Black hole in the expanding universe with arbitrary power-law expansion
Maeda, Kei-ichi; Nozawa, Masato
2010-06-15
We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordstroem (RN) black hole and the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the D-dimensional Einstein-Maxwell-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a (D-1)-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential n{sub T}, the U(1) charge Q, and the nonextremality {tau}. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
2013-12-01
Bessel integrals of type {int_0^infty {k^{μ+2}{e}^{-ak2-(b+{i} ω)k}j_l^{2} (pk)dk}} are studied, where the squared spherical Bessel function j {/l 2} is averaged with a modulated Gaussian power-law density. 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. The averages can be calculated in closed form as finite Hankel series, which allow high-precision evaluation. In the case of integer power-law exponents μ, singularities emerge in the series coefficients, which requires ɛ expansion. The pole extraction and regularization of singular Hankel series is performed, for integer Gaussian power-law densities as well as for the special case of Kummer averages (a = 0 in the exponential of the integrand). The singular ɛ residuals are used to derive combinatorial identities (sum rules) for the rational Hankel coefficients, which serve as consistency checks in precision calculations of the integrals. Numerical examples are given, and the Hankel evaluation of Gaussian and Kummer averages is compared with their high-index Airy approximation over a wide range of integer Bessel indices l.
NASA Astrophysics Data System (ADS)
Cohl, Howard S.
2013-06-01
We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we derive Fourier expansions in certain rotationally-invariant coordinate systems and Gegenbauer polynomial expansions in Vilenkin's polyspherical coordinates. We compare both of these expansions to generate addition theorems for the azimuthal Fourier coefficients.
Power-law cosmic expansion in f(R) gravity models
Goheer, Naureen; Larena, Julien; Dunsby, Peter K. S.
2009-09-15
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R{sup n} gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
NASA Astrophysics Data System (ADS)
Ito, Yuta; Nishimura, Jun; Tsuchiya, Asato
2015-11-01
Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to N = 512, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value N c ≃ 110, we find that (3+1)D expanding universe emerges dynamically with a clear large- N scaling property. Furthermore, the observed increase of the spatial extent with time t at sufficiently late times is consistent with a power-law behavior t 1/2, which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original supersymmetric model including fermionic matrices.
Exact equation for curved stationary flames with arbitrary gas expansion.
Kazakov, Kirill A
2005-03-11
An exact equation describing freely propagating stationary flames with arbitrary values of the gas expansion coefficient is obtained. This equation respects all conservation laws at the flame front, and provides a consistent nonperturbative account of the effect of vorticity produced by the curved flame on the front structure. It is verified that the new equation is in agreement with the approximate equations derived previously in the case of weak gas expansion.
NASA Astrophysics Data System (ADS)
Mehedi Faruk, Mir; Muktadir Rahman, Md.; Debnath, Dwaipayan; Sakhawat Hossain Himel, Md.
2016-04-01
Energy fluctuation of ideal Fermi gas trapped under generic power law potential U=\\sumi=1d ci \\vertxi/ai \\vert n_i has been calculated in arbitrary dimensions. Energy fluctuation is scrutinized further in the degenerate limit μ ≫ KBT with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can not only exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d = 3 but also can describe the outcome for any power law potential in arbitrary dimension.
The 1/N expansion of colored tensor models in arbitrary dimension
NASA Astrophysics Data System (ADS)
Gurau, R.; Rivasseau, V.
2011-09-01
In this paper we extend the 1/N expansion introduced in Gurau R., Ann. Henri Poincaré, 12 (2011) 829, to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres SD contribute to the leading order in the large-N limit.
ERIC Educational Resources Information Center
Thomas, Hoben
1981-01-01
Psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions are examined. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates given for several common estimation situations.…
Edee, Kofi; Abboud, Mira; Granet, Gérard; Cornet, Jean Francois; Gippius, Nikolay A
2014-04-01
We present a modal method for the computation of eigenmodes of cylindrical structures with arbitrary cross sections. These modes are found as eigenvectors of a matrix eigenvalue equation that is obtained by introducing a new coordinate system that takes into account the profile of the cross section. We show that the use of Hertz potentials is suitable for the derivation of this eigenvalue equation and that the modal method based on Gegenbauer expansion (MMGE) is an efficient tool for the numerical solution of this equation. Results are successfully compared for both perfectly conducting and dielectric structures. A complex coordinate version of the MMGE is introduced to solve the dielectric case. PMID:24695126
Anisotropic power-law inflation
Kanno, Sugumi; Soda, Jiro; Watanabe, Masa-aki E-mail: jiro@tap.scphys.kyoto-u.ac.jp
2010-12-01
We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.
Electric field in media with power-law spatial dispersion
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-04-01
In this paper, we consider electric fields in media with power-law spatial dispersion (PLSD). Spatial dispersion means that the absolute permittivity of the media depends on the wave vector. Power-law type of this dispersion is described by derivatives and integrals of non-integer orders. We consider electric fields of point charge and dipole in media with PLSD, infinite charged wire, uniformly charged disk, capacitance of spherical capacitor and multipole expansion for PLSD-media.
Lesage, Jonathan C; Bond, Jill V; Sinclair, Anthony N
2014-09-01
The problem of elastic wave propagation in an infinite bar of arbitrary cross section is studied via a generalized version of the Fourier expansion collocation method. In the current formulation, the exact three dimensional solution to Navier's equation in cylindrical coordinates is used to obtain the boundary traction vector as a periodic, piecewise continuous/differentiable function of the angular coordinate. Traction free conditions are then met by setting the Fourier coefficients of the boundary traction vector to zero without approximating the bounding surface by multi-sided polygons as in the method presented by Nagaya. The method is derived for a general cross section with no axial planes of symmetry. Using the general formulation it is shown that the symmetric and asymmetric modes decouple for cross sections having one axial plane of symmetry. An efficient algorithm for computing dispersion curves based on the current method is presented and used to obtain the fundamental longitudinal and flexural wave speeds for a bar of elliptical cross section. The results are compared to those obtained by previous researchers using exact and approximate treatments.
Power Laws in Firm Productivity
NASA Astrophysics Data System (ADS)
Mizuno, T.; Ishikawa, A.; Fujimoto, S.; Watanabe, T.
We estimate firm productivity for about 3.2 million firms from30 countries. We find that the distribution of firm productivity in each country, which is measured by total factor productivity (TFP), has a power law upper tail. However, the power law exponent of a TFP distribution in a country tends to be greater than that of a sales distribution in that country, indicating that the upper tail of a TFP distribution is less heavy compared to that of a sales distribution. We also find that the power law exponent of a TFP distribution tends to be greater than the power law exponents associated with the number of workers or tangible fixed assets. Given the idea that the sales of a firm is determined by the amount of various inputs employed by the firm (i.e., ``production function'' in the terminology of economics), these results suggest that the heavy tail of a sales distribution in a country comes not from the tail of a TFP distribution, but from the tail of the distribution of the number of workers or tangible fixed assets.
Perturbed power-law parameters from WMAP7
Joy, Minu; Souradeep, Tarun E-mail: tarun@iucaa.ernet.in
2011-02-01
We present a perturbative approach for studying inflation models with soft departures from scale free spectra of the power law model. In the perturbed power law (PPL) approach one obtains at the leading order both the scalar and tensor power spectra with the running of their spectral indices. In contrast to the widely used slow roll expansion method, for which ε and δ have to be small, PPL can look also at models with comparatively larger ε and δ with the condition that (ε+δ) is small. The PPL spectrum is confronted data and we show that the PPL parameters are well estimated from WMAP-7 data.
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz
2016-02-01
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system. PMID:26906812
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz
2016-02-01
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system.
Modeling of the thermal expansion behaviour of ZERODUR at arbitrary temperature profiles
NASA Astrophysics Data System (ADS)
Jedamzik, Ralf; Johansson, Thoralf; Westerhoff, Thomas
2010-07-01
Modeling of the thermal expansion behavior of ZERODUR® for the site conditions of the upcoming Extremely Large Telescope's (ELT's) allows an optimized material selection to yield the best performing ZERODUR® for the mirror substrates. The thermal expansion of glass ceramics is a function of temperature and a function of time, due to the structural relaxation behavior of the materials. The application temperature range of the upcoming ELT projects varies depending on the possible construction site between -13°C and +27°C. Typical temperature change rates during the night are in the range between 0.1°C/h and 0.3°C/h. Such temperature change rates are much smaller than the typical economic laboratory measurement rate, therefore the material behavior under these conditions can not be measured directly. SCHOTT developed a model approach to describe the structural relaxation behavior of ZERODUR®. With this model it is possible to precisely predict the thermal expansion behavior of the individual ZERODUR® material batches at any application temperature profile T(t). This paper presents results of the modeling and shows ZERODUR® material behavior at typical temperature profiles of different applications.
Power-law cosmology, SN Ia, and BAO
Dolgov, Aleksander; Halenka, Vitali; Tkachev, Igor E-mail: vithal@umich.edu
2014-10-01
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime a(t) ∼ t{sup β} with β close to 3/2 in a spatially flat universe is a good fit to these data.
Spectrum of power laws for curved hand movements
Huh, Dongsung; Sejnowski, Terrence J.
2015-01-01
In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead. PMID:26150514
Power law inflation with electromagnetism
Luo, Xianghui; Isenberg, James
2013-07-15
We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.
Convex and concave successions of power-law decays in small-angle scattering
NASA Astrophysics Data System (ADS)
Anitas, E. M.
2016-08-01
The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with fractal iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: convex/concave - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power- law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.
Isotropy theorem for arbitrary-spin cosmological fields
Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez E-mail: maroto@ucm.es
2014-03-01
We show that the energy-momentum tensor of homogeneous fields of arbitrary spin in an expanding universe is always isotropic in average provided the fields remain bounded and evolve rapidly compared to the rate of expansion. An analytic expression for the average equation of state is obtained for Lagrangians with generic power-law kinetic and potential terms. As an example we consider the behavior of a spin-two field in the standard Fierz-Pauli theory of massive gravity. The results can be extended to general space-time geometries for locally inertial observers.
Hierarchical networks, power laws, and neuronal avalanches
NASA Astrophysics Data System (ADS)
Friedman, Eric J.; Landsberg, Adam S.
