

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, E-mail: trvsst@ameslab.gov [Department of Physics and Astronomy and Ames Lab, Iowa State University Ames, Ames, Iowa 50011 (United States)

2014-10-28

206

A Power-Law Dependence of Bacterial Invasion on Mammalian Host Receptors

Pathogenic bacteria such as Listeria and Yersinia gain initial entry by binding to host target cells and stimulating their internalization. Bacterial uptake entails successive, increasingly strong associations between receptors on the surface of bacteria and hosts. Even with genetically identical cells grown in the same environment, there are vast differences in the number of bacteria entering any given cell. To gain insight into this variability, we examined uptake dynamics of Escherichia coli engineered to express the invasin surface receptor from Yersinia, which enables uptake via mammalian host ?1-integrins. Surprisingly, we found that the uptake probability of a single bacterium follows a simple power-law dependence on the concentration of integrins. Furthermore, the value of a power-law parameter depends on the particular host-bacterium pair but not on bacterial concentration. This power-law captures the complex, variable processes underlying bacterial invasion while also enabling differentiation of cell lines. PMID:25879937

Lee, Anna Jisu; Lopatkin, Allison; Yuan, Fan; You, Lingchong

2015-01-01

207

Effective velocity power laws for electron-neutral collision frequencies. [in ionosphere

NASA Technical Reports Server (NTRS)

Calculations of electron transport coefficients in the ionosphere are simplified if the electron-neutral collision frequency can be expressed as a power law in velocity. A new method for determining the effective power law representation for electron-neutral collision frequencies of arbitrary velocity dependence is presented. This method is applied to ionospheric gases in a model calculation. Comparison with similar results of Schunk and Walker and with exact calculations of transport coefficient correction factors demonstrates this technique to be more accurate than the other. Effective power law indexes are computed for both Banks' and Itikawa's collision frequencies. Relative differences between these indexes are found to be considerably larger than the differences between the collision frequencies themselves; however, the effects on transport calculations are shown to be smaller.

Comfort, R. H.

1975-01-01

208

Power-law X-ray and gamma-ray emission from relativistic thermal plasmas

NASA Technical Reports Server (NTRS)

A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.

Zdziarski, A. A.

1985-01-01

209

Fertility heterogeneity as a mechanism for power law distributions of recurrence times

NASA Astrophysics Data System (ADS)

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 ?, where the fertility of an event is the number of triggered events of first generation, on the probability distribution function (PDF) f(?) of the recurrence times ? between successive events. The other input of the model is an exponential law quantifying the PDF of waiting times between an event and its first generation triggered events, whose characteristic time scale is taken as our time unit. At short-time scales, we discover two intermediate power law asymptotics, f(?)˜?-(2-?) for ???c and f(?)˜?-? for ?c???1, where ?c is associated with the self-excited cascades of triggered events. For 1???1/?, we find a constant plateau f(?)?const, while at long times, 1/???, f(?)?e-?? has an exponential tail controlled by the arrival rate ? of exogenous events. These results demonstrate a novel mechanism for the generation of power laws in the distribution of recurrence times, which results from a power law distribution of fertilities in the presence of self-excitation and cascades of triggering.

Saichev, A.; Sornette, D.

2013-02-01

210

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

211

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

212

NASA Astrophysics Data System (ADS)

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the updating of their states. We show with numerical simulation that these aptitudes can contribute to group formation or speciation in social fields. Moreover, they can lead to power-law topological correlations of complex networks. By coupling updating states of nodes with variation of connections in a network, structural properties with power-laws and functions like multifractality, spontaneous ranking and evolutionary branching of node states can emerge simultaneously from the present self-organized model of coevolutionary processes.

Zhu, Chen-Ping; Zhou, Tao; Yang, Hui-Jie; Xiong, Shi-Jie; Gu, Zhi-Ming; Shi, Da-Ning; He, Da-Ren; Wang, Bing-Hong

2008-02-01

213

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

214

Effect of Body Perturbations on Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Hypersonic-slender-body theory, in the limit as the free-stream Mach number becomes infinite, is used to find the effect of slightly perturbing the surface of slender two-dimensional and axisymmetric power law bodies, The body perturbations are assumed to have a power law variation (with streamwise distance downstream of the nose of the body). Numerical results are presented for (1) the effect of boundary-layer development on two dimensional and axisymmetric bodies, (2) the effect of very small angles of attack (on tow[dimensional bodies), and (3) the effect of blunting the nose of very slender wedges and cones.

Mirels, Harold; Thornton, Philip R.

1959-01-01

215

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

216

Power Law Entropy Corrected New-Agegraphic Dark Energy in Ho?ava-Lifshitz Cosmology

We investigate the new agegraphic dark energy (NADE) model with power-law corrected entropy in the framework of Ho\\v{r}ava-Lifshitz cosmology. For a non-flat universe containing the interacting power-law entropy-corrected NADE (PLECNADE) with dark matter, we obtain the differential equation of the evolution of density parameter as well as the deceleration parameter. To study parametric behavior, we used an interesting form of state parameter as function of redshift $\\omega_{\\Lambda}(z)=\\omega_0+\\omega_1 z$. We found that phantom crossing occurs for the state parameter for a non-zero coupling parameter, thus supporting interacting dark energy model.

K. Karami; A. Sheykhi; Mubasher Jamil; R. Myrzakulov; S. Ghaffari; A. Abdolmaleki

2012-03-31

217

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

218

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

219

Tweedie convergence: A mathematical basis for Taylor's power law, 1/f noise, and multifractality

NASA Astrophysics Data System (ADS)

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality.

Kendal, Wayne S.; Jørgensen, Bent

2011-12-01

220

Percolation and fire spread with power-law flame radiations

NASA Astrophysics Data System (ADS)

Percolation and non-equilibrium front propagation in a two-dimensional network modeling wildfire spread is studied. The model includes a deterministic long-range interaction induced by flame radiation. It includes also a time weighting process due to the flame residence time and the activation (ignition) energy of the exposed combustible. For the square power decreasing radiation interaction, three weight-dependent regimes were previously found; a dynamical, a static, and a non-propagative regime (Zekri N. et al. Phys. Lett. A, 376 (2012) 2522). The weight effect on the percolation threshold is found here independent of the deterministic interaction. Using the Family-Vicsek scaling ansatz, the front dynamical exponents belong to the Edwards-Wilkinson model universality class at the saturation of the dynamical regime. They are weight dependent beyond saturation.

Khelloufi, K.; Baara, Y.; Zekri, N.

2013-07-01

221

Power loss in open cavity diodes and a modified Child Langmuir Law

Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.

Debabrata Biswas; Raghwendra Kumar; R. R. Puri

2005-07-26

222

Power loss in open cavity diodes and a modified Child-Langmuir law

Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.

Biswas, Debabrata; Kumar, Raghwendra; Puri, R.R. [Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India); Human Resource Development Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India)

2005-09-15

223

Performance of a 5-MW(e) binary geothermal-electric power plant

A 5-MW(e) Pilot Geothermal Power Plant was built by the Idaho National Engineering Laboratory (INEL), at Raft River, Idaho, as an integral part of the Department of Energy's plan for commercial development of geothermal energy. The purpose of the plant was to investigate the technical feasibility of utilizing a moderate temperature hydrothermal resource (275 to 300/sup 0/F) to generate electrical power in an environmentally acceptable manner. The plant used a dual-boiling binary cycle with isobutane as the working fluid, and drew thermal energy from a 280/sup 0/F liquid-dominated resource. This paper presents the results of that testing, and compares both component and system performance to the performance predicted prior to operation.

Bliem, C.J.; Fullmer, K.S.; Kochan, R.J.

1983-01-01

224

Raft River 5MW(e) binary geothermal-electric power plant: operation and performance

A 5MW(e) Pilot Geothermal Power Plant was built at Raft River, Idaho, as an integral part of the Department of Energy's plan for commercial development of geothermal energy. The purpose of the plant was to investigate the technical feasibility of utilizing a moderate temperature hydrothermal resource (275 to 300/sup 0/F) to generate electrical power in an environmentally acceptable manner. The plant used a dual-boiling binary cycle with isobutane as the working fluid, and drew thermal energy from a 280/sup 0/F liquid-dominated resource. This paper presents the results of that testing, comparing the system performance to the performance predicted prior to operation along with a summary of operational experience.

Bliem, C.J. Jr.

1983-01-01

225

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

226

Thermodynamics of higher dimensional topological dilation black holes with a power-law Maxwell field

NASA Astrophysics Data System (ADS)

In this paper, we extend the study on the nonlinear power-law Maxwell field to dilaton gravity. We introduce the (n +1 ) -dimensional action in which gravity is coupled to a dilaton and power-law nonlinear Maxwell field, and we obtain the field equations by varying the action. We construct a new class of higher dimensional topological black hole solutions of Einstein-dilaton theory coupled to a power-law nonlinear Maxwell field and investigate the effects of the nonlinearity of the Maxwell source as well as the dilaton field on the properties of the spacetime. Interestingly enough, we find that the solutions exist provided one assumes three Liouville-type potentials for the dilaton field, and in the case of the Maxwell field, one of the Liouville potentials vanishes. After studying the physical properties of the solutions, we compute the mass, charge, electric potential and temperature of the topological dilaton black holes. We also study the thermodynamics and thermal stability of the solutions and disclose the effects of the dilaton field and the power-law Maxwell field on the thermodynamics of these black holes. Finally, we comment on the dynamical stability of the obtained solutions in four dimensions.

Zangeneh, M. Kord; Sheykhi, A.; Dehghani, M. H.

2015-02-01

227

Off-center HII regions in power-law density distributions

The expansion of ionization fronts in uniform and spherically symmetric power-law density distributions is a well-studied topic. However, in many situations, such as a star formed at the edge of a molecular cloud core, an offset power-law density distribution would be more appropriate. In this paper a few of the main issues of the formation and expansion of HII regions in such media are outlined and results are presented for the particular cases where the underlying power laws are 1/r^2 and 1/r^3. A simple criterion is developed for determining whether the initial photoionized region will be unbounded, which depends on the power-law exponent and the ratio of the equivalent Stroemgren radius produced by the star in a uniform medium to the stellar offset distance. In the expansion stage, the ionized volumes will eventually become unbounded unless pressure balance with the external medium is reached before the ionization front velocity becomes supersonic with respect to the ionized gas.

S. J. Arthur

2007-05-05

228

Power-law mass inflation in Einstein-Yang-Mills-Higgs black holes.

NASA Astrophysics Data System (ADS)

Analytical formulas are presented describing a generic singularity inside static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills-Higgs theory with a triplet and/or doublet Higgs field. The singularity is spacelike and exhibits a 'power-law mass inflation'. Alternatively this asymptotic behavior may be interpreted as a pointlike singularity in the Kantowski-Sachs closed anisotropic cosmology.

Gal'Tsov, D. V. G.; Donets, E. E.

1997-12-01

229

Deviations from uniform power law scaling in nonstationary time series Gandhimohan M. Viswanathan,1

. This highly ir- regular behavior has recently motivated investigators 2Â7 to apply time-series analysesDeviations from uniform power law scaling in nonstationary time series Gandhimohan M. Viswanathan,1 C.-K. Peng,1,2 H. Eugene Stanley,1 and Ary L. Goldberger2 1 Center for Polymer Studies

230

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

231

The Berners-Lee Hypothesis: Power laws and Group Structure in Flickr

An intriguing hypothesis, first suggested by Tim Berners-Lee, is that the structure of online groups should conform to a power law distribution. We relate this hypothesis to earlier work around the Dunbar Number, which is a sup- posed limit to the number of social contacts a user can have in a group. As pre- liminary results, we show that the

Andrea Baldassarri; Alain Barrat; A. Capocci; Harry Halpin; Ulrike Lehner; Jose Ramasco; Valentin Robu; Dario Taraborelli

2008-01-01

232

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 $2.5\\sigma$ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio $r$ are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: $r_{\\rm LD}=0.11\\pm{0.024}$. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Mo...

Vazquez, J Alberto; Ma, Yin-Zhe; Hobson, M P

2013-01-01

233

Transient Anomaly Imaging in Visco-Elastic Media Obeying a Frequency Power-Law

Transient Anomaly Imaging in Visco-Elastic Media Obeying a Frequency Power-Law Elie Bretin Lili Imaging and Back propagation, for an ideal medium to detect an anomaly in a visco-elastic medium from wave 4 we present anomaly imaging procedures and reconstruction methods in visco-elastic media. Numerical

Boyer, Edmond

234

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

235

The implementation of a Faraday's law machines laboratory for teaching power system and transformers

A Faraday's law machines laboratory for teaching power system and transformers has been implemented. The major goal of this laboratory is to facilitate the experimental studies in a safe, low-cost, and convenient way for our undergraduate students. This article describes the status and future plan of the laboratory. Meanwhile, several illustrative pictures, including laboratory layout, innovative equipment, and example waveforms

Cheng-Hong Chang

1995-01-01

236

] It is demonstrated that a near-linear subsurface runoff response from a short and relatively steep slope segment linear nature of the subsurface runoff response from the hillslope, as Harman et al. [2009] employed distributions (e.g., bounded power law (BPL)) of the storage coefficient and in the limit; when the number

Szilagyi, Jozsef

237

Large amplitude oscillatory shear flow of gluten dough: A model power-law gel

In a previous paper [T. S. K. Ng and G. H. McKinley, J. Rheol.52(2), 417–449 (2008)], we demonstrated that gluten gels can best be understood as a polymericnetwork with a power-law frequency response that reflects the ...