2013-03-01
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions—even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
Hierarchical networks, power laws, and neuronal avalanches.
Friedman, Eric J; Landsberg, Adam S
2013-03-01
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
One-dimensional quantum liquids with power-law interactions: the Luttinger staircase.
Dalmonte, M; Pupillo, G; Zoller, P
2010-10-01
We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|(β), with β>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary β and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a "Luttinger staircase." Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.
One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase
Dalmonte, M.; Pupillo, G.; Zoller, P.
2010-10-01
We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|{sup {beta}}, with {beta}>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary {beta} and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a 'Luttinger staircase'. Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.
Broken Power-law Distributions from Low Coronal Compression Regions or Shocks
NASA Astrophysics Data System (ADS)
Schwadron, N. A.; Lee, M. A.; Gorby, M.; Lugaz, N.; Spence, H. E.; Desai, M.; Török, T.; Downs, C.; Linker, J.; Lionello, R.; Mikić, Z.; Riley, P.; Giacalone, J.; Jokipii, J. R.; Kota, J.; Kozarev, K.
2015-09-01
Coronal Mass Ejection (CME) expansion regions low in the corona (< 2 - 3 Rs) are highly efficient for the acceleration of energetic particles. Because the acceleration occurs over a finite spatial region, there is a regime where particles diffuse away and escape from the acceleration sites, leading to the formation of broken power-law distributions. This paper highlights recent results indicating that CME expansion and acceleration in the low corona may cause rapid particle acceleration and create large solar energetic particle events with broken power-law distributions.
Relativity, nonextensivity, and extended power law distributions.
Silva, R; Lima, J A S
2005-11-01
A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory. PMID:16383791
Zipf's law, power laws and maximum entropy
NASA Astrophysics Data System (ADS)
Visser, Matt
2013-04-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.
Variational Principle for the Pareto Power Law
NASA Astrophysics Data System (ADS)
Chakraborti, Anirban; Patriarca, Marco
2009-11-01
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.
Fractal power law in literary English
NASA Astrophysics Data System (ADS)
Gonçalves, L. L.; Gonçalves, L. B.
2006-02-01
We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.
Relativity, nonextensivity, and extended power law distributions.
Silva, R; Lima, J A S
2005-11-01
A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.
Anomalous thermodynamic power laws in nodal superconductors
NASA Astrophysics Data System (ADS)
Quintanilla, Jorge; Mazidian, Bayan; Annett, James F.; Hillier, Adrian D.
2013-03-01
Unconventional superconductors are frequently identified by the observation of power law behaviour on low temperature thermodynamic properties such as specific heat. These power laws generally derive from the linear spectrum near points or lines of zeros, or nodes, in the superconducting energy gap on the Fermi surface. Here we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. Some of these new types of nodes typically occur when there are transitions between different types of gap node topology, for example when point or line nodes first appear as a function of some physical parameter. We derive anomalous, non-integer thermodynamic power laws associated with these new nodal types and predict their occurrence in iron pnictide superconductors and in the noncentrosymmetric system Li2Pd3-xPtxB. This works was supported by EPSRC and STFC (U.K.) J.Q. gratefully acknowledges funding from HEFCE and STFC through the South-East Physics network (SEPnet).
Exact solutions of unsteady boundary layer equations for power-law non-Newtonian fluids
NASA Astrophysics Data System (ADS)
Polyanin, A. D.
2015-08-01
A number of new exact solutions (with the generalized and functional separation of variables) of unsteady equations of a planar and asymmetric boundary layer of power-law non-Newtonian fluids are described. To find the solutions, the Crocco transformation reducing the order of the equations considered and simpler point transformations are used. Two theorems allowing one to generalize exact solutions of the unsteady axisymmetric boundary layer equations including additional arbitrary functions into them are proven.
Diffusion Processes on Power-Law Small-World Networks
NASA Astrophysics Data System (ADS)
Kozma, Balazs; Hastings, Matthew B.; Korniss, G.
2005-03-01
We consider diffusion driven processes on power-law small-world networks: a random walk process related to folded polymers and surface growth related to synchronization problems. The random links introduced in small-world networks often lead to mean-field coupling (as if the random links were annealed) but in some systems mean-field predictions break down, like diffusion in one dimension. This break-down can be understood treating the random links perturbatively where the mean field prediction appears as the lowest order term of a naive perturbation expansion. Our results were obtained using self-consistent perturbation theory ootnotetextB. Kozma, M. B. Hastings, and G. Korniss, Phys. Rev. Lett. 92, 108701 (2004). and can also be understood in terms of a scaling theory. We find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents.
Power law behavior in chemical reactions.
Claycomb, J R; Nawarathna, D; Vajrala, V; Miller, J H
2004-12-22
Reactions between metals and chloride solutions have been shown to exhibit magnetic field fluctuations over a wide range of size and time scales. Power law behavior observed in these reactions is consistent with models said to exhibit self-organized criticality. Voltage fluctuations observed during the dissolution of magnesium and aluminum in copper chloride solution are qualitatively similar to the recorded magnetic signals. In this paper, distributions of voltage and magnetic peak sizes, noise spectra, and return times are compared for both reactions studied. PMID:15606263
Power law behavior in chemical reactions
NASA Astrophysics Data System (ADS)
Claycomb, J. R.; Nawarathna, D.; Vajrala, V.; Miller, J. H.
2004-12-01
Reactions between metals and chloride solutions have been shown to exhibit magnetic field fluctuations over a wide range of size and time scales. Power law behavior observed in these reactions is consistent with models said to exhibit self-organized criticality. Voltage fluctuations observed during the dissolution of magnesium and aluminum in copper chloride solution are qualitatively similar to the recorded magnetic signals. In this paper, distributions of voltage and magnetic peak sizes, noise spectra, and return times are compared for both reactions studied.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Edee, Kofi; Abboud, Mira; Granet, Gérard; Cornet, Jean Francois; Dauchet, Jéremi
2014-10-01
The work presented here focuses on the numerical modeling of cylindrical structure eigenmodes with an arbitrary cross section using Gegenbauer polynomials. The new eigenvalue equation leads to considerable reduction in computation time compared to the previous formulation. The main idea of this new formulation involves considering that the numerical scheme can be partially separated into two independent parts and the size of the eigenvalue matrix equation may be reduced by a factor of 2. We show that the ratio of the computation times between the first and current versions follows a linear relation with respect to the number of polynomials. PMID:25401241
Breakup of Threads of Power Law Fluids
NASA Astrophysics Data System (ADS)
Basaran, Osman A.; Suryo, Ronald
2004-11-01
Non-Newtonian liquids are used in many applications involving drop/jet breakup, e.g. atomization coating and crop spraying. Much has been learned on the breakup of Newtonian threads through local scaling analyses, experiment, and simulation. By contrast, little is known about pinch-off of non-Newtonian threads. Recently, we have studied the pinch-off of a thread of a power law fluid by solving a set of 1-d slender-jet equations in physical and self-similar spaces [Doshi et al. JNNFM 113, 1 (2003); PF 16, 585 (2004)]. Dynamics close to pinch-off is of course self-similar and local analysis yields scaling exponents that govern the variation with time to breakup of thread radius, axial length, and axial velocity. Remarkably, interface shapes in the vicinity of the singularity are found to be non-slender if the power law exponent n<0.6 for breakup under creeping flow conditions and if n<2/3 when inertia is important. The governing system of 3-d, axisymmetric (2-d) equations are solved here to elucidate the pinch-off dynamics when thread profiles in the vicinity of the singularity are non-slender.
Spectra that behave like power-laws are not necessarily power-laws
NASA Astrophysics Data System (ADS)
Podesta, John J.
2016-02-01
It is shown that measured power spectral densities (spectra) that closely resemble power-law spectra may, in fact, have mathematical forms that are not power laws in the mathematical sense. If power spectral estimates show a good fit to a straight line on a log-log plot over a finite frequency range, that is not sufficient evidence to conclude that the mathematical form of the spectrum is, in fact, a power-law over that range. It is also pointed out that to accurately fit a power-law function to experimental data using linear least squares techniques in log-log space, as is often done in practice, it is essential that the data is uniformly distributed along the abscissa in log-space (in the stochastic sense) or, otherwise, the data must be linearly interpolated onto a uniform grid to ensure that the data employed in the fitting procedure is equally weighted along the abscissa. These two important points are not widely appreciated by researchers in the field and the pitfalls associated with commonly used fitting techniques are often overlooked in the analysis of solar wind data.
Poissonian renormalizations, exponentials, and power laws
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Universal Power Law Governing Pedestrian Interactions
NASA Astrophysics Data System (ADS)
Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.
2014-12-01
Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.
Power Law Mapping in Human Area Perception
NASA Astrophysics Data System (ADS)
Longjas, Anthony; Legara, Erika Fille; Monterola, Christopher
We investigate how humans visually perceive and approximate area or space allocation through visual area experiments. The participants are asked to draw a circle concentric to the reference circle on the monitor screen using a computer mouse with area measurements relative to the area of the reference circle. The activity is repeated for triangle, square and hexagon. The area estimated corresponds to the area estimates of a participant (perceived) for a corresponding requested area to be drawn (stimulus). The area estimated fits very well (goodness of fit R2 > 0.97) to a power law given by r2α where r is the radius of the circle or the distance of the edge for triangle, square and hexagon. The power law fit demonstrates that for all shapes sampled, participants underestimated area for stimulus that are less than ~100% of the reference area and overestimated area for stimulus greater than ~100% of the reference area. The value of α is smallest for the circle (α∘ ≈ 1.33) and largest for triangle (α△ ≈ 1.56) indicating that in the presence of a reference area with the same shape, circle is perceived to be smallest among the figures considered when drawn bigger than the reference area, but largest when drawn smaller than the reference area. We also conducted experiments on length estimation and consistent with the results of Dehaene et al., Science 2008, we recover a linear relationship between the perceived length and the stimulus. We show that contrary to number mapping into space and/or length perception, human's perception of area is not corrected by the introduction of cultural interventions such as formal education.
Bellez, Sami; Bourlier, Christophe; Kubické, Gildas
2015-03-01
This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning.
The power law as an emergent property.