Ng, Trevor S. K.

238

A Power-law Distribution of Solar Magnetic Fields Over More Than Five Decades in Flux

A Power-law Distribution of Solar Magnetic Fields Over More Than Five Decades in Flux C. E. Parnell. Welsch University of California, Berkeley Space Sciences Laboratory, 7 Gauss Way, CA 94720 welsch, MD 20771 #12;Â 2 Â ABSTRACT Solar flares, coronal mass ejections, and indeed phenomena on all scales

Parnell, Clare E.

239

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence

NASA Astrophysics Data System (ADS)

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.

Kendal, Wayne S.; Jørgensen, Bent

2011-06-01

240

Simple, Accurate, Approximate Orbits in the Logarithmic and a Range of Power-Law Galactic Potentials

Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known $1/r$ (Keplerian) and logarithmic potentials. These approximate orbits, called p-ellipses, retain some of the basic geometric properties of ellipses. They satisfy and generalize Newton's apsidal precession formula, which is one of the reasons for their surprising accuracy. Because of their simplicity the p-ellipses make very useful tools for studying trends among power-law potentials, and especially the occurence of closed orbits. The occurence of closed or nearly closed orbits in different potentials highlights the possibility of period resonances between precessing, eccentric orbits and circular orbits, or between the precession period of multi-lobed closed orbits and satellite periods. These orbits and their resonances promise to help illuminate a number of problems in galaxy and accretion disk dynamics.

Curtis Struck

2005-12-09

241

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

242

As geothermal resources that are more expensive to develop are utilized for power generation, there will be increased incentive to use more efficient power plants. This is expected to be the case with Enhanced Geothermal System (EGS) resources. These resources will likely require wells drilled to depths greater than encountered with hydrothermal resources, and will have the added costs for stimulation to create the subsurface reservoir. It is postulated that plants generating power from these resources will likely utilize the binary cycle technology where heat is rejected sensibly to the ambient. The consumptive use of a portion of the produced geothermal fluid for evaporative heat rejection in the conventional flash-steam conversion cycle is likely to preclude its use with EGS resources. This will be especially true in those areas where there is a high demand for finite supplies of water. Though they have no consumptive use of water, using air-cooling systems for heat rejection has disadvantages. These systems have higher capital costs, reduced power output (heat is rejected at the higher dry-bulb temperature), increased parasitics (fan power), and greater variability in power generation on both a diurnal and annual basis (larger variation in the dry-bulb temperature). This is an interim report for the task ‘Air-Cooled Condensers in Next- Generation Conversion Systems’. The work performed was specifically aimed at a plant that uses commercially available binary cycle technologies with an EGS resource. Concepts were evaluated that have the potential to increase performance, lower cost, or mitigate the adverse effects of off-design operation. The impact on both cost and performance were determined for the concepts considered, and the scenarios identified where a particular concept is best suited. Most, but not all, of the concepts evaluated are associated with the rejection of heat. This report specifically addresses three of the concepts evaluated: the use of recuperation, the use of turbine reheat, and the non-consumptive use of EGS make-up water to supplement heat rejection

Daniel S. Wendt; Greg L. Mines

2010-09-01

243

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

244

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

245

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

246

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

247

A more powerful exact test of noninferiority from binary matched-pairs data.

Assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design. This paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives. There are two new elements presented in this paper. First, we introduce the likelihood ratio statistic as an alternative to the previously proposed score statistic of Nam (Biometrics 1997; 53:1422-1430). Second, we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of Berger and Boos (Am. Stat. Assoc. 1994; 89:1012-1016) or traditional full maximization. Based on an extensive numerical study, we recommend tests based on the score statistic, the nuisance parameter being controlled by estimation followed by maximization. PMID:18314932

Lloyd, Chris J; Moldovan, Max V

2008-08-15

248

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

249

This paper was delivered as a Provocation at a Symposium in Honor of Professor Frank Michelman, hosted at Harvard Law School in February 2012. Using Professor Michelman’s extraordinary body of work in comparative constitutional law, the essay explores the importance of the oft-neglected normative dimension of comparative analysis. Far from endorsing a binary choice between legal function and legal culture,

Vlad Perju

2012-01-01

250

Evidence of Power-Law Flow in the Upper Mantle Beneath Southern Alaska

NASA Astrophysics Data System (ADS)

During the first 2.5 years following the 2002 M = 7.9 Denali, Alaska strike-slip earthquake, a large array of Global Positioning System (GPS) receivers recorded rapid postseismic surface motions extending at least 300 km from the rupture and at rates of more than 100 mm/yr in the near-field. In an initial study, we used 3-D viscoelastic finite element models to infer that observed cumulative far-field (> 100 km) surface displacements were best explained by rapid viscoelastic flow in the mantle below a depth of 60 km, with a component of lower crustal relaxation between 30 and 50 km depth [Freed et al., JGR, 2005]. Here we extend the study by refining the model to match time-series data (daily measurements from continuous GPS receivers, semi-annual data for campaign sites) that show very rapid early postseismic transients that slow dramatically with time. Our model considered power-law rheologic structure where strain rate equals C(d) times stress raised to the power n, where C(d) is a depth-dependent constant incorporating the influence of all rheologic parameters normally found in power-law expressions (A, Q, T, etc.). For each assumption of the power-law exponent n, we iteratively solved for the C(d) that provided the minimum misfit to the time-series data. We focus our initial modeling efforts on far-field sites where the contribution to the displacements of afterslip is probably minimal, based on reasonable afterslip models, so that the time-dependence of afterslip is not aliased into our estimation of viscosity structure. We found that far-field time-series observations cannot be explained by a Newtonian rheology (n = 1), as such rheologies cannot match the rate of decay of the displacements. Across both the lower crust and upper mantle, an average power-law exponent of n = 2 provides a reasonable solution, while higher exponents under-estimate longer term strain rates. Consideration of models in which the power-law varies between the crust and mantle find that time-series data is best fit by a composite rheology of a mantle with a power-law exponent of n = 3.5 and a lower crust with a power-law of n = 1. Because of trade-offs between parameters such as activation energy, water fugacity, and temperature, a unique rheologic environment cannot be defined. However, this solution can be shown to be consistent with diffusion creep of a feldspar dominated crust overlying dislocation creep of wet olivine, making this composite rheologic model our most appealing solution. Our results illustrate the importance of considering the absolute stress field in power-law solutions, and provide insights into the 3-D distribution of stress, strain rate, and effective viscosity within the Alaskan lithosphere as a function of time after the Denali earthquake. This evolution shows that coseismic stress changes induce a temporary weak lithospheric rheology leading to observed rapid postseismic surface deformations, eventually reverting to a much stronger rheology capable of supporting long-term topographic loads. Once the contributions of a deep viscoelastic rheology is accounted for to explain observed far-field displacements following the Denali earthquake, residual near-field displacements enable inference of contributions from time-dependent afterslip and poroelastic rebound in the shallow crust.

Freed, A. M.; Bürgmann, R.; Calais, E.; Freymueller, J. T.

2005-12-01

251

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

252

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the updating of their states. We show with numerical simulation that these aptitudes can contribute to group formation or speciation in social fields. Moreover, they can lead to power-law topological correlations of complex networks. By coupling updating states of nodes with variation of connections in a network, structural properties with power-laws and functions like multifractality, spontaneous ranking and evolutionary branching of node states can emerge out simultaneously from the present self-organized model of coevolutionary process.

Zhu, Chen-Ping; Yang, Hui-Jie; Xiong, Shi-Jie; Gu, Zhi-Ming; Shi, Da-Ning; He, Da-Ren; Wang, Bing-Hong

2007-01-01

253

Speed-invariant encoding of looming object distance requires power law spike rate adaptation.

Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli. PMID:23898185

Clarke, Stephen E; Naud, Richard; Longtin, André; Maler, Leonard

2013-08-13

254

Why Noether Symmetry of F( R) Theory Yields Three-Half Power Law?

NASA Astrophysics Data System (ADS)

Noether symmetry of F( R) theory of gravity in vacuum or in matter dominated era yields F(R) ? R^{3/2}. We show that this particular curvature invariant term is very special in the context of isotropic and homogeneous cosmological model as it makes the first fundamental form h ij cyclic. As a result, it allows a unique power law solution, typical for this particular fourth order theory of gravity, both in the vacuum and in the matter dominated era. This power law solution has been found to be quite good to explain the early stage but not so special and useful to explain the late stage of cosmological evolution. The usefulness of Palatini variational technique in this regard has also been discussed.

Sarkar, Kaushik; Sk, Nayem; Ruz, Soumendranath; Debnath, Subhra; Sanyal, Abhik Kumar

2013-05-01

255

Speed-invariant encoding of looming object distance requires power law spike rate adaptation

Neural representations of a moving object’s distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent’s response to “looming” object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent’s response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent’s firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli. PMID:23898185

Clarke, Stephen E.; Naud, Richard; Longtin, André; Maler, Leonard

2013-01-01

256

Steady-state power-law creep in inclusion matrix composite materials

This work is devoted to the prediction of the constitutive steady-state creep behavior of matrix inclusion composites. Both phases are characterized by power-law constitutive equations. The three phase model is extended to viscoplastic equations. If both phases have the same strain rate sensitivity,the effective behavior of the composite is characterized by an effective prefactor. If not, an effective strain rate sensitivity is defined, which is a function of the applied strain rate and of the volume fraction of the phases. All the results are compared with the classical self-consistent ones. A limit case which may be related to the grain boundary sliding accommodated by intragranular power-law creep is also studied.

Herve, E. [Ecole Polytechnique, Palaiseau (France). Lab. de Mecanique des Solides] [Ecole Polytechnique, Palaiseau (France). Lab. de Mecanique des Solides; Dendievel, R. [Institut National Polytechnique de Grenoble, Saint Martin d`Heres (France). Lab. Genie Physique et Mecanique des Materiaux] [Institut National Polytechnique de Grenoble, Saint Martin d`Heres (France). Lab. Genie Physique et Mecanique des Materiaux; Bonnet, G. [Geodynamique des Structures, Bagneux (France)] [Geodynamique des Structures, Bagneux (France)

1995-11-01

257

Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?

We study the time evolution of Solar Flares activity by looking at the statistics of quiescent times $\\tau_{L}$ between successive bursts. The analysis of 20 years of data reveals a power law distribution with exponent $\\alpha \\simeq 2.4$ which is an indication of complex dynamics with long correlation times. The observed scaling behavior is in contradiction with the Self-Organized Criticality models of Solar Flares which predict Poisson-like statistics. Chaotic models, including the destabilization of the laminar phases and subsequent restabilization due to nonlinear dynamics, are able to reproduce the power law for the quiescent times. In the case of the more realistic Shell Model of MHD turbulence we are able to reproduce all the observed distributions.

Guido Boffetta; Vincenzo Carbone; Paolo Giuliani; Pierluigi Veltri; Angelo Vulpiani

1999-04-23

258

Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources

NASA Technical Reports Server (NTRS)

Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.

Fiorito, Ralph; Titarchuk, Lev

2004-01-01

259

Power law for the permeabiltiy in a two dimensional disordered porous medium

NASA Astrophysics Data System (ADS)

We report numerical calculations of the permeability as a function of porosity for a two-dimensional disordered porous medium. This medium is modeled using the well known “Swiss Cheese” model. The fluid is simulated using a cellular automata algorithm. We find that for relatively high porosities the permeability decays exponentially with the density of obstacles. As a consequence of this exponential behavior, a power-law dependence of the permeability as a function of the porosity is obtained, for this model system. We find that the power-law exponent is given by the ratio between two characteristic scales. One scale is given by the inverse of the area of one obstacle, and is approximately equal to the density of obstacles necessary to reach the percolation threshold. The other scale is equal to the average change in the density of obstacles necessary for the permeability to be reduced to about 1/ e of its original value.

Reyes, Leonardo I.; V, Ricardo Parades; Gutiérrez, Gustavo

1999-12-01

260

The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function

This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modeling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like...

Basu, Shantanu; Auddy, Sayantan

2015-01-01

261

Input-anticipating critical reservoirs show power law forgetting of unexpected input events.

Usually reservoir computing shows an exponential memory decay. This letter investigates under which circumstances echo state networks can show a power law forgetting. That means traces of earlier events can be found in the reservoir for very long time spans. Such a setting requires critical connectivity exactly at the limit of what is permissible according to the echo state condition. However, for general matrices, the limit cannot be determined exactly from theory. In addition, the behavior of the network is strongly influenced by the input flow. Results are presented that use certain types of restricted recurrent connectivity and anticipation learning with regard to the input, where power law forgetting can indeed be achieved. PMID:25774542

Mayer, Norbert Michael

2015-05-01

262

Recent Progress on the Analysis of Power-law Features in Complex Cellular Networks

Complex interactions between different kinds of bio-molecules and essential nutrients are responsible for cellular functions.\\u000a Rapid advances in theoretical modeling and experimental analyses have shown that drastically different biological and non-biological\\u000a networks share a common architecture. That is, the probability that a selected node in the network has exactly k edges decays as a power-law. This finding has definitely opened

J. C. Nacher; T. Akutsu

2007-01-01

263

Creeping flows of power-law fluids through periodic arrays of elliptical cylinders

Results from numerical simulations and lubrication theory are presented for creeping flows of power-law fluids through periodic arrays of elliptical cylinders. Flows are considered in the plane perpendicular to the axes of the cylinders, both along an axis of the array (on-axis flow) and at an angle to the axes of the array (off-axis flows). Results are presented for the

J. K. Woods; P. D. M. Spelt; P. D. Lee; T. Selerland; C. J. Lawrence

2003-01-01

264

Deviation from power law of the global earthquake seismic moment distribution

The distribution of earthquake seismic moment is of capital importance to evaluate seismic hazard, in particular regarding the most extreme events. Likelihood-ratio tests let to compare the performance of the most suitable probabilistic models when ?tted to the global CMT catalog. The conclusion is that the truncated gamma model outperforms the power law and the tapered Gutenberg-Richter models, being able to explain the empirical data both before and after the great Sumatra-Andaman earthquake of 2004.

Serra, Isabel

2015-01-01

265

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

266

A power-law distribution for tenure lengths of sports managers

NASA Astrophysics Data System (ADS)

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.

Aidt, Toke S.; Leong, Bernard; Saslaw, William C.; Sgroi, Daniel

2006-10-01

267

Spectral properties of empirical covariance matrices for data with power-law tails

NASA Astrophysics Data System (ADS)

We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the system. The method is applicable to a class of random matrices with radial measures including those with heavy (power-law) tails in the probability distribution. As an example we apply it to a multivariate Student distribution.

Burda, Zdzis?aw; Görlich, Andrzej T.; Wac?aw, Bart?omiej

2006-10-01

268

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

Second Law Analysis for Process and Energy Engineering: Use in a Steam/Power Cycle I Dominick Sama Richard Gaggloli Daniel Finkenthal William Cooley Unlverlsty of Lowell Introduction The objective of this paper Is to demonstrate how the use... playa part in the foregoing case study. Acknowledgement ThIs wQrk was supported In part by the Center for Producl!vlty Enhancement, University of Lowell. References ASME Vol. AES I, Analysis of Energy Systems: Design! and Operation, 1985 (A...

Sama, D.; Sanhong, Q.

269

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

270

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

271

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

272

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

273

Comparison of generalized Reynolds and Navier Stokes equations for flow of a power law fluid

NASA Technical Reports Server (NTRS)

This paper compares a finite element solution of a modified Reynolds equation with a finite difference solution of the Navier-Stokes equation for a power law fluid. Both the finite element and finite difference formulation are reviewed. Solutions to spiral flow in parallel and conical geometries are compared. Comparison with experimental results are also given. The effects of the assumptions used in the Reynolds equation are discussed.

Mullen, R. L.; Prekwas, A.; Braun, M. J.; Hendricks, R. C.

1987-01-01

274

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

275

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

276

Improved power-law estimates from multiple samples provided by millennium climate simulations

NASA Astrophysics Data System (ADS)

Using the long annual mean temperature time series provided by millennium Earth System Model simulations and a method of discrete Fourier transform with varying starting point and length of time window together with averaging, we get good fits to power laws between two characteristic oscillatory timescales of the model climate: multidecadal (50-80 years) and El Nino (3-6 years) timescales. For global mean temperature, we fit ? ˜ 0.35 in a relation S( f) ˜ f - ? in a simulation without external climate forcing and ? over 0.7 in a simulation with external forcing included. The power law is found both with and without external forcing despite the forcings, e.g. the volcanic forcing, not showing similar behaviour, indicating a nonlinear temperature response to time-varying forcing. We also fit a power law with ? ˜ 8 to the narrow frequency range between El Nino frequencies (up to 1/(3.2 years)) and the Nyquist frequency (1/(2 years)). Also, monthly mean temperature time series are considered and a decent power-law fit for frequencies above 1/year is obtained. Regional variability in best-fit ? is explored, and the impact of choosing the frequency range on the result is illustrated. When all resolved frequencies are used, land areas seem to have lower ?s than ocean areas on average, but when fits are restricted to frequencies below 1/(6 years), this difference disappears, while regional differences still remain. Results compare well with measurements both for global mean temperature and for the central England temperature record.

Henriksson, S. V.; Räisänen, P.; Silen, J.; Järvinen, H.; Laaksonen, A.

2015-02-01

277

Cutoff frequencies in diffusion-type power-law profile waveguides

The cutoff frequencies Vc0 of strongly asymmetric planar waveguides with diffusion-type power-law refractive-index profiles g(X)=Xp are found to be the solutions of J-? (2?Vc0)=0 with ?=1\\/(p+2). To a high degree of accuracy, the cutoff frequencies can be approximated by linear functions of the profile parameter p. The effect of the cover, as well as that of the refractive-index gradient in

Hagen Renner

1997-01-01

278

Universal scaling of dissolved oxygen distribution at the sediment-water interface: A power law

Dissolved oxygen (DO) distribution at the sediment-water interface of a flow over a smooth bed is investigated for Reynolds numbers .360 and ,4,090. These conditions are commonly encountered in streams, wetlands, and lakes. A power-law scaling of DO distribution is derived and compared with experimental data. The scaling analysis is based on DO flux at the sediment-water interface in a

Miki Hondzo; Tom Feyaerts; Richard Donovan; Ben L. O'Connor

2005-01-01

279

Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?

The statistics of quiescent times tauL between successive bursts of solar flares activity, performed using 20 years of data, displays a power law distribution with exponent alpha~=2.4. This is an indication of an underlying complex dynamics with long correlation times. The observed scaling behavior is in contradiction with the self-organized criticality models of solar flares which predict Poisson-like statistics. Chaotic

Guido Boffetta; Vincenzo Carbone; Paolo Giuliani; Pierluigi Veltri; Angelo Vulpiani

1999-01-01

280

NASA Astrophysics Data System (ADS)

We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.

Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.

2014-09-01

281

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

282

Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power-law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.

Itzhak Fouxon; Harald A. Posch

2011-12-28

283

On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.

Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.

2011-01-01

284

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

285

Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, a{sub sym}/T, extracted in previous work and that of the pairing term, a{sub p}/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I=N-Z value, the corrected yields of isotopes relative to the yield of {sup 12}C show a power law distribution Y(N,Z)/Y({sup 12}C){approx}A{sup -}{tau} in the mass range 1{<=}A{<=}30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted {tau} value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be {tau}{sup prim}=2.4{+-}0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.

Huang, M. [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); Graduate University of Chinese Academy of Sciences, Beijing 100049 (China); Cyclotron Institute, Texas A and M University, College Station, Texas 77843 (United States); Wada, R.; Hagel, K.; Barbui, M.; Bottosso, C.; Materna, T.; Natowitz, J. B.; Qin, L.; Rodrigues, M. R. D.; Sahu, P. K.; Schmidt, K. J. [Cyclotron Institute, Texas A and M University, College Station, Texas 77843 (United States); Chen, Z. [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); Cyclotron Institute, Texas A and M University, College Station, Texas 77843 (United States); Keutgen, T. [FNRS and IPN, Universite Catholique de Louvain, B-1348 Louvain-Neuve (Belgium); Kowalski, S. [Institute of Physics, Silesia University, Katowice (Poland); Bonasera, A. [Cyclotron Institute, Texas A and M University, College Station, Texas 77843 (United States); Laboratori Nazionali del Sud, INFN, via Santa Sofia, 62, I-95123 Catania (Italy); Wang, J. [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China)

2010-11-15

286

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

287

Dust-acoustic waves and stability in the permeating dusty plasma. II. Power-law distributions

The dust-acoustic waves and the stability theory for the permeating dusty plasma with power-law distributions are studied by using nonextensive q-statistics. In two limiting physical cases, when the thermal velocity of the flowing dusty plasma is much larger than, and much smaller than the phase velocity of the waves, we derived the dust-acoustic wave frequency, the instability growth rate, and the instability critical flowing velocity. As compared with the formulae obtained in part I [Gong et al., Phys. Plasmas 19, 043704 (2012)], all formulae of the present cases and the resulting plasma characteristics are q-dependent, and the power-law distribution of each plasma component of the permeating dusty plasma has a different q-parameter and thus has a different nonextensive effect. Further, we make numerical analyses of an example that a cometary plasma tail is passing through the interplanetary space dusty plasma and we show that these power-law distributions have significant effects on the plasma characteristics of this kind of plasma environment.

Gong Jingyu; Du Jiulin [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China); Liu Zhipeng [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China); Department of Fundamental Subject, Tianjin Institute of Urban Construction, Tianjin 300384 (China)

2012-08-15

288

Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns. PMID:25779306

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

2015-01-01

289

NASA Astrophysics Data System (ADS)

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

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

2015-03-01

290

On the interplay between short and long term memory in the power-law cross-correlations setting

NASA Astrophysics Data System (ADS)

We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equal to an average of separate Hurst exponents of the analyzed processes. Strength of short term memory has no effect on these asymptotic properties. Implications of these findings for the power-law cross-correlations concept are further discussed.

Kristoufek, Ladislav

2015-03-01

291

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 (R-114) and Refrigerant-22 (R-22) in combinations from pure R-114 to pure R-22 was calculated for such cycles. Various alternatives were considered: (1) minimum geofluid outlet temperature constraint/no constraint, (2) dry turbine expansion/expansion through vapor dome, and (3) use of turbine exhaust gas recuperator/no recuperator. Results of the study indicate that the halocarbon mixtures are at least as good as the hydrocarbon mixtures previously analyzed for a 360 F resource. The magnitude of the net geofluid effectiveness (net energy produced per unit mass geofluid flow) for the R-114/R-22 mixtures is the same as for the best hydrocarbon mixture previously analyzed. The percentage improvement in effectiveness in using mixtures over using the pure fluids as working fluids is comparable for both classes of working fluids.

Bliem, C.J.

1987-01-01

292

NASA Astrophysics Data System (ADS)

Understanding runoff generation is important for management of freshwater systems. Determining transit time distributions of streamwaters and how they change with discharge gives information on the flowpaths and recharge sources of streams - vital information for determining the responses of streams to stressors such as pollution, landuse change, or climate change. This work takes a first look at unique information on how transit time distributions change with discharge in some New Zealand catchments. Transit time distributions of streamwaters have been determined from tritium measurements on single samples in this work. This allows changes with stream discharge to be observed, in contrast to previous isotope studies which have given averaged transit time distributions based on series of samples. In addition, tritium reveals the wide spectrum of ages present in streams whereas oxygen-18 or chloride variations only show the younger ages (Stewart et al., 2010). It was found that the mean transit time (MTT) data could be reasonably represented by straight lines in log-log plots, indicating power law relationships between MTT and discharge. Similar power law behaviour has been observed for the rock forming elements such as silica in streamwaters (Godsey et al., 2009). Case studies are presented for two New Zealand catchments, both with volcanic ash substrates. Toenepi is a dairy catchment near Hamilton, which shows well-constrained power law relationships between MTT and discharge, and between silica concentration and discharge (Morgenstern et al., 2010). Baseflow MTTs vary from 2.5 to 157 years. Tutaeuaua is a pastoral farming catchment near Taupo. Results for nested catchments along the stream also show power law relationships for both MTT and silica with discharge. Streamwater MTTs vary from 1 to 11 years. The results indicate that (1) relatively old waters dominate many streams, (2) streamwater ages vary with discharge, and (3) age, like silica, varies according to power law relationships with stream discharge. References: Godsey, S.E., Kirchner, J.W., Clow, D.W. Hydrological Processes 23, 1844-1864, 2009. Morgenstern, U., Stewart M. K., Stenger, R. Hydrology and Earth System Sciences 14, 2289-2301, 2010. Stewart, M.K., Morgenstern, U., McDonnell, J.J. Hydrological Processes 24(12), 1646-1659, 2010.