Anderson, R B
2001-10-01
Recent work has shown that the power function, a ubiquitous characteristic of learning, memory, and sensation, can emerge from the arithmetic averaging of exponential curves. In the present study, the forgetting process was simulated via computer to determine whether power curves can result from the averaging of other types of component curves. Each of several simulations contained 100 memory traces that were made to decay at different rates. The resulting component curves were then arithmetically averaged to produce an aggregate curve for each simulation. The simulations varied with respect to the forms of the component curves: exponential, range-limited linear, range-limited logarithmic, or power. The goodness of the aggregate curve's fit to a power function relative to other functions increased as the amount of intercomponent slope variability increased, irrespective of component-curve type. Thus, the power law's ubiquity may reflect the pervasiveness of slope variability across component functions. Moreover, power-curve emergence may constitute a methodological artifact, an explanatory construct, or both, depending on the locus of the effect. PMID:11820749
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning. PMID:25711183
A Universal Power Law Governing Pedestrian Interactions
NASA Astrophysics Data System (ADS)
Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.
2015-03-01
Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena. Work at Argonne National Laboratory is supported by the U.S. Department of Energy, under Contract No. DE-AC02-06CH11357. Work at the University of Minnesota is supported by MnDRIVE Initiative on Robotics, Sensors, and Advanced Manufacturing.
Discovery of power-laws in chemical space.
Benz, Ryan W; Swamidass, S Joshua; Baldi, Pierre
2008-06-01
Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank/ frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80/20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases. PMID:18522387
The paternity of the power law of human motor control.
Kvålseth, T O
1993-02-01
It is pointed out that, contrary to a recent paternity claim, the power law of human motor control was first discovered by this author more than ten years ago. The classical Fitts' law is shown to be a special case of the power law.
Fractional power-law spatial dispersion in electrodynamics
Tarasov, Vasily E.; Trujillo, Juan J.
2013-07-15
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media.
Resurrecting power law inflation in the light of Planck results
Unnikrishnan, Sanil; Sahni, Varun E-mail: varun@iucaa.ernet.in
2013-10-01
It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter f{sub N{sub L}{sup equil}} are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our model is structurally similar to that of a canonical scalar field and has a power law form for the kinetic term. A simple extension of our model resolves the graceful exit problem which usually afflicts models of power law inflation.
Distortion of power law blinking with binning and thresholding
NASA Astrophysics Data System (ADS)
Amecke, Nicole; Heber, André; Cichos, Frank
2014-03-01
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 αon/off ≳ 1.6, especially if αon ≠ αoff 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.
Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.
Zhao, Cunlu; Yang, Chun
2013-03-01
EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field.
Thresholded Power law Size Distributions of Instabilities in Astrophysics
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2015-11-01
Power-law-like size distributions are ubiquitous in astrophysical instabilities. There are at least four natural effects that cause deviations from ideal power law size distributions, which we model here in a generalized way: (1) a physical threshold of an instability; (2) incomplete sampling of the smallest events below a threshold x0; (3) contamination by an event-unrelated background xb; and (4) truncation effects at the largest events due to a finite system size. These effects can be modeled in the simplest terms with a “thresholded power law” distribution function (also called generalized Pareto [type II] or Lomax distribution), N(x){dx}\\propto {(x+{x}0)}-a{dx}, where x0 > 0 is positive for a threshold effect, while x0 < 0 is negative for background contamination. We analytically derive the functional shape of this thresholded power law distribution function from an exponential growth evolution model, which produces avalanches only when a disturbance exceeds a critical threshold x0. We apply the thresholded power law distribution function to terrestrial, solar (HXRBS, BATSE, RHESSI), and stellar flare (Kepler) data sets. We find that the thresholded power law model provides an adequate fit to most of the observed data. Major advantages of this model are the automated choice of the power law fitting range, diagnostics of background contamination, physical instability thresholds, instrumental detection thresholds, and finite system size limits. When testing self-organized criticality models that predict ideal power laws, we suggest including these natural truncation effects.
Statistical analyses support power law distributions found in neuronal avalanches.
Klaus, Andreas; Yu, Shan; Plenz, Dietmar
2011-01-01
The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Punctuated equilibrium and power law in economic dynamics
NASA Astrophysics Data System (ADS)
Gupta, Abhijit Kar
2012-02-01
This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called 'feedback' was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of 'fitness' and 'selection' in the present model of economic evolution.
Fractal ladder models and power law wave equations
Kelly, James F.; McGough, Robert J.
2009-01-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816
Hidden power law patterns in the top European football leagues
NASA Astrophysics Data System (ADS)
Da Silva, Sergio; Matsushita, Raul; Silveira, Eliza
2013-11-01
Because sports are stylized combat, sports may follow power laws similar to those found for wars, individual clashes, and acts of terrorism. We show this fact for football (soccer) by adjusting power laws that show a close relationship between rank and points won by the clubs participating in the latest seasons of the top fifteen European football leagues. In addition, we use Shannon entropy for gauging league competitive balance. As a result, we are able to rank the leagues according to competitiveness.
NASA Astrophysics Data System (ADS)
Baqersad, Javad; Niezrecki, Christopher; Avitabile, Peter
2015-09-01
Health monitoring of rotating structures such as wind turbines and helicopter rotors is generally performed using conventional sensors that provide a limited set of data at discrete locations near or on the hub. These sensors usually provide no data on the blades or inside them where failures might occur. Within this paper, an approach was used to extract the full-field dynamic strain on a wind turbine assembly subject to arbitrary loading conditions. A three-bladed wind turbine having 2.3-m long blades was placed in a semi-built-in boundary condition using a hub, a machining chuck, and a steel block. For three different test cases, the turbine was excited using (1) pluck testing, (2) random impacts on blades with three impact hammers, and (3) random excitation by a mechanical shaker. The response of the structure to the excitations was measured using three-dimensional point tracking. A pair of high-speed cameras was used to measure displacement of optical targets on the structure when the blades were vibrating. The measured displacements at discrete locations were expanded and applied to the finite element model of the structure to extract the full-field dynamic strain. The results of the paper show an excellent correlation between the strain predicted using the proposed approach and the strain measured with strain-gages for each of the three loading conditions. The approach used in this paper to predict the strain showed higher accuracy than the digital image correlation technique. The new expansion approach is able to extract dynamic strain all over the entire structure, even inside the structure beyond the line of sight of the measurement system. Because the method is based on a non-contacting measurement approach, it can be readily applied to a variety of structures having different boundary and operating conditions, including rotating blades.
Mode coupling evolution in arbitrary inflationary backgrounds
Bernardeau, Francis
2011-02-01
The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact that such calculations can be mapped, for super-horizon scales, into those of a classical system, we express the expected correlation functions in terms of classical quantities, power spectra, Green functions, that can be easily computed in the long-wavelength limit. Explicit results are presented that extend those already known for a de Sitter background. In particular the expressions of the late time amplitude of bispectrum and trispectrum, as well as the whole high-order correlation structure, are given in terms of the expansion factor behavior. When compared to the case of a de Sitter background, power law inflation and chaotic inflation induced by a massive field are found to induce high order correlation functions the amplitudes of which are amplified by almost one order of magnitude. These results indicate that the dependence of the related non-Gaussian parameters — such as f{sub NL} — on the wave-modes is at percent level.
Distortion of power law blinking with binning and thresholding
Amecke, Nicole; Heber, André; Cichos, Frank
2014-03-21
Fluorescence intermittency is a random switching between emitting (on) and non-emitting (off) periods found for many single chromophores such as semiconductor quantum dots and organic molecules. The statistics of the duration of on- and off-periods are commonly determined by thresholding the emission time trace of a single chromophore and appear to be power law distributed. Here we test with the help of simulations if the experimentally determined power law distributions can actually reflect the underlying statistics. We find that with the experimentally limited time resolution real power law statistics with exponents α{sub on/off} ≳ 1.6, especially if α{sub on} ≠ α{sub off} would not be observed as such in the experimental data after binning and thresholding. Instead, a power law appearance could simply be obtained from the continuous distribution of intermediate intensity levels. This challenges much of the obtained data and the models describing the so-called power law blinking.
Power-Law Scaling in the Brain Surface Electric Potential
Miller, Kai J.; Sorensen, Larry B.; Ojemann, Jeffrey G.; den Nijs, Marcel
2009-01-01
Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form from 80 to 500 Hz. This scaling index, , is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, , increases. We observe a “knee” in the spectra at , implying the existence of a characteristic time scale . Below , we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory “asynchronous,” scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent “synchronous” rhythm-based paradigm. PMID:20019800
Robust Statistical Detection of Power-Law Cross-Correlation
NASA Astrophysics Data System (ADS)
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-06-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram.
Power-law relations in random networks with communities.
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S H
2016-07-01
Most random graph models are locally tree-like-do not contain short cycles-rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ. In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ=γ-1. PMID:27575143
General 2.5 power law of metallic glasses.
Zeng, Qiaoshi; Lin, Yu; Liu, Yijin; Zeng, Zhidan; Shi, Crystal Y; Zhang, Bo; Lou, Hongbo; Sinogeikin, Stanislav V; Kono, Yoshio; Kenney-Benson, Curtis; Park, Changyong; Yang, Wenge; Wang, Weihua; Sheng, Hongwei; Mao, Ho-Kwang; Mao, Wendy L
2016-02-16
Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its "disordered" structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous "composition" change of 4f-localized "big Ce" to 4f-itinerant "small Ce," indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs. PMID:26831105
Power-law relations in random networks with communities
NASA Astrophysics Data System (ADS)
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.
2016-07-01
Most random graph models are locally tree-like—do not contain short cycles—rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ . In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ =γ -1 .
Statistical Models of Power-law Distributions in Homogeneous Plasmas
Roth, Ilan
2011-01-04
A variety of in-situ measurements in space plasmas point out to an intermittent formation of distribution functions with elongated tails and power-law at high energies. Power-laws form ubiquitous signature of many complex systems, plasma being a good example of a non-Boltzmann behavior for distribution functions of energetic particles. Particles, which either undergo mutual collisions or are scattered in phase space by electromagnetic fluctuations, exhibit statistical properties, which are determined by the transition probability density function of a single interaction, while their non-asymptotic evolution may determine the observed high-energy populations. It is shown that relaxation of the Brownian motion assumptions leads to non-analytical characteristic functions and to generalization of the Fokker-Planck equation with fractional derivatives that result in power law solutions parameterized by the probability density function.