Stewart, Michael; Morgenstern, Uwe

2013-04-01

293

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

294

Double Power-law Distribution of Magnetic Energy in the Solar Corona over an Active Region

NASA Astrophysics Data System (ADS)

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 2/8?) and the ohmic dissipation power (ODP, j 2/?), in which j is the electric current density (c/4?? × B) and ? 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 ~1.0 × 104 erg cm-3 and ~2.0 × 10-15 W cm-3 (assuming ? = 105 ?-1 m-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; Wiegelmann, Thomas; Inhester, Bernd

2013-02-01

295

ERIC Educational Resources Information Center

Proposes a simple procedure based on an expansion of the exponential terms of Raoult's law by applying it to the case of the benzene-toluene mixture. The results with experimental values are presented as a table. (YP)

Cardinali, Mario Emilio; Giomini, Claudio

1989-01-01

296

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

297

Edge effect on the power law distribution of granular avalanches Kinga A. Lrincz and Rinke J-law-distributed avalanche sizes to quasiperiodic system-spanning avalanches. Conversely, by removing ledges the incidence of system- spanning avalanches is significantly reduced. This may offer a perspective on new avalanche

Wijngaarden, Rinke J.

298

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

299

Numerical study of unsteady stenosis flow: parametric evaluation of power-law model.

Currently the best indicator for surgical treatment of arterio-sclerosis is the degree of stenosis. Although X-ray angiography is currently the standard, cost and morbidity are distinct disadvantages. By modelling stenosis and studying its biofluid mechanics, one can apply its results in the field of arterial disease research. This formed the motivation for this work. A non-Newtonian (power law) incompressible Navier-Stokes (N-S) solver was developed using the method of operator splitting and artificial compressibility. The vehicle used is the computational fluid dynamics (CFD) numerical library FASTFLO. The power-law model developed is then used to do a parametric study of the effect of 'n' on blood flow mechanics where 'n' is the power index that determines the haematocrit of blood. A pulsatile pressure wave over a cardiac cycle of a second was used to simulate transient flow over a hypothetical two-dimensional stenotic geometry. By comparing the different velocity pressure, wall shear stress and viscosity profiles, it has been found when 'n' increases, the vortex formation and peak wall shear stress decreases (magnitudes of < 1.5 Pa). Since the formation of vortices and low oscillatory wall shear stress on the stenotic wall is detrimental to the well-being of the arterial tract, it can therefore be inferred that there might be a relationship between the diseased state of blood (power law) and early genesis of atherosclerosis. However, the conclusion of this paper marks the advent of new research directions in this field of study. PMID:11204243

Ng, E Y; Siauw, W L; Goh, W E

2000-01-01

300

The decay of excited aluminum-cluster anions (Al{sub n}{sup -}, n=4 and 5) has been investigated in a cryogenic linear ion-beam trap. A power-law is found to accurately reproduce the time dependence of the observed decay rates at early storage times, although the exponents are significantly larger than the typically observed 1/t decay. It is shown that the power-law exponent is, at most, weakly dependent on the cluster electron affinity and heat capacity. A previous power-law exponent model for small clusters is also shown to be in disagreement with both investigated species. The attribution of a drop in the decay rate at later times to radiative cooling as observed in larger molecules also does not appear justified in our case. A strong dependence of the power-law exponent on the ambient temperature was observed.

Froese, M. W.; Blaum, K.; Fellenberger, F.; Grieser, M.; Lange, M.; Laux, F.; Menk, S.; Orlov, D. A.; Repnow, R.; Sieber, T.; Hahn, R. von; Wolf, A. [Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg (Germany); Toker, Y. [Department of Particle Physics, Weizmann Institute of Science, Rehovot, 76100 (Israel)

2011-02-15

301

Energy dependent power spectral states and origin of aperiodic variability in black hole binaries

We found the black hole candidate MAXI J1659-152 showed distinct power spectra, i.e., a power-law noise (PLN) vs. band-limited noise (BLN) plus quasi-periodic oscillations (QPOs), below and above about 2 keV respectively, in the observations with the Swift and the RXTE during the 2010 outburst, indicating a high energy cut-off of the PLN and a low energy cut-off of the BLN and the QPOs around 2 keV. The emergence of the PLN and the fading of the BLN and the QPOs initially took place from below 2 keV when the source entered the hard intermediate state and finally 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 X-ray and the hard X-ray bands. Our results indicate that the PLN is associated with the optically thick disk in both hard and intermediate states, and power spectral state is independent of the X-ray energy spectral state in a broadband view. We suggest that in the hard a...

Yu, Wenfei

2013-01-01

302

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

303

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

304

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

305

Power laws, that is, power spectral densities (PSDs) exhibiting 1/f(?) behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency 1/f(?) power laws with power-law exponents analytically identified as ??(I) = 1/2 for the soma membrane current, ??(p) = 3/2 for the current-dipole moment, and ??(V) = 2 for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink (1/f) noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how 1/f(?) 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

2014-11-01

306

Pinch-off dynamics of liquid threads of power law fluids surrounded by a passive ambient fluid are studied theoretically by fully two-dimensional (2-D) computations and one-dimensional (1-D) ones based on the slender-jet approximation for 0n?1, where n is the power law exponent, and 0?Oh??, where Oh??0\\/??R is the Ohnesorge number and ?0, ?, ?, and R stand for the zero-deformation-rate viscosity,

Ronald Suryo; Osman A. Basaran

2006-01-01

307

Effect of phase morphology on bulk strength for power-law materials

NASA Astrophysics Data System (ADS)

The strength of a polyphase aggregate comprising power-law materials is a function of the constitutive laws of the phases present, the arrangement of those phases and environmental conditions such as temperature. Primarily for geological applications, we consider the degree to which the arrangement of the phases has a significant influence on bulk strength. Calculations based on current single-mineral experimental data indicate that the absolute and relative strength differences between the upper and lower theoretical bounds vary widely with mineral pair, environmental conditions and strain rate. For example, at 850 °C, some pairs, such as plagioclase-clinopyroxene, are highly sensitive to phase morphology, whereas others, such as quartz-plagioclase, are not. Using a finite-element implementation of asymptotic expansion homogenization, we have calculated the bulk strength of natural and synthetic microstructures across macroscale strain gradients. We find that phase morphology does not change sufficiently in most cases to be the dominant factor in bulk strength variation. Thus on its own, phase morphology in an aggregate of power-law materials does not appear to be a major control on bulk strength under typical viscous geological conditions. However, phase morphology does affect microscale stress and strain rate patterns, which in turn can induce microscale variations in constitutive laws and diffusional pathways. These factors, including reactions and changing deformation mechanisms, are strongly influenced by phase morphology and do cause strength variation in rocks. As a result, any parametrization of rock strength needs to account for evolving modal mineralogy and deformation mechanisms in addition to morphological changes alone.

Gerbi, Christopher; Johnson, Scott E.; Cook, Alden; Vel, Senthil S.

2014-01-01

308

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

309

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

310

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

311

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

312

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

313

Universal inverse power-law distribution for temperature and rainfall in the UK region

NASA Astrophysics Data System (ADS)

Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.

Selvam, A. M.

2014-06-01

314

NASA Astrophysics Data System (ADS)

Drylands are important ecosystems that cover about 40% of the Earth's land surface and provide goods and services for about 30% of the Earth's inhabitants. Dryland vegetation is almost universally patchy reflecting the resource limitation endemic to these areas and this patchiness unquestionably results from some type of self-organization. Understanding the function of these ecosystems is critical for their effective management and for understanding how they will be affected by changes in climate and land use as well as by invasion of non-native species. There are three main paradigms that have emerged in the literature to explain dryland ecosystem structure and dynamics. The connectivity paradigm posits that spatiotemporal patterns of vegetation observed in drylands are a result of the lateral movement of resources and disturbance along connected pathways. Other authors have examined the impact of local-scale interactions that give rise to large-scale patterns in the form of power law distributions of vegetation patches. Deviation from power law distributions as a sign of imminent, catastrophic change has been a common thread in this line of research. The sudden and often irreversible change observed in dryland ecosystems has led others to emphasize the importance of feedbacks that lead to the existence of alternative stable states and hysteresis in drylands. This latter view is closely aligned with the state-and-transition model approach. Here we show, through a series of conceptual and mathematical model arguments, that these three approaches - connectivity, power law distributions, and alternative stable states - can in many circumstances be considered equivalent. They are, in essence, different facets of a common set underlying processes. This transdisciplinary, integrated perspective should help understand how spatial processes interact to create pattern and patchiness in dryalnds as well as other ecosystems worldwide.

Okin, Gregory; D'Odorico, Paolo

2013-04-01

315

Air-chemistry "turbulence": power-law scaling and statistical regularity

NASA Astrophysics Data System (ADS)

With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, plain/hill, and industrial/agricultural locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, and intermediate (20 ~ 30 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of -5/3 and -1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. These exponents are mostly independent of the averages and standard deviations of time series measured at various geographic settings, i.e., the spatial inhomogeneities. In other words, they possess dominant universal structures. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, -3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are important structural information, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.

Hsu, H.-M.; Lin, C.-Y.; Guenther, A.; Tribbia, J. J.; Liu, S. C.

2011-08-01

316

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

317

Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids

The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.

Maloney, C. E. [Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Robbins, M. O. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States)

2009-06-05

318

Strain pseudospins with power-law interactions: Glassy textures of a cooled coupled-map lattice

We consider a spin-1 model of strain pseudospins S(r&ar;)=0,±1 that arise from a triple-well Landau free energy for a square\\/rectangle or ``austenite-martensite'' structural transformation of a two-dimensional lattice. The pseudospin model has elastic-compatibility-induced power-law anisotropic (PLA) interactions and no quenched disorder. The iteratively solved local mean-field equations for form a temperature-dependent PLA-coupled nonlinear-map lattice, where t is the iteration ``time.''

S. R. Shenoy; T. Lookman

2008-01-01

319

Underdamped strain dynamics of a martensitic model with power-law interactions

NASA Astrophysics Data System (ADS)

Focusing on conversion-time delays in athermal martensites, we present our results on underdamped strain dynamics of triple-well Landau free-energies with power-law anisotropic interactions for square-rectangle ferroelastic transition. After a temperature quench of 2% initial martensite seeds, the deterministic underdamped strain dynamics shows, interestingly, both fast conversions below a temperature and incubation delays above it, as in experiment and Monte Carlo simulations. On increasing damping constant, the fast conversions transform to incubation delays. Surprisingly, conversion-time delays have Vogel-Fulcher divergences as in Monte Carlo simulations. Microstructural evolutions are in good agreement with earlier studies.

Shankaraiah, N.; Puri, Sanjay; Shenoy, S. R.

2014-04-01

320

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

321

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

322

The flow of Newtonian and power law fluids in elastic tubes

NASA Astrophysics Data System (ADS)

We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier-Stokes equations.

Sochi, Taha

2014-12-01

323

Light Fragment Production and Power Law Behavior in Au + Au Collisions

Using charged-particle-exclusive measurements of Au+Au collisions in the LBL Bevalac`s EOS time projection chamber, we investigate momentum-space densities of fragments up to {sup 4}He as a function of fragment transverse momentum, azimuth relative to the reaction plane, rapidity, multiplicity, and beam energy. Most features of these densities above a transverse momentum threshold are consistent with momentum-space coalescence, and, in particular, the increase in sideward flow with fragment mass is generally well described by a momentum-space power law.

Wang, S.; Albergo, S.; Bieser, F.; Brady, F.P.; Caccia, Z.; Cebra, D.A.; Chacon, A.D.; Chance, J.L.; Choi, Y.; Costa, S.; Elliott, J.B.; Gilkes, M.L.; Hauger, J.A.; Hirsch, A.S.; Hjort, E.L.; Insolia, A.; Justice, M.; Keane, D.; Kintner, J.; Lisa, M.A.; Matis, H.S.; McMahan, M.; McParland, C.; Olson, D.L.; Partlan, M.D.; Porile, N.T.; Potenza, R.; Rai, G.; Rasmussen, J.; Ritter, H.G.; Romanski, J.; Romero, J.L.; Russo, G.V.; Scharenberg, R.P.; Scott, A.; Shao, Y.; Srivastava, B.K.; Symons, T.J.M.; Tincknell, M.L.; Tuve, C.; Warren, P.G.; Weerasundara, D.; Wieman, H.H.; Wolf, K.L. [Lawrence Berkeley Laboratory, Berkeley, California 94720 (United States)] [Lawrence Berkeley Laboratory, Berkeley, California 94720 (United States); [Kent State University, Kent, Ohio 44242 (United States); [Purdue University, West Lafayette, Indiana 47907 (United States); [University of California, Davis, California 95616 (United States); [Texas A& M University, College Station, Texas 77843 (United States); [Universita di Catania and INFN-Sezione di Catania, 95129 Catania (Italy); (EOS Collaboration)

1995-04-03

324

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

325

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

326

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

327

The Common Law Power of the Legislature: Insurer Conversions and Charitable Funds

New York's Empire Blue Cross and Blue Shield conversion from nonprofit to for-profit form has considerable legal significance. Three aspects of the conversion make the case unique: the role of the state legislature in directing the disposition of the conversion assets, the fact that it made itself the primary beneficiary of those assets, and the actions of the state attorney general defending the state rather than the public interest in the charitable assets. Drawing on several centuries of common law rejecting the legislative power to direct the disposition of charitable funds, this article argues that the legislature lacked power to control the conversion and direct the disposition of its proceeds and that its actions not only undermined the nonprofit form but also raised constitutional concerns. PMID:15960770

Horwitz, Jill R; Fremont-Smith, Marion R

2005-01-01

328

Quantum phase transitions and thermodynamics of the power-law Kondo model

NASA Astrophysics Data System (ADS)

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, ?(?)˜|?|r, with exponent -1

Mitchell, Andrew K.; Vojta, Matthias; Bulla, Ralf; Fritz, Lars

2013-11-01

329

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

330

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

331

Ruling out the power-law form of the scalar primordial spectrum

NASA Astrophysics Data System (ADS)

Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3? CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large r and at the same time provide suppression in scalar primordial spectrum at large scales.

Hazra, Dhiraj Kumar; Shafieloo, Arman; Smoot, George F.; Starobinsky, Alexei A.

2014-06-01

332

Ruling out the power-law form of the scalar primordial spectrum

Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than $3\\sigma$ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4] can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5] can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio ($r$) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large $r$ and at the same time provide suppression in scalar primordial spectrum at large scales.

Dhiraj Kumar Hazra; Arman Shafieloo; George F. Smoot; Alexei A. Starobinsky

2014-07-16

333

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

NASA Astrophysics Data System (ADS)

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.

Radicchi, Filippo

2014-11-01

334

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

335

THE POWER-LAW SPECTRA OF ENERGETIC PARTICLES DURING MULTI-ISLAND MAGNETIC RECONNECTION

Power-law distributions are a near-universal feature of energetic particle spectra in the heliosphere. Anomalous cosmic rays (ACRs), super-Alfvenic ions in the solar wind, and the hardest energetic electron spectra in flares all have energy fluxes with power laws that depend on energy E approximately as E {sup -1.5}. We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omnidirectional particle distribution f (v, t) that is solved in closed form to reveal v {sup -5} (corresponding to an energy flux varying as E {sup -1.5}) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state, the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems.

Drake, J. F.; Swisdak, M. [Department of Physics and the Institute for Physical Science and Technology Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD (United States); Fermo, R., E-mail: drake@umd.edu, E-mail: swisdak@umd.edu, E-mail: rfermo@bu.edu [Institute for Research in Electronics and Applied Physics, Astronomy Department, Boston University, Boston, MA (United States)

2013-01-20

336

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

337

Transition from Exponential to Power Law Income Distributions in a Chaotic Market

NASA Astrophysics Data System (ADS)

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ? (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo

338

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

339

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

340

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

341

Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.

We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between R and R+dR is proportional to R(-(a+1)), where a>2. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range interaction, we argue that in our problem, the critical exponents take their short-range values for a>3-?(sr) whereas they depend on a for a<3-?(sr) where ?(sr) is the anomalous dimension for the usual percolation problem. The mean-field regime obtained in the fluid problem corresponds to the fully covered regime, a?2, in the percolation problem. We propose an approximate renormalization scheme to determine the correlation length exponent ? and the percolation threshold. We carry out Monte Carlo simulations and determine the exponent ? as a function of a. The determined values of ? show that it is independent of the parameter a for a>3-?(sr) and is equal to that for the lattice percolation problem, whereas ? varies with a for 2

Sasidevan, V

2013-08-01

342

NASA Astrophysics Data System (ADS)

We analyze the exit dynamics of pedestrians who are initially confined in a room. Pedestrians are modeled as cellular automata and compete to escape via a known exit at the soonest possible time. A pedestrian could move forward, backward, left or right within each iteration time depending on adjacent cell vacancy and in accordance with simple rules that determine the compulsion to move and physical capability relative to his neighbors. The arching signatures of jamming were observed and the pedestrians exited in bursts of various sizes. Power-law behavior is found in the burst-size frequency distribution for exit widths w greater than one cell dimension ( w>1). The slope of the power-law curve varies with w from -1.3092 (w=2) to -1.0720 (w=20) . Streaming which is a diffusive behavior, arises in large burst sizes and is more likely in a single-exit room with w=1 and leads to a counterintuitive result wherein an average exit throughput Q is obtained that is higher than with w=2,3, or 4. For a two-exit room ( w=1), Q is not greater than twice the yield of a single-exit room. If the doors are not separated far enough (<4 w), Q becomes even significantly less due to a collective slow-down that emerges among pedestrians crossing in each other's path (disruptive interference effect). For the same w and door number, Q is also higher with relaxed pedestrians than with anxious ones.

Perez, Gay Jane; Tapang, Giovanni; Lim, May; Saloma, Caesar

2002-09-01

343

Power laws in microrheology experiments on living cells: comparative analysis and modelling

We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a micrometric bead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient $G_e(\\omega)$ is retrieved. Both $J(t)$ and $G_e(\\omega)$ exhibit power law behavior: $J(t)= A(t/t_0)^\\alpha$ and $\\bar G_e(\\omega)\\bar = G_0 (\\omega/\\omega_0)^\\alpha$, with the same exponent $\\alpha\\approx 0.2$. This power law behavior is very robust ; $\\alpha$ is distributed over a narrow range, and shows almost no dependance on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors $A_0$ and $G_0$appear very sensitive to these parameters. Whereas the exponents $\\alpha$ are normally distribu...

Balland, M; Icard, D; Fereol, S; Asnacios, A; Browaeys, J; Henon, S; Gallet, F; Balland, Martial; Desprat, Nicolas; Icard, Delphine; Fereol, Sophie; Asnacios, Atef; Browaeys, Julien; Henon, Sylvie; Gallet, Francois

2006-01-01

344

Universal correlations and power-law tails in financial covariance matrices

NASA Astrophysics Data System (ADS)

We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.

Akemann, G.; Fischmann, J.; Vivo, P.

2010-07-01

345

On the sensitivity of tidal network characterization to power law estimation

NASA Astrophysics Data System (ADS)

Long-term simulations (3000 yr) of an idealized basin using different tidal ranges (1, 2 and 3 m) and grain sizes (120, 480 and 960 ?m) have been performed in order to cover a range of hydrodynamic and sedimentary conditions. Two different cell sizes (50 and 100 m) have been used to study the impact of cell size on tidal network development. The probability distributions of the drainage area and the drainage volume have been computed for every simulation (during an ebb and a flood phase). Power law distributions are observed in drainage area and drainage volume distribution. As an objective estimation of the exponent of a power law is an open issue, different approaches (linear binning, normalized logarithmic binning, cumulative distribution function and maximum likelihood) proposed by White et al. (2008) to estimate the exponent have been used to carry out a sensitivity analysis. Our findings indicate that although all methods results in high and significant correlation coefficients, more work is needed to develop a universal, objective estimation of the exponent.

Jiménez, M.; Castanedo, S.; Zhou, Z.; Coco, G.; Medina, R.; Rodriguez-Iturbe, I.

2014-04-01

346

Nonuniversal power law scaling in the probability distribution of scientific citations

We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations (“classics”) are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The “tipping point” at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975–1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited. PMID:20805513

Peterson, George J.; Pressé, Steve; Dill, Ken A.

2010-01-01

347

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

NASA Astrophysics Data System (ADS)

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L ? mp between the mean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p ? 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q ? 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x1 family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution ofx galaxies are discussed.

Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

2015-04-01

348

Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses

NASA Technical Reports Server (NTRS)

We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.

Wijers, Ralph A. M. J.; Lubin, Lori M.

1994-01-01

349

Emergence of a band-limited power law in the aftershock decay rate of a slider-block model

, and that the power law exponent increases. These results support the inference that the correlation time of the power an earthquake, aftershocks are seismic events of smaller magnitude occurring in the neighbourhood of the rupture [1968], Narteau et al. [2002] devel- op a model of aftershock decay rate based on a Markov process

Narteau, ClÃ©ment

350

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

351

Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT

Purpose: To determine the x-ray photon energy dependence of the anatomic power spectrum of the breast when imaged with dedicated breast computed tomography (CT). Methods: A theoretical framework for scaling the empirically determined anatomic power spectrum at one x-ray photon energy to that at any given x-ray photon energy when imaged with dedicated breast CT was developed. Theory predicted that when the anatomic power spectrum is fitted with a power curve of the form k f{sup -{beta}}, where k and {beta} are fit coefficients and f is spatial frequency, the exponent {beta} would be independent of x-ray photon energy (E), and the amplitude k scales with the square of the difference in energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues. Twenty mastectomy specimens based numerical phantoms that were previously imaged with a benchtop flat-panel cone-beam CT system were converted to 3D distribution of glandular weight fraction (f{sub g}) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of f{sub g} and after converting to linear attenuation coefficients at monoenergetic x-ray photon energies of 20-80 keV in 5 keV intervals. The 1D power spectra along the axes were extracted and fitted with a power curve of the form k f{sup -{beta}}. The energy dependence of k and {beta} were analyzed. Results: For the 20 mastectomy specimen based numerical phantoms used in the study, the exponent {beta} was found to be in the range of 2.34-2.42, depending on the axis of measurement. Numerical simulations agreed with the theoretical predictions that for a power-law anatomic spectrum of the form k f{sup -{beta}}, {beta} was independent of E and k(E) =k{sub 1}[{mu}{sub g}(E) -{mu}{sub a}(E)]{sup 2}, where k{sub 1} is a constant, and {mu}{sub g}(E) and {mu}{sub a}(E) represent the energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues, respectively. Conclusions: Numerical simulations confirmed the theoretical predictions that in dedicated breast CT, the spatial frequency dependence of the anatomic power spectrum will be independent of x-ray photon energy, and the amplitude of the anatomic power spectrum scales by the square of difference in linear attenuation coefficients of fibroglandular and adipose tissues.

Vedantham, Srinivasan; Shi, Linxi; Glick, Stephen J.; Karellas, Andrew [Department of Radiology, University of Massachusetts Medical School, Worcester, Massachusetts 01655 (United States)

2013-01-15

352

Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons

Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of Vm activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the Vm reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the “effective” connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI. PMID:19779556

Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves

2009-01-01

353

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\\phi) = \\Lambda^4[1 \\pm \\cos(\\phi/f)], naturally gives rise to inflation if $f \\sim M_{Pl}$ and $\\Lambda \\sim M_{GUT}$. We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models. We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires $f > 0.3 M_{Pl}$. The primordial density fluctuation spectrum generated is a non-scale-invariant power law, $P(k) \\propto k^{n_s}$, with $n_s \\simeq 1 - (M^2_{Pl}/8\\pi f^2)$, leading to more power on large length scales than the $n_s = 1$ Harrison-Zeldovich spectrum. The standard CDM model with $0 \\la n_s \\la 0.6-0.7$ could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors, $b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to $n_s >0.6$, or $f > 0.3 M_{Pl}$ as well. For extended and power law inflation models, this constraint is even tighter, $n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.

Fred Adams; J. R. Bond; Katherine Freese; Joshua Frieman; Angela Olinto

1992-07-17

354

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 wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Lastly, we propose several experiments to check the prediction of the present theoretical work.

Biman Bagchi

2014-04-20

355

NASA Astrophysics Data System (ADS)

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 wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Lastly, we propose several experiments to check the prediction of the present theoretical work.

Bagchi, Biman

2014-05-01

356

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

357

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

358

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

359

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

360

We study transport in quasi-one-dimensional systems consisting of n connected parallel chains of length L with a power-law distribution of bond conductivities P(sigma)~sigma-alpha alpha<1, sigma<=1. When the transverse bonds are perfect conductors, we find that the conventional law for the transport exponents in one-dimensional systems is not universal but depends sensitively on n. For n finite, there exists a critical

Shlomo Havlin; Armin Bunde; Haim Weissman; Amnon Aharony

1987-01-01

361

: This paper traces the development of Canadian extradition law from the formation of a pro-extradition consensus in the 1860s to the passage of a new Canadian statute in 1877, to that actâ€™s final ratification by Britain in 1883. This process of law reform illustrates Britainâ€™s continuing legal power in Canada. Throughout the 1870s and 1880s imperial authorities suppressed, delayed,

Bradley Miller

2009-01-01

362

This paper traces the development of Canadian extradition law from the formation of a pro-extradition consensus in the 1860s to the passage of a new Canadian statute in 1877, to that actâ€™s final ratification by Britain in 1883. This process of law reform illustrates Britainâ€™s continuing legal power in Canada. Throughout the 1870s and 1880s imperial authorities suppressed, delayed, and

Bradley Miller

2009-01-01

363

Enhancing the Predictive Power of Bath Law Through Earthquake-Type Selection

NASA Astrophysics Data System (ADS)

The empirical Bath law states that the magnitude difference D1 between a mainshock and its largest aftershock is about 1.2, independently of the mainshock magnitude. Systematic analysis performed on global and regional catalogs confirm this average value of 1.2 but also shows a large dispersion of about 0.4. This dispersion greatly limits the predictive power Bath law and a physical interpretation of its value. Aftershocks are usually assumed to occur as a result of stress transfer during an earthquake which suggests that D1, and therefore its variability, would be linked to some earthquake rupture properties. In this study, we explore this hypothesis by looking at earthquakes with specific rupture properties. Among the different types of parameters tested, we find that D1 is systematically higher than 1.2 for tsunami earthquakes and also bilateral ruptures. Different physical interpretations of these results will be discussed. But in the case of tsunami earthquakes, the fact that the events rupture through the shallow part of subduction wedge where the material is less consolidated and requires higher fracture energy, provides a simple explanation. Our results are drawn from a limited number of events (less than 10) because tsunami earthquakes and bilateral ruptures are rare or difficult to unambiguously identify. Hence, we cannot totally exclude that our results are affected by a sampling bias. However, the observations are systematically above 1.2 and give a average D1 of 1.7. This difference implies that the largest aftershock expected for this types of ruptures would be 4 times smaller than predicted by the original Bath law.