Testing power-law cross-correlations: rescaled covariance test
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2013-10-01
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.
Edge effect on the power law distribution of granular avalanches.
Lorincz, Kinga A; Wijngaarden, Rinke J
2007-10-01
Many punctuated phenomena in nature are claimed [e.g., by the theory of self-organized criticality (SOC)] to be power-law distributed. In our experiments on a three-dimensional pile of long-grained rice, we find that by only changing the boundary condition of the system, we switch from such power-law-distributed avalanche sizes to quasiperiodic system-spanning avalanches. Conversely, by removing ledges the incidence of system-spanning avalanches is significantly reduced. This may offer a perspective on new avalanche prevention schemes. In addition, our findings may help to explain why the archetype of SOC, the sandpile, was found to have power-law-distributed avalanches in some experiments, while in other experiments quasiperiodic system-spanning avalanches were found.
Robustness of quantum dot power-law blinking.
Bharadwaj, Palash; Novotny, Lukas
2011-05-11
Photon emission from quantum dots (QDs) and other quantum emitters is characterized by abrupt jumps between an "on" and an "off" state. In contrast to ions and atoms however, the durations of bright and dark periods in colloidal QDs curiously defy a characteristic time scale and are best described by a power-law probability distribution, i.e., ρ(τ) ∝ τ(-α). We controllably couple a single colloidal QD to a single gold nanoparticle and find that power-law blinking is preserved unaltered even as the gold nanoparticle drastically modifies the excitonic decay rate of the QD. This resilience of the power law to change provides evidence that blinking statistics are not swayed by environment-induced variations in kinetics and provides clues toward the mechanism responsible for universal fluorescence intermittency.
General 2.5 power law of metallic glasses
Zeng, Qiaoshi; Lin, Yu; Liu, Yijin; Zeng, Zhidan; Shi, Crystal Y.; Zhang, Bo; Lou, Hongbo; Sinogeikin, Stanislav V.; Kono, Yoshio; Kenney-Benson, Curtis; Park, Changyong; Yang, Wenge; Wang, Weihua; Sheng, Hongwei; Mao, Ho-kwang; Mao, Wendy L.
2016-01-01
Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its “disordered” structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous “composition” change of 4f-localized “big Ce” to 4f-itinerant “small Ce,” indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs. PMID:26831105
Functional modulation of power-law distribution in visual perception
NASA Astrophysics Data System (ADS)
Shimono, Masanori; Owaki, Takashi; Amano, Kaoru; Kitajo, Keiichi; Takeda, Tsunehiro
2007-05-01
Neuronal activities have recently been reported to exhibit power-law scaling behavior. However, it has not been demonstrated that the power-law component can play an important role in human perceptual functions. Here, we demonstrate that the power spectrum of magnetoencephalograph recordings of brain activity varies in coordination with perception of subthreshold visual stimuli. We observed that perceptual performance could be better explained by modulation of the power-law component than by modulation of the peak power in particular narrow frequency ranges. The results suggest that the brain operates in a state of self-organized criticality, modulating the power spectral exponent of its activity to optimize its internal state for response to external stimuli.
Between disorder and order: A case study of power law
NASA Astrophysics Data System (ADS)
Cao, Yong; Zhao, Youjie; Yue, Xiaoguang; Xiong, Fei; Sun, Yongke; He, Xin; Wang, Lichao
2016-08-01
Power law is an important feature of phenomena in long memory behaviors. Zipf ever found power law in the distribution of the word frequencies. In physics, the terms order and disorder are Thermodynamic or statistical physics concepts originally and a lot of research work has focused on self-organization of the disorder ingredients of simple physical systems. It is interesting what make disorder-order transition. We devise an experiment-based method about random symbolic sequences to research regular pattern between disorder and order. The experiment results reveal power law is indeed an important regularity in transition from disorder to order. About these results the preliminary study and analysis has been done to explain the reasons.
NASA Astrophysics Data System (ADS)
Pandya, Alex; Zhang, Zhaowei; Chandra, Mani; Gammie, Charles F.
2016-05-01
Synchrotron emission and absorption determine the observational appearances of many astronomical systems. In this paper, we describe a numerical scheme for calculating synchrotron emissivities and absorptivities in all four Stokes parameters for arbitrary gyrotropic electron distribution functions, building on earlier work by Leung, Gammie, and Noble. We use this technique to evaluate the emissivities and the absorptivities for a thermal (Maxwell-Jüttner), isotropic power-law, and an isotropic kappa distribution function. The latter contains a power-law tail at high particle energies that smoothly merges with a thermal core at low energies, as is characteristic of observed particle spectra in collisionless plasmas. We provide fitting formulae and error bounds on the fitting formulae for use in codes that solve the radiative transfer equation. The numerical method and the fitting formulae are implemented in a compact C library called symphony. We find that the kappa distribution has a source function that is indistinguishable from a thermal spectrum at low frequency and transitions to the characteristic self-absorbed synchrotron spectrum, \\propto {ν }5/2, at high frequency; the linear polarization fraction for a thermal spectrum is near unity at high frequency; and all distributions produce O(10%) circular polarization at low frequency for lines of sight sufficiently close to the magnetic field vector.
Weather-driven model indicative of spatiotemporal power laws.
Song, Weiguo; Zheng, Hongyang; Wang, Jian; Ma, Jian; Satoh, Kohyu
2007-01-01
In the traditional Drossel-Schwabl forest fire model (DS model), the frequency distributions of fire size and fire interval follow a power law and an exponential law, respectively. However, it is found that the frequency-interval distribution of actual forest fires is not exponential, but a power law with periodical fluctuations which may be caused by the daily cycle of weather parameters. Therefore, a weather driven forest fire model (WD model) is built considering actual hourly weather records, with which the fire igniting probability is calculated. The simulation results indicate that the frequency-interval distribution of the WD model agrees with that of actual forest fire data and, at the same time, the frequency-size distributions of the WD and the DS models are in accordance with each other. In the further analysis of the temporal property of weather data, it is found that the change of weather data also exhibits a power-law relation with periodic fluctuations, implying that the external driving from weather parameters is the essential reason for the power-law distribution of fire intervals. The results suggest that natural systems may be coupled with each other and that the decoupling of systems is important to identifying system characteristics. PMID:17358226
Electrokinetically modulated peristaltic transport of power-law fluids.
Goswami, Prakash; Chakraborty, Jeevanjyoti; Bandopadhyay, Aditya; Chakraborty, Suman
2016-01-01
The electrokinetically modulated peristaltic transport of power-law fluids through a narrow confinement in the form of a deformable tube is investigated. The fluid is considered to be divided into two regions - a non-Newtonian core region (described by the power-law behavior) which is surrounded by a thin wall-adhering layer of Newtonian fluid. This division mimics the occurrence of a wall-adjacent cell-free skimming layer in blood samples typically handled in microfluidic transport. The pumping characteristics and the trapping of the fluid bolus are studied by considering the effect of fluid viscosities, power-law index and electroosmosis. It is found that the zero-flow pressure rise is strongly dependent on the relative viscosity ratio of the near-wall depleted fluid and the core fluid as well as on the power-law index. The effect of electroosmosis on the pressure rise is strongly manifested at lower occlusion values, thereby indicating its importance in transport modulation for weakly peristaltic flow. It is also established that the phenomenon of trapping may be controlled on-the-fly by tuning the magnitude of the electric field: the trapping vanishes as the magnitude of the electric field is increased. Similarly, the phenomenon of reflux is shown to disappear due to the action of the applied electric field. These findings may be applied for the modulation of pumping in bio-physical environments by means of external electric fields.
Parameter identifiability of power-law biochemical system models.
Srinath, Sridharan; Gunawan, Rudiyanto
2010-09-01
Mathematical modeling has become an integral component in biotechnology, in which these models are frequently used to design and optimize bioprocesses. Canonical models, like power-laws within the Biochemical Systems Theory, offer numerous mathematical and numerical advantages, including built-in flexibility to simulate general nonlinear behavior. The construction of such models relies on the estimation of unknown case-specific model parameters by way of experimental data fitting, also known as inverse modeling. Despite the large number of publications on this topic, this task remains the bottleneck in canonical modeling of biochemical systems. The focus of this paper concerns with the question of identifiability of power-law models from dynamic data, that is, whether the parameter values can be uniquely and accurately identified from time-series data. Existing and newly developed parameter identifiability methods were applied to two power-law models of biochemical systems, and the results pointed to the lack of parametric identifiability as the root cause of the difficulty faced in the inverse modeling. Despite the focus on power-law models, the analyses and conclusions are extendable to other canonical models, and the issue of parameter identifiability is expected to be a common problem in biochemical system modeling. PMID:20197073
Medical practices display power law behaviors similar to spoken languages
2013-01-01
Background Medical care commonly involves the apprehension of complex patterns of patient derangements to which the practitioner responds with patterns of interventions, as opposed to single therapeutic maneuvers. This complexity renders the objective assessment of practice patterns using conventional statistical approaches difficult. Methods Combinatorial approaches drawn from symbolic dynamics are used to encode the observed patterns of patient derangement and associated practitioner response patterns as sequences of symbols. Concatenating each patient derangement symbol with the contemporaneous practitioner response symbol creates “words” encoding the simultaneous patient derangement and provider response patterns and yields an observed vocabulary with quantifiable statistical characteristics. Results A fundamental observation in many natural languages is the existence of a power law relationship between the rank order of word usage and the absolute frequency with which particular words are uttered. We show that population level patterns of patient derangement: practitioner intervention word usage in two entirely unrelated domains of medical care display power law relationships similar to those of natural languages, and that–in one of these domains–power law behavior at the population level reflects power law behavior at the level of individual practitioners. Conclusions Our results suggest that patterns of medical care can be approached using quantitative linguistic techniques, a finding that has implications for the assessment of expertise, machine learning identification of optimal practices, and construction of bedside decision support tools. PMID:24007376
Power laws of wealth, market order volumes and market returns
NASA Astrophysics Data System (ADS)
Solomon, Sorin; Richmond, Peter
2001-10-01
Using the Generalized Lotka Volterra model adapted to deal with mutiagent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a ‘fair’ market, the wealth distribution among individual investors fulfills a power law. We then argue that ‘fair play’ for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent α∼ {3}/{2}. In particular, we relate it to the average number of individuals L depending on the average wealth: α∼ L/( L-1). Then we connect it to certain power exponents characterizing the stock markets. We find that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent β∼α∼ {3}/{2}. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order γ∼2 α∼3. These results are consistent with recent experimental measurements of these power law exponents (S. Maslov, M. Mills, Physica A 299 (2001) 234 for β; P. Gopikrishnan et al., Phys. Rev. E 60 (1999) 5305 for γ).
Electrokinetically modulated peristaltic transport of power-law fluids.
Goswami, Prakash; Chakraborty, Jeevanjyoti; Bandopadhyay, Aditya; Chakraborty, Suman
2016-01-01
The electrokinetically modulated peristaltic transport of power-law fluids through a narrow confinement in the form of a deformable tube is investigated. The fluid is considered to be divided into two regions - a non-Newtonian core region (described by the power-law behavior) which is surrounded by a thin wall-adhering layer of Newtonian fluid. This division mimics the occurrence of a wall-adjacent cell-free skimming layer in blood samples typically handled in microfluidic transport. The pumping characteristics and the trapping of the fluid bolus are studied by considering the effect of fluid viscosities, power-law index and electroosmosis. It is found that the zero-flow pressure rise is strongly dependent on the relative viscosity ratio of the near-wall depleted fluid and the core fluid as well as on the power-law index. The effect of electroosmosis on the pressure rise is strongly manifested at lower occlusion values, thereby indicating its importance in transport modulation for weakly peristaltic flow. It is also established that the phenomenon of trapping may be controlled on-the-fly by tuning the magnitude of the electric field: the trapping vanishes as the magnitude of the electric field is increased. Similarly, the phenomenon of reflux is shown to disappear due to the action of the applied electric field. These findings may be applied for the modulation of pumping in bio-physical environments by means of external electric fields. PMID:26524260
Jose, Prasanth P; Bagchi, Biman
2004-06-15
Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law
Jose, Prasanth P; Bagchi, Biman
2004-06-15
Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W.
2002-01-01
A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from
Deviation from Power Law Behavior in Landslide Phenomenon
NASA Astrophysics Data System (ADS)
Li, L.; Lan, H.; Wu, Y.
2013-12-01
Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law
Bose-Einstein condensation with a finite number of particles in a power-law trap
Jaouadi, A.; Telmini, M.; Charron, E.
2011-02-15
Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number N of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation temperature T{sub c} in terms of a power series in x{sub 0}={epsilon}{sub 0}/k{sub B}T{sub c}, where {epsilon}{sub 0} denotes the zero-point energy of the trapping potential. This expression, which applies in Cartesian, cylindrical, and spherical power-law traps, is given analytically at infinite order. It is also given numerically for specific potential shapes as an expansion in powers of x{sub 0} up to the second order. We show that, for a harmonic trap, the well-known first-order shift of the critical temperature {Delta}T{sub c}/T{sub c{proportional_to}}N{sup -1/3} is inaccurate when N{<=}10{sup 5}, the next order (proportional to N{sup -1/2}) being significant. We also show that finite-size effects on the condensation temperature cancel out in a cubic trapping potential, e.g., V(r){proportional_to}r{sup 3}. Finally, we show that in a generic power-law potential of higher order, e.g., V(r){proportional_to}r{sup {alpha}} with {alpha}>3, the shift of the critical temperature becomes positive. This effect provides a large increase of T{sub c} for relatively small atom numbers. For instance, an increase of about +40% is expected with 10{sup 4} atoms in a V(r){proportional_to}r{sup 12} trapping potential.
Power law in a microcanonical ensemble with scaling volume fluctuations
Begun, V. V.; Gazdzicki, M.; Gorenstein, M. I.
2008-08-15
Volume fluctuations are introduced in a statistical modeling of relativistic particle collisions. The microcanonical ensemble is used, and the volume fluctuations are assumed to have specific scaling properties. This leads to the KNO scaling of the particle multiplicity distributions as measured in p+p interactions. A striking prediction of the model is a power law form of the single particle momentum spectrum at high momenta. Moreover, the mean multiplicity of heavy particles also decreases as a function of the particle mass according to a power law. Finally, it is shown that the dependence of the momentum spectrum on the particle mass and momentum reduces to the dependence on the particle energy. These results resemble the properties of particle production in collisions of high energy particles.
Power law behavior of the zigzag transition in Yukawa clusters
Sheridan, T. E.; Magyar, Andrew L.
2010-11-15
We provide direct experimental evidence that the width of a Yukawa cluster exhibits power law behavior during the one-dimensional (1D) to two-dimensional (2D) zigzag transition. Configurations of small dusty (complex) plasma clusters confined in a biharmonic potential well are characterized as the well anisotropy is varied. When the anisotropy is large the particles are in a 1D straight-line configuration. As the anisotropy is decreased the cluster undergoes a zigzag transition to a 2D configuration. The measured dependence of cluster width on anisotropy follows a power law. A second transition from the zigzag to an elliptical configuration is also observed. The results are in very good agreement with a model of identical particles interacting through a Yukawa potential.
Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---
NASA Astrophysics Data System (ADS)
Kaizoji, T.
In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, P (S > x) ˜ x^{-α}, with an exponent that moves in the range of 1.09 < α < 1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.
Diffusion with stochastic resetting at power-law times
NASA Astrophysics Data System (ADS)
Nagar, Apoorva; Gupta, Shamik
2016-06-01
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ˜τ-(1 +α );α >0 ? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α <1 , to one that is time independent for α >1 . The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.
Anomalous thermodynamic power laws near topological transitions in nodal superconductors
NASA Astrophysics Data System (ADS)
Mazidian, B.; Quintanilla, J.; Hillier, A. D.; Annett, J. F.
2013-12-01
Unconventional superconductors are most frequently identified by the observation of power-law behavior on low-temperature thermodynamic or transport properties, such as specific heat. Here, we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example, when point or line nodes first appear as a function of some physical parameter. We identify anomalous, noninteger thermodynamic power laws associated with these new nodal types, and give physical examples of superconductors in which they might be observed experimentally, including the noncentrosymmetric superconductor Li2Pd3-xPtxB.
Power laws and elastic nonlinearity in materials with complex microstructure
NASA Astrophysics Data System (ADS)
Scalerandi, M.
2016-01-01
Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities.
Power law relationships for rain attenuation and reflectivity
NASA Technical Reports Server (NTRS)
Devasirvatham, D. M. J.; Hodge, D. B.
1978-01-01
The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.
Power-law behavior in social and economical phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Keizo; Miyazima, Sasuke
2004-12-01
We have already found power-law behavior in various phenomena such as high-tax payer, population distribution, name distribution, passenger number at stations, student number in a university from high schools, and so on. We can explain why these phenomena show such interesting behaviors by doing simulations based on adequate models. We have come to the conclusion that there are fractal structures underlying those phenomena.
Automated piecewise power-law modeling of biological systems.
Machina, Anna; Ponosov, Arkady; Voit, Eberhard O
2010-09-01
Recent trends suggest that future biotechnology will increasingly rely on mathematical models of the biological systems under investigation. In particular, metabolic engineering will make wider use of metabolic pathway models in stoichiometric or fully kinetic format. A significant obstacle to the use of pathway models is the identification of suitable process descriptions and their parameters. We recently showed that, at least under favorable conditions, Dynamic Flux Estimation (DFE) permits the numerical characterization of fluxes from sets of metabolic time series data. However, DFE does not prescribe how to convert these numerical results into functional representations. In some cases, Michaelis-Menten rate laws or canonical formats are well suited, in which case the estimation of parameter values is easy. However, in other cases, appropriate functional forms are not evident, and exhaustive searches among all possible candidate models are not feasible. We show here how piecewise power-law functions of one or more variables offer an effective default solution for the almost unbiased representation of uni- and multivariate time series data. The results of an automated algorithm for their determination are piecewise power-law fits, whose accuracy is only limited by the available data. The individual power-law pieces may lead to discontinuities at break points or boundaries between sub-domains. In many practical applications, these boundary gaps do not cause problems. Potential smoothing techniques, based on differential inclusions and Filippov's theory, are discussed in Appendix A. PMID:20060428
Robust Statistical Detection of Power-Law Cross-Correlation
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-01-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630
Robust Statistical Detection of Power-Law Cross-Correlation.
Blythe, Duncan A J; Nikulin, Vadim V; Müller, Klaus-Robert
2016-01-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630
Coalescence of Drops of a Power-law Fluid
NASA Astrophysics Data System (ADS)
Kamat, Pritish; Thete, Sumeet; Basaran, Osman
2014-11-01
Drop coalescence is crucial in a host of industrial, household, and natural processes that involve dispersions. Coalescence is a rate-controlling process in breaking emulsions and strongly influences drop-size-distributions in sprays. In a continuum approach, coalescence begins by the formation of a microscopic, non-slender bridge connecting the two drops. Indefinitely large axial curvature at the neck results in local lowering of pressure that drives fluid from the bulk of the drops toward the neck, thereby causing the bridge radius r (t) and height z (t) to increase in time t. The coalescence of Newtonian drops in air has heretofore been thoroughly studied. Here, we extend these earlier studies by analyzing the coalescence of drops of power-law fluids because many fluids encountered in real applications, including cosmetic creams, shampoos, grease, and paint, exhibit power-law (deformation-rate thinning) rheology. On account of the non-slender geometry of the liquid bridge connecting the two drops (z << r) , we analyze the resulting free surface flow problem by numerical simulation. Among other results, we present and discuss the nature of flows and scaling behaviors for r and z as functions of the initial viscosity and power-law index (0 < n <= 1) .
Econophysical anchoring of unimodal power-law distributions
NASA Astrophysics Data System (ADS)
Eliazar, Iddo I.; Cohen, Morrel H.