Sladen, A.

2012-12-01

364

Structural Diversity of Protein Segments Follows a Power-Law Distribution

The local structures of protein segments were classified and their distribution was analyzed to explore the structural diversity of proteins. Representative proteins were divided into short segments using a sliding L-residue window. Each set of local structures consisting of consecutive 1–31 amino acids was classified using a single-pass clustering method. The results demonstrate that the local structures of proteins are very unevenly distributed in the protein universe. The distribution of local structures of relatively long segments shows a power-law behavior that is formulated well by Zipf's law, implying that a protein structure possesses recursive and fractal characteristics. The degree of effective conformational freedom per residue as well as the structure entropy per residue decreases gradually with an increasing value of L and then converges to constant values. This suggests that the number of protein conformations resides within the range between 1.2L and 1.5L and that 10- to 20-residue segments are already proteinlike in terms of their structural diversity. PMID:16731566

Sawada, Yoshito; Honda, Shinya

2006-01-01

365

Taylor's law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin–Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA. PMID:23427171

Cohen, Joel E.; Xu, Meng; Schuster, William S. F.

2013-01-01

366

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

367

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

368

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

369

Overall potentials and extremal surfaces of power law or ideally plastic composites

NASA Astrophysics Data System (ADS)

A METHOD is proposed for bounding the overall properties of a class of composite materials in terms of the properties of the individual phases and of their arrangement. It applies to power law materials and, as a special case, to rigid ideally plastic materials. A link between the overall potential of a nonlinear composite and the overall energy of a fictitious linear composite is presented with no assumptions on the arrangement of the phases. With this method, any upper bound available for linear materials can easily be transposed to nonlinear materials. A new characterizing of the external surface of ideally plastic composites is given. The possible applications of these bounds are illustrated in a study on two-phase isotropic composites and the predictions of the bounds are compared with Finite Element cell calculations.

Suquet, P. M.

1993-06-01

370

Quantum probes of timelike naked singularities in $2+1-$ dimensional power - law spacetimes

The formation of naked singularities in $2+1-$ dimensional power - law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field respectively, are considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon and Dirac equations are used to probe the classical timelike naked singularities developed at $r=0$. We show that when the classically singular spacetimes probed with scalar waves, the considered spacetimes remains singular. However, the spinorial wave probe of the singularity in the metric of a self-interacting real scalar field remains quantum regular. The notable outcome in this study is that the quantum regularity/singularity can not be associated with the energy conditions.

O. Gurtug; M. Halilsoy; S. Habib Mazharimousavi

2015-01-29

371

Mechanics of adhesive contact on a power-law graded elastic half-space

NASA Astrophysics Data System (ADS)

We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E= E0( z/ c0) k (0< k<1) while Poisson's ratio ? remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of P cr=-( k+3) ?R? ?/2 where ? ? is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k=0, the Gibson solid when k?1 and ?=0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off.

Chen, Shaohua; Yan, Cong; Zhang, Peng; Gao, Huajian

2009-09-01

372

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

373

Correspondence between $f(G)$ Gravity and Holographic Dark Energy via Power-law Solution

In this paper, we discuss cosmological application of holographic Dark Energy (HDE) in the framework of $f(G)$ modified gravity. For this purpose, we construct $f(G)$ model with the inclusion of HDE and a well-known power law form of the scale factor $a(t)$. The reconstructed $f(G)$ is found to satisfy a sufficient condition for a realistic modified gravity model. We find quintessence behavior of effective equation of state (EoS) parameter $\\omega_{DE}$ through energy conditions in this context. Also, we observe that the squared speed of sound $v_s^2$ remains negative which shows the instability of HDE $f(G)$ model.

Abdul Jawad; Antonio Pasqua; Surajit Chattopadhyay

2012-11-22

374

Hydrodynamic dispersion in a hierarchical network with a power-law distribution of conductances.

Dispersion is studied on a two-dimensional hierarchical pore network with a power-law distribution of conductances, i.e., P(g) approximately g(mu-1), with gepsilon(0,1), and mu is the disorderliness parameter (mu > 0). A procedure for computing tracer dispersion transport on hierarchical networks was developed. The results show that the effective diffusion coefficient of the network scales similarly as conduction on the same lattice. This means that the disorder length scales for conduction and diffusion processes are the same, and can be predicted from percolation theory. The dispersivity, xi identical with D(||)/U, was found to diverge rapidly as mu-->0. The result is in agreement with the model developed by Bouchaud and Georges (C.R. Acad. Sci. (Paris) 307 1431, 1988). A limiting value of mu approximately 0.45 was found, below which the convection-dispersion equation is no longer valid. PMID:15903571

Alvarado, Vladimir

2005-03-01

375

The power law for the Buffon needle probability of the four-corner Cantor set

Let $C_n$ be the $n$-th generation in the construction of the middle-half Cantor set. The Cartesian square $K_n$ of $C_n$ consists of $4^n$ squares of side-length $4^{-n}$. The chance that a long needle thrown at random in the unit square will meet $K_n$ is essentially the average length of the projections of $K_n$, also known as the Favard length of $K_n$. A classical theorem of Besicovitch implies that the Favard length of $K_n$ tends to zero. It is still an open problem to determine its exact rate of decay. Until recently, the only explicit upper bound was $\\exp(- c\\log_* n)$, due to Peres and Solomyak. ($\\log_* n$ is the number of times one needs to take log to obtain a number less than 1 starting from $n$). We obtain a power law bound by combining analytic and combinatorial ideas.

Nazarov, Fedor; Volberg, Alexander

2008-01-01

376

Power law classification scheme of time series correlations. On the example of G20 group

NASA Astrophysics Data System (ADS)

A power law classification scheme (PLCS) of time series correlations is proposed. It is shown that PLCS provides the ability to classify nonlinear correlations and measure their stability. PLCS has been applied to gross domestic product (GDP) per capita of G20 members and their correlations analysed. It has been shown that the method does not only recognise linear correlations properly, but also allows to point out converging time series as well as to distinguish nonlinear correlations. PLCS is capable of crash recognition as it is shown in the Argentina example. Finally the strength of correlations and the stability of correlation matrices have been used to construct a minimum spanning tree (MST). The results were compared with those based on the ultrametric distance (UD). Comparing the structures of MST, UD and PLCS indicates that the latter one is more complicated, but better fits the expected economic relations within the G20.

Mi?kiewicz, Janusz

2013-05-01

377

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

378

Power law relationship between parameters of earthquakes and precursory electrical phenomena

NASA Astrophysics Data System (ADS)

A number of Seismic Electric signals data have been accumulated during the last two decades that also includes the signals observed before the magnitude 6 class earthquakes that occurred in Greece very recently i.e., the first two months of 2008. Using all the available data we investigate whether a possible interconnection exists between the lead time of Seismic Electric Signals and the stress drop of subsequent earthquakes. We show that for "non thrust" earthquakes a power law relation emerges with an exponent value around 0.29, the possible physical meaning of which is discussed. This value is very close to the range of critical exponents that govern the fracture processes and is also comparable with the value of the slope, found much earlier by the VAN group, in the linear relation between the logarithm of the SES amplitude and the earthquake magnitude.

Dologlou, E.

2008-09-01

379

Conductance statistics for the power-law banded random matrix model

We study numerically the conductance statistics of the one-dimensional (1D) Anderson model with random long-range hoppings described by the Power-law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single-mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT){proportional_to}T{sup M2/2}, for T<<

Martinez-Mendoza, A. J.; Mendez-Bermudez, J. A. [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Apartado Postal J-48, Puebla 72570 (Mexico); Varga, Imre [Elmeleti Fizika Tanszek, Fizikai Intezet, Budapesti Mu''szaki es Gazdasagtudomanyi Egyetem, H-1521 Budapest (Hungary); Fachbereich Physik und Wissenschaftliches Zentrum fuer Materialwissenschaften, Philipps Universitaet Marburg, D-35032 Marburg (Germany)

2010-12-21

380

Power-law persistence in the atmosphere A detailed study of long temperature records

We use several variants of the detrended fluctuation analysis to study the appearance of long-term persistence in temperature records, obtained at 95 stations all over the globe. Our results basically confirm earlier studies. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, decays for large s as a power law, C(s) ~ s^(-gamma). For continental stations, including stations along the coast lines, we find that gamma is always close to 0.7. For stations on islands, we find that gamma ranges between 0.3 and 0.7, with a maximum at gamma = 0.4. This is consistent with earlier studies of the persistence in sea surface temperature records where gamma is close to 0.4. By varying the degree of detrending in the fluctuation analysis we obtain also information about trends in the temperature records.

Eichner, J F; Bunde, A; Havlin, S; Schellnhuber, H J; Eichner, Jan F.; Koscielny-Bunde, Eva; Bunde, Armin; Havlin, Shlomo; Schellnhuber, Hans J.

2002-01-01

381

Modification of Buckley-Leverett and JBN methods for power-law fluids

In of non-Newtonian fluids for mobility control is a standard operation in oil recovery. While the description of the fluid theology during the simultaneous flow of two immiscible phases is in general complicated, significant progress is possible when one of the fluids is of the power-law type. In the latter case the standard methods for flow description and analysis of experimental data must be modified. This paper results such an approach for one-dimensional immiscible displacement. We consider the application of the Buckley-Leverett method and the modification of the JBN technique for measurement of relative permeabilities. The effects of rate and fluid rheology on the displacement features are investigated. It is shown that substantial errors may arise by the direct use of the original JBN method in interpreting unsteady-state experiments. A general modification of the technique is also proposed. 14 refs., 5 figs.

Salman, M.; Baghdikian, S.Y.; Handy, L.L.; Yortsos, Y.C.

1990-05-01

382

Efficiency and its bounds for thermal engines at maximum power using Newton's law of cooling.

We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case, this model can simulate Otto, Joule-Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as that from Esposito et al. [Phys. Rev. Lett. 105, 150603 (2010)] are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines. PMID:22400551

Yan, H; Guo, Hao

2012-01-01

383

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

384

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

385

Size distribution effect on the power law regime of the structure factor of fractal aggregates.

We consider the large qR(g), where q is the magnitude of the scattering wave vector and R(g) is the aggregate radius of gyration, part of the structure factor of fractal aggregates, and quantify the coefficient C of the power law, S(q) approximately C(qR(g))(-D), where D is the fractal dimension, for various structure factors proposed in the literature. With the aid of earlier work, we conclude the most accurate structure factors have C=1.0. We then calculate the effects of polydispersity on this coefficient, and show the effects are significant, enough so to allow a measurement of the distribution width. These concepts are accurately supported with scattering data from a diffusion limited aerosol and a reaction limited colloid. PMID:11970655

Sorensen, C M; Wang, G M

1999-12-01

386

Size distribution effect on the power law regime of the structure factor of fractal aggregates

NASA Astrophysics Data System (ADS)

We consider the large qRg, where q is the magnitude of the scattering wave vector and Rg is the aggregate radius of gyration, part of the structure factor of fractal aggregates, and quantify the coefficient C of the power law, S(q)~C(qRg)-D, where D is the fractal dimension, for various structure factors proposed in the literature. With the aid of earlier work, we conclude the most accurate structure factors have C=1.0. We then calculate the effects of polydispersity on this coefficient, and show the effects are significant, enough so to allow a measurement of the distribution width. These concepts are accurately supported with scattering data from a diffusion limited aerosol and a reaction limited colloid.

Sorensen, C. M.; Wang, G. M.

1999-12-01

387

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

388

Origins of power-law degree distribution in the heterogeneity of human activity in social networks

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.