2013-09-01
The sciences are abundant with size distributions whose densities have a unimodal shape and power-law tails both at zero and at infinity. The quintessential examples of such unimodal and power-law (UPL) distributions are the sizes of income and wealth in human societies. While the tails of UPL distributions are precisely quantified by their corresponding power-law exponents, their bulks are only qualitatively characterized as unimodal. Consequently, different statistical models of UPL distributions exist, the most popular considering lognormal bulks. In this paper we present a general econophysical framework for UPL distributions termed ‘the anchoring method’. This method: (i) universally approximates UPL distributions via three ‘anchors’ set at zero, at infinity, and at an intermediate point between zero and infinity (e.g. the mode); (ii) is highly versatile and broadly applicable; (iii) encompasses the existing statistical models of UPL distributions as special cases; (iv) facilitates the introduction of new statistical models of UPL distributions and (v) yields a socioeconophysical analysis of UPL distributions.
Scaling range of power laws that originate from fluctuation analysis
NASA Astrophysics Data System (ADS)
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Eliminating a Confounding Factor in Power Law Parameter Interpretation
NASA Astrophysics Data System (ADS)
Karst, N.; Dralle, D.; Thompson, S. E.
2015-12-01
Power law models of the form y = -axb are used to represent a wide range of phenomena in the physical, biological and social sciences. Power laws are well known to display a "scale-free property", meaning that the value of the exponent b is independent of the unit of measurement (the "scale") of the state variable x. While this makes estimation of the exponent robust, it raises significant estimation challenges for the linear multiplier a. Specifically, if both the multiplier a and exponent b are allowed to vary when undertaking an empirical fitting procedure, then physical units used to measure x induce a formal (i.e., entirely nonphysical) dependence between a and b, because the fitted value of a will contain a (potentially large) multiplicative factor that varies depending on the scale of x. This is problematic for two reasons: (i) if a is to be empirically estimated, but admits a physical interpretation, then the scale-dependent factor can confound the physically meaningful value (ii) the formal relationship between a and b due to the scaling of the relationship obscures any true relationship between the parameters and could motivate a spurious interpretation of their co-variation. To correct this issue, we present a technique to remove the formal correlation between a and b, and demonstrate an application of the technique in the context of streamflow recession analysis, where the falling limb of the hydrograph is modeled using a simple power law relationship, dq/dt = -aqb. Following the decorrelation of (a, b) recession parameter pairs, physically intuitive seasonal patterns, greatly obscured in the original data, are clearly found.
Power-law correlations of landslide areas in central Italy
NASA Astrophysics Data System (ADS)
Guzzetti, Fausto; Malamud, Bruce D.; Turcotte, Donald L.; Reichenbach, Paola
2002-02-01
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 range 0.03 km 2< AL<4 km 2. Data set B contains 4233 landslides that were triggered by a sudden change in temperature on 1 January 1997, resulting in extensive melting of snow cover. An inventory of these snow-melt-triggered landslides was obtained from aerial photographs taken 3 months after the event. These landslides also correlate well with a power-law relation with exponent -2.5, over the range 0.001 km 2< AL<0.1 km 2. We show that the correlation of data set B is essentially identical to the correlation of 11 000 landslides triggered by the 17 January 1994 Northridge, California earthquake. We attribute a rollover for small landslides in data set A to incompleteness of the record due to erosion and other processes, and to limitations in the reconnaissance mapping technique used to complete the inventory. On the other hand, we conclude that rollovers for small landslides in data set B and the California earthquake data are real and are associated with the surface morphology. We conclude that the power-law distribution is valid over a wide range of landslide areas and discuss possible reasons. We also discuss the contribution of the snow-melt- and earthquake-triggered landslide events to the total landslide inventory.
Analytical Limit Distributions from Random Power-Law Interactions
NASA Astrophysics Data System (ADS)
Zaid, Irwin; Mizuno, Daisuke
2016-07-01
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
Power-law photoluminescence decay in quantum dots
Král, Karel; Menšík, Miroslav
2014-05-15
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.
Universal power law for front propagation in all fiber resonators.
Coulibaly, S; Taki, M; Tlidi, M
2014-01-13
We consider a bistable system consisting of all fiber cavity driven by an external injected continuous wave. We report on front propagation in a high finesse cavity. We study the asymptotic behavior of the front velocity. We show that the front velocity is affected by the distance from the critical point associated with bistability. We provide a scaling low governing its evolution near the up-switching point of the bistable curve. We show also that the velocity of front propagation obeys a generic power law when the front velocity approaches asymptotically its linear growing value.
Power laws, discontinuities and regional city size distributions
Garmestani, A.S.; Allen, C.R.; Gallagher, C.M.
2008-01-01
Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classes in the city size distributions are snapshots of stable states within urban systems in flux. ?? 2008.
Power-law time distribution of large earthquakes.
Mega, Mirko S; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea; Vinciguerra, Sergio
2003-05-01
We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.
Adhesion of nanoscale asperities with power-law profiles
NASA Astrophysics Data System (ADS)
Grierson, David S.; Liu, Jingjing; Carpick, Robert W.; Turner, Kevin T.
2013-02-01
The behavior of single-asperity micro- and nanoscale contacts in which adhesion is present is important for the performance of many small-scale mechanical systems and processes, such as atomic force microscopy (AFM). When analyzing such problems, the bodies in contact are often assumed to have paraboloidal shapes, thus allowing the application of the familiar Johnson-Kendall-Roberts (JKR), Derjaguin-Müller-Toporov (DMT), or Maugis-Dugdale (M-D) adhesive contact models. However, in many situations the asperities do not have paraboloidal shapes and, instead, have geometries that may be better described by a power-law function. An M-D-n analytical model has recently been developed to extend the M-D model to asperities with power-law profiles. We use a combination of M-D-n analytical modeling, finite element (FE) analysis, and experimental measurements to investigate the behavior of nanoscale adhesive contacts with non-paraboloidal geometries. Specifically, we examine the relationship between pull-off force, work of adhesion, and range of adhesion for asperities with power-law-shaped geometries. FE analysis is used to validate the M-D-n model and examine the effect of the shape of the adhesive interaction potential on the pull-off force. In the experiments, the extended M-D model is applied to analyze pull-off force measurements made on nanoscale tips that are engineered via gradual wear to have power-law shapes. The experimental and modeling results demonstrate that the range of the adhesive interaction is a crucial parameter when quantifying the adhesion of non-paraboloidal tips, quite different than the familiar paraboloidal case. The application of the M-D-n model to the experimental results yields an unusually large adhesion range of 4-5 nm, a finding we attribute to either the presence of long-range van der Waals forces or deviations from continuum theory due to atomic-scale roughness of the tips. Finally, an adhesion map to aid in analysis of pull-off force
Elastohydrodynamic analysis using a power law pressure-viscosity relation
NASA Technical Reports Server (NTRS)
Loewenthal, S. H.; Zaretsky, E. V.
1973-01-01
An isothermal elastohydrodynamic (EHD) inlet analysis of the Grubin type which considers a power law pressure-viscosity relation and a finite pressure at the inlet edge of the Hertzian contact zone was performed. Comparisons made with published X-ray EHD film thickness data for a synthetic paraffinic oil and when conventional EHD theory showed that the present theory exhibits a slightly stronger film thickness load dependence than do previous isothermal EHD theories but far less than that exhibited by the measured data.
Beyond the power law: Uncovering stylized facts in interbank networks
NASA Astrophysics Data System (ADS)
Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen
2015-06-01
We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.
Power Laws in Real Estate Prices during Bubble Periods
NASA Astrophysics Data System (ADS)
Ohnishi, Takaaki; Mizuno, Takayuki; Shimizu, Chihiro; Watanabe, Tsutomu
How can we detect real estate bubbles? In this paper, we propose making use of information on the cross-sectional dispersion of real estate prices. During bubble periods, prices tend to go up considerably for some properties, but less so for others, so that price inequality across properties increases. In other words, a key characteristic of real estate bubbles is not the rapid price hike itself but a rise in price dispersion. Given this, the purpose of this paper is to examine whether developments in the dispersion in real estate prices can be used to detect bubbles in property markets as they arise, using data from Japan and the U.S. First, we show that the land price distribution in Tokyo had a power-law tail during the bubble period in the late 1980s, while it was very close to a lognormal before and after the bubble period. Second, in the U.S. data we find that the tail of the house price distribution tends to be heavier in those states which experienced a housing bubble. We also provide evidence suggesting that the power-law tail observed during bubble periods arises due to the lack of price arbitrage across regions.
Power law deformation of Wishart Laguerre ensembles of random matrices
NASA Astrophysics Data System (ADS)
Akemann, Gernot; Vivo, Pierpaolo
2008-09-01
We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of β, in terms of the orthogonal polynomials of the standard Wishart-Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Marčenko-Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on β and the difference M-N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart-Laguerre ensembles. To illustrate these findings, the generalized Marčenko-Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices.
NASA Astrophysics Data System (ADS)
Stefańska, Patrycja
2016-07-01
We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Z e . Calculations are based on the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997), 10.1088/0953-4075/30/4/007; erratum R. Szmytkowski, J. Phys. B 30, 2747(E) (1997), 10.1088/0953-4075/30/11/023], combined with the theory of hypergeometric functions. The final result is of an elementary form and agrees with corresponding formulas obtained earlier by other authors for some particular states of the atom.
Passive mechanical behavior of human neutrophils: power-law fluid.
Tsai, M A; Frank, R S; Waugh, R E
1993-01-01
The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c
Resetting of fluctuating interfaces at power-law times
NASA Astrophysics Data System (ADS)
Gupta, Shamik; Nagar, Apoorva
2016-11-01
What happens when the time evolution of a fluctuating interface is interrupted by resetting to a given initial configuration after random time intervals τ distributed as a power-law ∼ {τ }-(1+α ); α \\gt 0? For an interface of length L in one dimension, and an initial flat configuration, we show that depending on α, the dynamics in the limit L\\to ∞ exhibit a spectrum of rich long-time behavior. It is known that without resetting, the interface width grows unbounded with time as {t}β in this limit, where β is the so-called growth exponent characteristic of the universality class for a given interface dynamics. We show that introducing resetting leads to fluctuations that are bounded at large times for α \\gt 1. Corresponding to such a reset-induced stationary state is a distribution of fluctuations that is strongly non-Gaussian, with tails decaying as a power-law. The distribution exhibits a distinctive cuspy behavior for a small argument, implying that the stationary state is out of equilibrium. For α \\lt 1, on the contrary, resetting to the flat configuration is unable to counter the otherwise unbounded growth of fluctuations in time, so that the distribution of fluctuations remains time dependent with an ever-increasing width, even at long times. Although stationary for α \\gt 1, the width of the interface grows forever with time as a power-law for 1\\lt α \\lt {α }({{w})}, and converges to a finite constant only for larger α, thereby exhibiting a crossover at {α }({{w})}=1 + 2β . The time-dependent distribution of fluctuations exhibits for α \\lt 1 and for small arguments further interesting crossover behavior from cusp to divergence across {α }({{d})}=1-β . We demonstrate these results by exact analytical results for the paradigmatic Edwards–Wilkinson (EW) dynamical evolution of the interface, and further corroborate our findings by extensive numerical simulations of interface models in the EW and Kardar–Parisi–Zhang universality
Comment on "Bose-Einstein condensation with a finite number of particles in a power-law trap"
NASA Astrophysics Data System (ADS)
Noronha, José M. B.
2015-07-01
In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011), 10.1103/PhysRevA.83.023616] the authors derive an analytical finite-size expansion for the Bose-Einstein condensation critical temperature of an ideal Bose gas in a generic power-law trap. In the case of a harmonic trap, this expansion adds higher-order terms to the well-known first-order correction. We point out a delicate point in connection to these results, showing that the claims of Jaouadi et al. should be treated with caution. In particular, for a harmonic trap, the given expansion yields results that, depending on what is considered to be the critical temperature of the finite system, do not generally improve on the established first-order correction. For some nonharmonic traps, the results differ at first order from other results in the literature.
Solitary and shock waves in discrete double power law materials
NASA Astrophysics Data System (ADS)
Herbold, Eric; Nesterenko, Vitali
2007-06-01
A novel strongly nonlinear metamaterial is composed using a periodic arrangement of toroidal rings between plates. The toroids are considered massless strongly nonlinear springs where the force versus displacement relationship is described by two additive power-law relationships. In these systems the nonlinearity is due to the dramatic change of the contact plane, which starts as an arbitrarily thin circle then increases in thickness with increasing compression. Solitary and shock waves are examined numerically and experimentally using three different types of polymer or rubber o-rings allowing mitigation of higher amplitude shock impulses in comparison with granular systems. In these systems a train of pulses can consist of two separate groups related to two strongly nonlinear regimes with different values of exponents, depending on the amplitude. In experiments two types of shock waves (monotonic or oscillatory) were observed depending on the type of o-rings.
Bubble coalescence in a power-law fluid
NASA Astrophysics Data System (ADS)
Kamat, Pritish; Thete, Sumeet; Basaran, Osman
2015-11-01
As two spherical gas bubbles in a liquid are slowly brought together, the liquid film or sheet between them drains and ultimately ruptures, forming a circular hole that connects them. The high curvature near the edge of the liquid sheet drives flow radially outward, causing the film to retract and the radius of the hole to increase with time. Recent experimental and theoretical work in this area has uncovered self-similarity and universal scaling regimes when two bubbles coalesce in a Newtonian fluid. Motivated by applications such as polymer and composites processing, food and drug manufacture, and aeration/deaeration systems where the liquids often exhibit deformation-rate thinning rheology, we extend the recent Newtonian studies to bubble coalescence in power-law fluids. In our work, we use a combination of thin-film theory and full 3D, axisymmetric computations to probe the dynamics in the aftermath of the singularity.
Optimized dynamical decoupling for power-law noise spectra
Pasini, S.; Uhrig, G. S.
2010-01-15
We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal pi pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder.
Exponential and power laws in public procurement markets
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav; Skuhrovec, Jiri
2012-07-01
We analyze for the first time a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40000 public procurements in the Czech Republic between 2006 and 2011, focusing on the distributional properties of the variables of interest. We uncover several scaling laws —the exponential law for the number of bidders, and the power laws for the total revenues and total spendings of the participating companies, which even follows Zipf's law for the 100 most spending institutions. We propose an analogy between extensive and non-extensive systems in physics and the public procurement market situations. Through an entropy maximization, such analogy yields some interesting results and policy implications with respect to the Maxwell-Boltzmann and Pareto distributions in the analyzed quantities.
Power-law creep and residual stresses in carbopol microgels
NASA Astrophysics Data System (ADS)
Lidon, Pierre; Manneville, Sebastien
We report on the interplay between creep and residual stresses in carbopol microgels. When a constant shear stress σ is applied below the yield stress σc, the strain is shown to increase as a power law of time, γ (t) =γ0 +(t / τ) α , with and exponent α ~= 0 . 38 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some characteristic value of about σc / 10 , the microgels experience a more complex creep behavior that we link to the existence of residual stresses and to weak aging of the system after preshear. The influence of the preshear protocol, of boundary conditions and of microgel concentration on residual stresses is investigated. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.
Unexpected power-law stress relaxation of entangled ring polymers
NASA Astrophysics Data System (ADS)
Kapnistos, M.; Lang, M.; Vlassopoulos, D.; Pyckhout-Hintzen, W.; Richter, D.; Cho, D.; Chang, T.; Rubinstein, M.
2008-12-01
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.
Deviations from uniform power law scaling in nonstationary time series
NASA Technical Reports Server (NTRS)
Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.
1997-01-01
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
Economic demography in fuzzy spatial dilemmas and power laws
NASA Astrophysics Data System (ADS)
Fort, H.; Pérez, N.
2005-03-01
Adaptive agents, playing the iterated Prisoner's Dilemma (IPD) in a two-dimensional spatial setting and governed by Pavlovian strategies ("higher success-higher chance to stay"), are used to approach the problem of cooperation between self-interested individuals from a novel angle: We investigate the effect of different possible measures of success (MS) used by players to asses their performance in the game. These MS involve quantities such as: the player's utilities U, his cumulative score (or "capital") W, his neighborhood "welfare", etc. To handle an imprecise concept like "success" the agents use fuzzy logic. The degree of cooperation, the "economic demography" and the "efficiency" attained by the system depend dramatically on the MS. Specifically, patterns of "segregation" or "exploitation" are observed for some MS. On the other hand, power laws, that may be interpreted as signatures of critical self-organization (SOC), constitute a common feature for all the MS.
Power law tails in the Italian personal income distribution
NASA Astrophysics Data System (ADS)
Clementi, F.; Gallegati, M.
2005-05-01
We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977-2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of our analysis show a shift of the distribution and a change of the indexes specifying it over time. As regards the first issue, we test the hypothesis that the evolution of both gross domestic product and personal income is governed by similar mechanisms, pointing to the existence of correlation between these quantities. The fluctuations of the shape of income distribution are instead quantified by establishing some links with the business cycle phases experienced by the Italian economy over the years covered by our dataset.
Power-law weighted networks from local attachments
NASA Astrophysics Data System (ADS)
Moriano, P.; Finke, J.
2012-07-01
This letter introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on extended power-law weighted networks with both a desired scaling exponent and a fixed clustering coefficient. The analytical results show that the connectivity distribution converges to the scaling behavior often found in social and engineering systems. To illustrate the approach of the proposed framework we generate network substrates that resemble steady state properties of the empirical citation distributions of i) publications indexed by the Institute for Scientific Information from 1981 to 1997; ii) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and iii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.
Analytical Limit Distributions from Random Power-Law Interactions.
Zaid, Irwin; Mizuno, Daisuke
2016-07-15
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated. PMID:27472105
Power laws of complex systems from extreme physical information
NASA Astrophysics Data System (ADS)
Frieden, B. Roy; Gatenby, Robert A.
2005-09-01
Many complex systems obey allometric, or power, laws y=Yxa . Here y⩾0 is the measured value of some system attribute a , Y⩾0 is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values n/4 , n=0,±1,±2,… . Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1) . Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I-J=extremum of extreme physical information is found to provide such a cause. It describes the flow of Fisher information J→I from an attribute value a on the cell level to its exterior observation y . Data y are formed via a system channel function y≡f(x,a) , with f(x,a) to be found. Extremizing the difference I-J through variation of f(x,a) results in a general allometric law f(x,a)≡y=Yxa . Darwinian evolution is presumed to cause a second extremization of I-J , now with respect to the choice of a . The solution is a=n/4 , n=0,±1,±2… , defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by only two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradients
Power laws of complex systems from extreme physical information.
Frieden, B Roy; Gatenby, Robert A
2005-09-01
Many complex systems obey allometric, or power, laws y=Y x(a) . Here y > or = 0 is the measured value of some system attribute a , Y> or =0 is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values n/4 , n=0, +/-1, +/-2.... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1) . Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I-J=extremum of extreme physical information is found to provide such a cause. It describes the flow of Fisher information J-->I from an attribute value a on the cell level to its exterior observation y . Data y are formed via a system channel function y identical to f (x,a) , with f (x,a) to be found. Extremizing the difference I-J through variation of f (x,a) results in a general allometric law f (x,a) identical to y=Y x(a) . Darwinian evolution is presumed to cause a second extremization of I-J , now with respect to the choice of a . The solution is a=n/4 , n=0,+/-1,+/-2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by only two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradients. PMID:16241509
The flow of a power-law fluid in the near-wake of a flat plate
NASA Astrophysics Data System (ADS)
Zhou, Min; Ladeinde, Foluso; Bluestein, Danny
2006-08-01
The analysis of the near-wake flow downstream of a flat plate is reported in this paper for the case of a non-Newtonian (power-law) constitutive model. To our knowledge, the present paper is the first to address this problem, as previous work on near-wakes has been limited to the use of a Newtonian model. The motivation for this work comes from the biomedical engineering problem of blood flow around the bileaflet of a mechanical heart valve. In the present paper, the series method has been used to calculate the flow near the centerline of the wake, while an asymptotic method has been used for larger distances from the centerline. The effects of power-law inlet conditions on the wake flow are reported for various values of the power-law index n, within the range 0.7≤n ≤1.3. The present analysis has been successfully validated by comparing the results for n =1 to the near-wake results by Goldstein [Proc. Cambridge Philos. Soc. 26, 1 (1930)]. We generalized the equations for arbitrary values of n, without any special considerations for n =1. Therefore, the accurate results observed for n =1 validate our procedure as a whole. The first major finding is that a fluid with smaller n develops faster downstream, such that decreasing n leads to monotonically increasing velocities compared to fluids with large n values. Another finding is that the non-Newtonian effects become more significant as the downstream distance increases. Finally, these effects tend to be more pronounced in the vicinity of the wake centerline compared to larger y locations.