Muchnik, Lev; Parra, Lucas C; Reis, Saulo D S; Andrade,, Jose S; Havlin, Shlomo; Makse, Hernan A

2013-01-01

389

3-d quantum stabilizer codes with a power law energy barrier

We introduce a new primitive, called welding, for combining two stabilizer codes to produce a new stabilizer code. We apply welding to construct surface codes and then use the surface codes to construct solid codes, a variant of a 3-d toric code with rough and smooth boundaries. Finally, we weld solid codes together to produce a $(O(L^3),1,O(L^{4/3}))$ stabilizer code with an energy barrier of $O(L^{2/3})$, which solves an open problem of whether a power law energy barrier is possible for local stabilizer code Hamiltonians in three-dimensions. The previous highest energy barrier is $O(\\log L)$. Previous no-go results are avoided by breaking translation invariance.

Kamil Michnicki

2012-08-16

390

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

391

Power law X- and gamma-ray emission from relativistic thermal plasmas

NASA Technical Reports Server (NTRS)

Pair equilibrium in thermal plasmas emitting power law photon spectra by repeated Compton scatterings of a soft photon source active galactic nuclei was studied. Dependence of the spectral index on optical thickness and on temperature of the plasma is discussed. The equation for pair equilibrium is solved for the maximum steady luminosity. Analytical solutions for the subrelativistic region, and for the ultrarelativistic region are found. In the transrelativistic region the solutions are expressed by single integrals over the pair production cross sections, performed numerically. The constraints on soft photon source imposed by the condition that the soft photon flux cannot exceed the black-body flux are considered. For the Comptonized synchrotron radiation model a relation between magnetic field strength and output luminosity is found.

Zdziarski, A. A.

1984-01-01

392

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

393

When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h , the interplay between creation and annihilation of excitable waves leads to an average activity F . It has recently been suggested that in the low-stimulus regime (h approximately 0) the response function F(h) of hypercubic deterministic systems behaves as a power law, F approximately h{m} . Moreover, the response exponent m has been predicted to depend only on the dimensionality d of the lattice, m=1/(1+d) [T. Ohta and T. Yoshimura, Physica D 205, 189 (2005)]. In order to test this prediction, we study the response function of excitable lattices modeled by either coupled Morris-Lecar equations or Greenberg-Hastings cellular automata. We show that the prediction is verified in our model systems for d=1 , 2, and 3, provided that a minimum set of conditions is satisfied. Under these conditions, the dynamic range-which measures the range of stimulus intensities that can be coded by the network activity-increases with the dimensionality d of the network. The power law scenario breaks down, however, if the system can exhibit self-sustained activity (spiral waves). In this case, we recover a scenario that is common to probabilistic excitable media: as a function of the conductance coupling G among the excitable elements, the dynamic range is maximized precisely at the critical value G_{c} above which self-sustained activity becomes stable. We discuss the implications of these results in the context of neural coding. PMID:18643106

Ribeiro, Tiago L; Copelli, Mauro

2008-05-01

394

Quasinormal modes of nearly extremal Kerr spacetimes: Spectrum bifurcation and power-law ringdown

NASA Astrophysics Data System (ADS)

We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal-mode frequencies presented in a recent paper [H. Yang et al., Phys. Rev. D 87, 041502 (2013)]. One set of modes that we call “zero-damping modes” has vanishing imaginary part in the extremal limit and exists for all corotating perturbations (i.e. modes with azimuthal index m?0). The other set (the “damped modes”) retains a finite decay rate even for extremal Kerr black holes and exists only for a subset of corotating modes. As the angular momentum approaches its extremal value, the frequency spectrum bifurcates into these two distinct branches when both types of modes are present. We discuss the physical reason for the mode branching by developing and using a bound-state formulation for the perturbations of generic Kerr black holes. We also numerically explore the specific case of the fundamental l=2 modes, which have the greatest astrophysical interest. Using the results of these investigations, we compute the quasinormal-mode response of a nearly extremal Kerr black hole to perturbations. We show that many superimposed overtones result in a slow power-law decay of the quasinormal ringing at early times, which later gives way to exponential decay. This exceptional early-time power-law decay implies that the ringdown phase is long lived for black holes with large angular momentum, which could provide a promising strong source for gravitational-wave detectors.

Yang, Huan; Zimmerman, Aaron; Zengino?lu, An?l; Zhang, Fan; Berti, Emanuele; Chen, Yanbei

2013-08-01

395

Fatigue crack propagation rates in PMMA bone cement cannot be reduced to a single power law.

Cement mantles around metallic implants have pre-existing flaws (shrinkage induced cracks, laminations, and endosteal surface features) and their fatigue failure is related to the fatigue crack propagation (FCP) rate of bone cement. We estimated the relevant in vivo range of cyclic stress intensity factor (DeltaK) around a generic femoral stem (0-1 MPa square root(m)) and determined that previous FCP data did not adequately cover this range of DeltaK. Vacuum-mixed standard bone cement was machined into ASTM E647 standard compact notched tension specimens. These were subject to sinusoidal loading (R = 0.1) at 5 Hz in 37 degrees C DI water, covering a DeltaK range of 0.25-1.5 MPa square root(m) (including a decreasing DeltaK protocol). FCP-rate data is normally reduced to a power-law fit relating crack growth rate (da/dn) to DeltaK. However, a substantial discontinuity was observed in our data at around DeltaK = 1, so two power-law fits were used. Over the physiologically plausible range of DeltaK, cracks grew at a rate of 2.9 E -8 x DeltaK(2.6) m/cycle. Our data indicated that FCP-rates for 0.5 > DeltaK > 0.3 MPa square root(m) are between 10 E -8 and 10 E -8 m/cycle, 1 or 2 orders of magnitude greater than predicted by extrapolating from previous models based on higher DeltaK data. PMID:18161813

Race, Amos; Mann, Kenneth A

2008-07-01

396

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

397

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

398

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined. PMID:19333397

Papadopoulos, Anthony

2009-01-01

399

A special study was conducted to investigate the influences of minimum approach temperature differences occurring in supercritical-heater/vaporizer and evaporative-condenser heat rejection systems on geothermal-electric binary power plant performance and cost of electricity. For the systems investigated optimum pinch points for minimizing cost of electricity were estimated to range from 5 to 7/sup 0/F for the heater vaporizer. The minimum approach of condensing temperature to wet-bulb temperature for evaporative condensers was estimated to be about 30/sup 0/F in order to achieve the lowest cost of electricity.

Demuth, O.J.

1983-10-01

400

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

401

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

402

Why credit risk markets are predestined for exhibiting log-periodic power law structures

NASA Astrophysics Data System (ADS)

Recent research has established the existence of log-periodic power law (LPPL) patterns in financial institutions’ credit default swap (CDS) spreads. The main purpose of this paper is to clarify why credit risk markets are predestined for exhibiting LPPL structures. To this end, the credit risk prediction of two variants of logistic regression, i.e. polynomial logistic regression (PLR) and kernel logistic regression (KLR), are firstly compared to the standard logistic regression (SLR). In doing so, the question whether the performances of rating systems based on balance sheet ratios can be improved by nonlinear transformations of the explanatory variables is resolved. Building on the result that nonlinear balance sheet ratio transformations hardly improve the SLR’s predictive power in our case, we secondly compare the classification performance of a multivariate SLR to the discriminative powers of probabilities of default derived from three different capital market data, namely bonds, CDSs, and stocks. Benefiting from the prompt inclusion of relevant information, the capital market data in general and CDSs in particular increasingly outperform the SLR while approaching the time of the credit event. Due to the higher classification performances, it seems plausible for creditors to align their investment decisions with capital market-based default indicators, i.e., to imitate the aggregate opinion of the market participants. Since imitation is considered to be the source of LPPL structures in financial time series, it is highly plausible to scan CDS spread developments for LPPL patterns. By establishing LPPL patterns in governmental CDS spread trajectories of some European crisis countries, the LPPL’s application to credit risk markets is extended. This novel piece of evidence further strengthens the claim that credit risk markets are adequate breeding grounds for LPPL patterns.

Wosnitza, Jan Henrik; Leker, Jens

2014-01-01

403

GRASPING "THE INFLUENCE OF LAW ON SEA POWER" Commander James Kraska, JAGC, U.S. Navy

two decades international maritime law has evolved from a set of rules designed to avoid naval warfare- porary focus of international maritime law now is constructive and prospective, broadening partnerships and distributed maritime forces and spreading the rule of law at sea, and as a conse- quence, the strategic

Acton, Scott

404

We propose a novel algorithm based on the matrix pencil method to estimate the parameters of a class of signals modeled as damped power-law phase signals. This class arises pri- marily from the electromagnetic probing of dispersive geological and civil engineering materials as a consequence of the universal dielectric response. When stratified media are considered, direct application of conventional matrix-shifting

Khaled Chahine; Vincent Baltazart; Yide Wang

2011-01-01

405

ERIC Educational Resources Information Center

Results of a systematic investigation into university students' (n=236) misunderstandings of d.c. simple circuit operations are reported. These results provide evidence of various misconceptions present before and after teaching the following topics: a battery as a source of constant current; the functional relation expressed by Ohm's law; power…

Picciarelli, V.; And Others

1991-01-01

406

A numerical solution of the elastohydrodynamic lubrication problem for pure rolling with non-Newtonian lubricants is outlined. The non-Newtonian rheological model used is a modified power-law, ? = K · ?. At low shear rate, ? < ?b the lubricant is Newtonian, but when ? > ?b the lubricant becomes non-Newtonian, ? = K · ?. At high shear rate (?

Ove Isaksson

1986-01-01

407

Power law in properties of sulfur near the polymerization transition V. F. Kozhevnikov, J. M. Viner manuscript received 25 June 2001; published 13 November 2001 Sound velocity and attenuation in liquid sulfur.1%. A distinct feature in sound velocity was found near 159 °C where sulfur experiences an equilibrium

Kozhevnikov, Vladimir

408

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

409

of rate data of reversible, heterogeneous reactions which uses the power-law rate expression is described. Introduction The design of a catalytic reactor involves the need for a correlation relating the reaction rates appropriate rate expression is a lengthy process, involving postulation of reaction mechanisms, isothermal

Brauner, Neima

410

$D$-dimensional Schr\\"{o}dinger equation is addressed for square root power law potential. Bound state unnormalized eigenfunctions and the energy eigenvalues are obtained using wave function ansatz method. Some special cases are studied at the end to ensure the correctness of present work.

Tapas Das

2015-03-25

411

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...

412

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. In particular, a distinction between opportunistic cyber-crime and serious organized cyber-crime is found of quantitative analytic treatment. Cyber-crime can be viewed as an asymmetric conflict, in that the resources

Overill, Richard E.

413

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

414

We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF slope recovery in this paper are lower limits, as we do not explicitly consider all possible sources of uncertainty, including dynamical effects (e.g., mass segregation), unresolved binaries, and non-coeval populations. We briefly discuss how each of these effects can be incorporated into extensions of the present framework. Finally, we emphasize that the technique and lessons learned are applicable to more general problems involving power-law fitting.

Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.; Clifton Johnson, L.; Beerman, Lori C.; Williams, Benjamin F. [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States)] [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States); Hogg, David W.; Foreman-Mackey, Daniel T. [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States)] [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Rix, Hans-Walter; Gouliermis, Dimitrios [Max Planck Institute for Astronomy, Koenigstuhl 17, D-69117 Heidelberg (Germany)] [Max Planck Institute for Astronomy, Koenigstuhl 17, D-69117 Heidelberg (Germany); Dolphin, Andrew E. [Raytheon Company, 1151 East Hermans Road, Tucson, AZ 85756 (United States)] [Raytheon Company, 1151 East Hermans Road, Tucson, AZ 85756 (United States); Lang, Dustin [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States)] [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Bell, Eric F. [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States)] [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States); Gordon, Karl D.; Kalirai, Jason S. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)] [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Skillman, Evan D., E-mail: dweisz@astro.washington.edu [Minnesota Institute for Astrophysics, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States)

2013-01-10

415

NASA Astrophysics Data System (ADS)

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 108 yr.

Applegate, James H.; Shaham, Jacob

1994-11-01

416

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

417

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

418

from its original regime to that following a power-law function. I evaluate the effectiveness of the new concept by comparing it to conventional multi-stage hydraulic fracturing. The results of this investigation show that the power-law permeability...

Broussard, Ryan Sawyer

2013-02-08

419

NASA Astrophysics Data System (ADS)

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 N1/(? + 1), where ? is the power-law exponent, and a function periodic in N1/3. The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy ETh(n) on n, also scales like N1/(? + 1).

Cioslowski, Jerzy; Albin, Joanna

2013-09-01

420

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

421

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

2015-03-01

422

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

423

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

424

NASA Astrophysics Data System (ADS)

The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form wi(t+1)=?(t)wi(t)+aw¯(t)-bwi(t)w¯(t) is studied by computer simulations. The variables wi, i=1,...,N, are the individual system components and w¯(t)=(1/N)?iwi(t) is their average. The parameters a and b are constants, while ?(t) is randomly chosen at each time step from a given distribution. Models of this type describe the temporal evolution of a large variety of systems such as stock markets and city populations. These systems are characterized by a large number of interacting objects and the dynamics is dominated by multiplicative processes. The instantaneous probability distribution P(w,t) of the system components wi turns out to fulfill a Pareto power law P(w,t)~w-1-?. The time evolution of w¯(t) presents intermittent fluctuations parametrized by a Lévy-stable distribution with the same index ?, showing an intricate relation between the distribution of the wi's at a given time and the temporal fluctuations of their average.

Biham, Ofer; Malcai, Ofer; Levy, Moshe; Solomon, Sorin

1998-08-01

425

NASA Astrophysics Data System (ADS)

We employ the log-periodic power law (LPPL) to analyze the late-2000 financial crisis from the perspective of critical phenomena. The main purpose of this study is to examine whether LPPL structures in the development of credit default swap (CDS) spreads can be used for default classification. Based on the different triggers of Bear Stearns’ near bankruptcy during the late-2000 financial crisis and Ford’s insolvency in 2009, this study provides a quantitative description of the mechanism behind bank runs. We apply the Johansen-Ledoit-Sornette (JLS) positive feedback model to explain the rise of financial institutions’ CDS spreads during the global financial crisis 2007-2009. This investigation is based on CDS spreads of 40 major banks over the period from June 2007 to April 2009 which includes a significant CDS spread increase. The qualitative data analysis indicates that the CDS spread variations have followed LPPL patterns during the global financial crisis. Furthermore, the univariate classification performances of seven LPPL parameters as default indicators are measured by Mann-Whitney U tests. The present study supports the hypothesis that discrete scale-invariance governs the dynamics of financial markets and suggests the application of new and fast updateable default indicators to capture the buildup of long-range correlations between creditors.

Wosnitza, Jan Henrik; Denz, Cornelia

2013-09-01

426

Effects of power law primordial magnetic field on big bang nucleosynthesis

NASA Astrophysics Data System (ADS)

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 ?. The SI strength of the PMF is constrained from observational constraints on abundances of He4 and D. The minimum abundance of Li7/H as a function of ? slightly moves to a higher Li7/H value at a larger ? 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 He4 abundance, and that a lower limit on the allowed Li7 abundance is significantly higher than those observed in metal-poor stars.

Yamazaki, Dai G.; Kusakabe, Motohiko

2012-12-01

427

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

428

Interim Report on the Power Law Index of Interplanetary Suprathermal Ion Spectra

There is a continuing debate about the applicability of the theory presented by Fisk and Gloeckler (FG) regarding the formation of suprathermal ion tails in phase space density vs. velocity spectra; in the solar wind frame the FG theory predicts a power law index of-5 (which is equivalent to a differential intensity vs. energy index of-1.5). There has also been uncertainty and perhaps misunderstanding regarding the extent to which such spectra are actually observed; i.e., is there really a significant preference for the -5 index? Here we report the results of an interim technique we use to analyze {approx}1-100 keV/nucleon interplanetary suprathermal H{sup +}, He{sup +}, and He{sup ++}, spectra measured at the Cassini spacecraft by the Charge Energy Mass Spectrometer (CHEMS) instrument of the Magnetospheric Imaging Instrument (MIMI) suite during the cruise to Saturn. We analyzed 18 active periods and report a mean index in the solar wind frame of 4.9{+-}0.4 for protons, 5.2{+-}0.5 for He{sup +}, and 4.7{+-}0.2 for alpha particles. MIMI/CHEMS offers much needed independent observations of heliospheric ions in the suprathermal energy range.

Hill, M. E. [Johns Hopkins Applied Physics Laboratory, Laurel, Maryland 20723 (United States); Hamilton, D. C. [University of Maryland College Park, Maryland 20742 (United States)

2010-12-30

429

Power-law tails in probability density functions of molecular cloud column density

Power-law tails are often seen in probability density functions (PDFs) of molecular cloud column densities, and have been attributed to the effect of gravity. We show that extinction PDFs of a sample of five molecular clouds obtained at a few tenths of a parsec resolution, probing extinctions up to A$_{{\\mathrm{V}}}$ $\\sim$ 10 magnitudes, are very well described by lognormal functions provided that the field selection is tightly constrained to the cold, molecular zone and that noise and foreground contamination are appropriately accounted for. In general, field selections that incorporate warm, diffuse material in addition to the cold, molecular material will display apparent core+tail PDFs. The apparent tail, however, is best understood as the high extinction part of a lognormal PDF arising from the cold, molecular part of the cloud. We also describe the effects of noise and foreground/background contamination on the PDF structure, and show that these can, if not appropriately accounted for, induce spurious ...

Brunt, Chris

2015-01-01

430

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

431

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

432

Breakup characteristics of power-law liquid sheets formed by two impinging jets

NASA Astrophysics Data System (ADS)

The breakup characteristics of the shear-thinning power-law liquid sheets formed by two impinging jets have been investigated with the shadowgraph technique. This paper focuses on the effects of spray parameters (jet velocity), physical parameters (viscosity) and geometry parameters (impinging angle and nozzle cross-sectional shape) on the breakup behaviors of liquid sheets. The breakup mode, sheet length and expansion angle of the sheet are extracted from the spray images obtained by a high speed camera. Impinging angle and Weber number play the similar roles in promoting the breakup of liquid sheets. With the increase of jet velocity, five different breakup modes are observed and the expansion angle increases consistently after the closed-rim mode while the sheet length first increases and then decreases. But there exists a concave consisting of a fierce drop and a second rising process on the sheet length curve for the fluid with smaller viscosity. Different nozzle cross-sectional shapes emphasize significant effects on the sheet length and expansion angle of liquid sheets. At a fixed Weber number, the liquid sheet with greater viscosity has a greater sheet length and a smaller expansion angle due to the damping effect of viscosity.

Bai, Fuqiang; Diao, Hai; Zhang, Mengzheng; Chang, Qing; Wang, Endong; Du, Qing

2014-10-01

433

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

434

Cosmological evolution of Einstein-Aether models with power-law-like potential

NASA Astrophysics Data System (ADS)

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.

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

2014-05-01

435

Cosmic histories of star formation and reionization: an analysis with a power-law approximation

With a simple power-law approximation of high-redshift (?>3.5) star formation history, i.e., ?-dot {sub *}(z)?[(1+z)/4.5]{sup ??}, we investigate the reionization of intergalactic medium (IGM) and the consequent Thomson scattering optical depth for cosmic microwave background (CMB) photons. A constraint on the evolution index ? is derived from the CMB optical depth measured by the Wilkinson Microwave Anisotropy Probe (WMAP) experiment, which reads ? ? 2.18 lg N{sub ?}?3.89, where the free parameter N{sub ?} is the number of the escaped ionizing ultraviolet photons per baryon. At the same time, the redshift z{sub f} at which the IGM is fully ionized can also be expressed as a function of ? as well as N{sub ?}. By further taking into account the implication of the Gunn-Peterson trough observations to quasars for the full reionization redshift, i.e., 6?

Yu, Yun-Wei [Institute of Astrophysics, Central China Normal University, 152 Luoyu Road, Wuhan 430079 (China); Cheng, K.S. [Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong (China); Chu, M.C.; Yeung, S., E-mail: yuyw@phy.ccnu.edu.cn, E-mail: hrspksc@hku.hk, E-mail: mcchu@phy.cuhk.edu.hk, E-mail: terryys@gmail.com [Department of Physics and Institute of Theoretical Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong (China)

2012-07-01

436

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

437

A new exact and more powerful unconditional test of no treatment effect from binary matched pairs.

We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization, producing what I call an E+M P-value. The E+M P-value based on McNemar's statistic is shown numerically to dominate previous suggestions, including partially maximized P-values as described in Berger and Sidik (2003, Statistical Methods in Medical Research 12, 91-108). The latter method, however, may have computational advantages for large samples. PMID:18047530

Lloyd, Chris J

2008-09-01

438

Design and off-design operation of a dual-boiling binary geothermal power plant

The design of a 5 MW(e) geothermal plant using a binary fluid process is described. The second fluid is isobutane. This plant is presently under construction at Raft River, Idaho. A mathematical simulation of the plant is discussed. The heat exchangers were modeled by dividing them into segments in the direction of flow to permit local adjustments in heat transfer coefficients and fluid properties. Sensitivity of plant performance to geofluid temperature and flow rate, heat exchanger fouling and cooling water temperatures were investigated. Conventional correlations were used for the heat transfer coefficients except for the condensing coefficient, which was obtained from a recent study at Lawrence Berkeley Laboratory.

Bliem, C.J. Jr.

1980-01-01

439

Power laws and self-organized criticality in theory and nature

NASA Astrophysics Data System (ADS)

Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real-world phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts. The interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights. First, the energy level of the active node, for which h?hT, is reduced by an amount ?h, viz. h?h-?h. Second, the nearest neighbors of the active node, receive a fraction ? of the lost energy ?h. Denoting with e the relative location of nearest neighbors with respect to location of active node r?, we can write h?h+??h. For example, in the case of two dimensional (d=2) lattice we have e=(±1,0), (0,±1). The update is repeated as long as at least one active node remains, that is, until the energy configuration becomes stable. In Fig. 3 we illustrated the process of particle transport among nearest neighbors, also called an avalanche. Setting ?={12d assures local conservation of energy during an avalanche; a necessary condition for a true SOC behavior of the sandpile models, as we will discuss later. However, the energy is conserved only locally; it is important to allow the energy to dissipate at the lattice boundaries (grains falling off the table), which is achieved by keeping the boundary nodes empty. If the amount of transferred energy ?h-which is transferred upon site activation-equals the threshold value hT, one calls the model an Abelian SOC model, because in this case the order of the energy redistribution does not influence the stable state configuration reached in the end of the toppling process. The Abelian realization of the discrete height SOC model is better known as Bak-Tang-Wiesenfeld (BTW) sandpile model (Bak et al., 1987). In addition, setting ?h=?h, where ??(0,1] leads to a non-Abelian SOC model which was-in its continuous energy form-first analyzed by Zhang (1989), thus named Zhang sandpile model (see Table 2).Beside the BTW and the Zhang sandpile models, other variations of toppling rules exist.

Markovi?, Dimitrije; Gros, Claudius

2014-03-01

440

NASA Astrophysics Data System (ADS)

In the past few decades, many studies have been dedicated to the understanding of the interactions between tectonics and erosion, in many instances through the use of numerical models of landscape evolution. Among the numerous parameterizations that have been developed to predict river channel evolution, the stream power law, which links erosion rate to drainage area and slope, remains the most widely used. Despite its simple formulation, its power lies in its capacity to reproduce many of the characteristic features of natural systems (the concavity of river profile, the propagation of knickpoints, etc.). However, the three main coefficients that are needed to relate erosion rate to slope and drainage area in the stream power law remain poorly constrained. In this study, we present a novel approach to constrain the stream power law coefficients under the detachment-limited mode by combining a highly efficient landscape evolution model, FastScape, which solves the stream power law under arbitrary geometries and boundary conditions and an inversion algorithm, the neighborhood algorithm. A misfit function is built by comparing topographic data of a reference landscape supposedly at steady state and the same landscape subject to both uplift and erosion over one time step. By applying the method to a synthetic landscape, we show that different landscape characteristics can be retrieved, such as the concavity of river profiles and the steepness index. When applied on a real catchment (in the Whataroa region of the South Island in New Zealand), this approach provides well-resolved constraints on the concavity of river profiles and the distribution of uplift as a function of distance to the Alpine Fault, the main active structure in the area.

Croissant, T.; Braun, J.

2014-03-01

441

NASA Astrophysics Data System (ADS)

In the past few decades, many studies have been dedicated to our understanding of the interactions between tectonic and erosion and, in many instances, using numerical models of landscape evolution. Among the numerous parameterizations that have been developed to predict river channel evolution, the Stream Power Law, which links erosion rate to drainage area and slope, remains the most widely used. Despite its simple formulation, its power lies in its capacity to reproduce many of the characteristic features of natural systems (the concavity of river profile, the propagation of knickpoints, etc.). However, the three main coefficients that are needed to relate erosion rate to slope and drainage area in the Stream Power Law remain poorly constrained. In this study, we present a novel approach to constrain the Stream Power Law coefficients under the detachment limited mode by combining a highly efficient Landscape Evolution Model, FastScape, which solves the Stream Power Law under arbitrary geometries and boundary conditions and an inversion algorithm, the Neighborhood Algorithm. A misfit function is built by comparing topographic data of a reference landscape supposedly at steady state and the same landscape subject to both uplift and erosion over one time step. By applying the method to a synthetic landscape, we show that different landscape characteristics can be retrieved, such as the concavity of river profiles and the steepness index. When applied on a real catchment (in the Whataroa region of the South Island in New Zealand), this approach provide well resolved constraints on the concavity of river profiles and the distribution of uplift as a function of distance to the Alpine Fault, the main active structure in the area.

Croissant, T.; Braun, J.

2013-11-01