Shape of gas flow paths causes power law tailing
NASA Astrophysics Data System (ADS)
Kawanishi, T.; Sakami, A.; Hayashi, Y.
2004-12-01
In soil and/or groundwater remediation, we often see prolonged tailings: continuous outflow of low concentration pollutants for very long time, and in many cases power low behavior of late-time time-concentration curves. We considered that this kind of tailing can be caused by the shape of the gaseous flow introduced in saturated/unsaturated porous media. When gas is introduced to porous media, like air-sparging or soil vapor extraction, the shape of the gas flow path would be tree-like, or to some extent "fractal." So, there would be a distribution of the distance that a solute would have to travel by diffusion before getting to a gas/water interface, and we might expect that the distribution of this "diffusion distance" would be power-law-like. In order to see if tailing can be caused by this mechanism, simple column experiments were carried out. A column, 64 mm in inner diameter and 240 mm in height, was prepared and was packed with 1mm diameter glass beads. Nitrogen gas containing 5 % CO2 and 5% He was supplied from the bottom of the column, and after the water in the column is approximately saturated with CO2, the sparging gas was changed to pure nitrogen. The CO2 and He concentrations in the effluent gas was monitored and recorded. As the result, we saw tailing: the double-log plots of the concentration vs. time relationship was practically linear, and the absolute value of the slope in the double-log charts were 1.28, 0.95 and 0.83 according to the gas flow rates of 40, 80 and 120 ml/min, respectively. Slope less than 1.00 showed that these tailings cannot be explained by Freundlich-type adsorption behavior. Model analysis showed that this power low time-concentration behavior with the slope of approximately -1.0 can be explained by the power law distribution of diffusion distance \\textit{a} with PDF p(\\textit{a}) proportional to \\textit{a}^{-1}.
Saichev, A.; Sornette, D.
2004-10-01
We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes ('aftershocks'). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake ('productivity' or 'fertility'), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities {mu} is characterized by a power law {approx}1/{mu}{sup 1+{gamma}} and the bare Omori law for the memory of previous triggering mothers decays slowly as {approx}1/t{sup 1+{theta}}, with 0<{theta}<1 relevant for earthquakes. Using the tool of generating probability functions and a quasistatic approximation which is shown to be exact asymptotically for large durations, we show that the density distribution of total aftershock lifetimes scales as {approx}1/t{sup 1+{theta}}{sup sol{gamma}} when the average branching ratio is critical (n=1). The coefficient 1<{gamma}=b/{alpha}<2 quantifies the interplay between the exponent b{approx_equal}1 of the Gutenberg-Richter magnitude distribution {approx}10{sup -bm} and the increase {approx}10{sup {alpha}}{sup m} of the number of aftershocks with mainshock magnitude m (productivity), with 0.5<{alpha}<1. The renormalization of the
Saichev, A; Sornette, D
2004-10-01
We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes ("aftershocks"). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake ("productivity" or "fertility"), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities mu is characterized by a power law approximately 1/ mu(1+gamma) and the bare Omori law for the memory of previous triggering mothers decays slowly as approximately 1/ t(1+theta;) , with 0
NASA Astrophysics Data System (ADS)
Wang, Li-Hua; Li, Ji-Tao; Li, Shao-Feng; Liu, Quan-Tao
2016-06-01
We study a (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation with different diffractions and power-law nonlinearity in PT-symmetric potentials. Considering different PT-symmetric potentials, we obtain two kinds of analytical sech-type localized soliton solutions. From these solutions, we analytically discuss the powers and power-flow densities. Moreover, we study compression and expansion of localized structures in the periodic distributed amplification system.
Power-law cross-correlations estimation under heavy tails
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2016-11-01
We examine the performance of six estimators of the power-law cross-correlations-the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator-under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the α-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.
There is More than a Power Law in Zipf
Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano
2012-01-01
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law. PMID:23139862
Consistency relation in power law G-inflation
Unnikrishnan, Sanil; Shankaranarayanan, S. E-mail: shanki@iisertvm.ac.in
2014-07-01
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 ≤ −8n{sub T}, where r is the tensor-to-scalar-ratio and n{sub T} 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/|n{sub T}| 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 > −8n{sub T} or r ≤ −8n{sub T} depending on the model parameters. However, the subluminal propagation of speed of scalar field perturbations, as required by causality, restricts r ≤ −(32/3) n{sub T}.
Diffusion-limited aggregation with power-law pinning.
Hentschel, H G E; Popescu, M N; Family, F
2004-01-01
Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth R(-gamma)(N) (where R(N) is the radius of the N-particle cluster). For gamma>1 the growth pattern is in the same universality class as diffusion limited aggregation (DLA), while for gamma<1 the resulting patterns have a lower fractal dimension D(gamma) than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at gamma=1/2, significantly smaller than might be expected from the lower bound alpha(min) approximately 0.67 of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for D(gamma) both close to the breakdown of DLA universality class, i.e., gamma less, similar 1, and close to the pinning transition, i.e., gamma greater, similar 1/2. PMID:14995617
Power-law forgetting in synapses with metaplasticity
NASA Astrophysics Data System (ADS)
Mehta, A.; Luck, J. M.
2011-09-01
The idea of using metaplastic synapses to incorporate the separate storage of long- and short-term memories via an array of hidden states was put forward in the cascade model of Fusi et al. In this paper, we devise and investigate two models of a metaplastic synapse based on these general principles. The main difference between the two models lies in their available mechanisms of decay, when a contrarian event occurs after the build-up of a long-term memory. In one case, this leads to the conversion of the long-term memory to a short-term memory of the opposite kind, while in the other, a long-term memory of the opposite kind may be generated as a result. Appropriately enough, the response of both models to short-term events is not affected by this difference in architecture. On the contrary, the transient response of both models, after long-term memories have been created by the passage of sustained signals, is rather different. The asymptotic behaviour of both models is, however, characterised by power-law forgetting with the same universal exponent.
Non-Newtonian Power-Law Fluid Flow over a Shrinking Sheet
NASA Astrophysics Data System (ADS)
Fang, Tie-Gang; Tao, Hua; Zhong, Yong-Fang
2012-11-01
The boundary layer flow of power-law fluids over a shrinking sheet with mass transfer is revisited. Closed-form analytical solutions are found and presented for special cases. One of the presented solutions has an algebraic decay behavior. These analytical solutions might offer valuable insight into the nonlinear boundary layer flow for power-law fluids.
Power-law tail probabilities of drainage areas in river basins
Veitzer, S.A.; Troutman, B.M.; Gupta, V.K.
2003-01-01
The significance of power-law tail probabilities of drainage areas in river basins was discussed. The convergence to a power law was not observed for all underlying distributions, but for a large class of statistical distributions with specific limiting properties. The article also discussed about the scaling properties of topologic and geometric network properties in river basins.
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2015-03-01
The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).
Numerical tools for obtaining power-law representations of heavy-tailed datasets
NASA Astrophysics Data System (ADS)
Mansfield, Marc L.
2016-01-01
Many empirical datasets have highly skewed, non-Gaussian, heavy-tailed distributions, dominated by a relatively small number of data points at the high end of the distribution. Consistent with their role as stable distributions, power laws have frequently been proposed to model such datasets. However there are physical situations that require distributions with finite means. Such situations may call for power laws with high-end cutoffs. Here, I present a maximum-likelihood technique for determining an optimal cut-off power law to represent a given dataset. I also develop a new statistical test of the quality of fit. Results are demonstrated for a number of benchmark datasets. Non-power-law datasets can frequently be represented by power laws, but this is a trivial result unless the dataset spans a broad domain. Nevertheless, I demonstrate that there are non-power-law distributions, including broad log-normal distributions, whose tails can be fit to power laws over many orders of magnitude. Therefore, caution is called for whenever power laws are invoked to represent empirical data. Supplementary material in the form of one pdf file available from the Journal web page at: http://dx.doi.org/10.1140/epjb/e2015-60452-3
NASA Astrophysics Data System (ADS)
Eadie, Chris; Favis-Mortlock, David
2010-05-01
The choice of which statistical distribution to fit to historical discharge data is critical when attempting to predict the most extreme flows. It has been shown that depending upon the distribution selected, the calculated return periods can vary dramatically. Cunnane (1985) discussed the factors affecting the choice of distribution for river flow series data, and was able to show that small differences in the Extreme Value Type 1 (Gumbel), Type 2, and Type 3 can lead to large differences in the predicted return period. Indeed this divergence increases as the return period becomes larger: a finding which has obvious implications for fluvial management. Despite this, in many studies which fit a frequency-magnitude distribution to fluvial discharge data, the choice of distribution appears driven by regional convention, or even by some other apparently arbitrary factor. Benson (1968) analysed data for ten US stations, and compared the fit using the log-normal, gamma, Gumbel, log-Gumbel, Hazen and log-Pearson type 3 distributions. On the basis of this study alone, the standard approach to flow frequency estimation in the USA became the fitting of a log-Pearson type 3 (LP3) distribution (US Water Resources Council, 1982). While several other countries have adopted a similar approach, usage of the LP3 distribution is not geographically universal. Hydrologists in the United Kingdom conventionally utilise a fitted generalised logistic distribution for flow frequency estimation (Robson and Reed, 1999) while Chinese hydrologists utilise the log-normal distribution (Singh, 2002). Choice of fitted distribution is obviously crucial, since selecting one distribution rather than another will change the estimated probabilities of future droughts and floods, particularly the largest and rarest events. Malamud et al. (1996) showed that a flood of equivalent size to that experienced on the Mississippi in 1993 has a recurrence interval on the order of 100 years when a power-law
On the structure and phase transitions of power-law Poissonian ensembles
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Oshanin, Gleb
2012-10-01
Power-law Poissonian ensembles are Poisson processes that are defined on the positive half-line, and that are governed by power-law intensities. Power-law Poissonian ensembles are stochastic objects of fundamental significance; they uniquely display an array of fractal features and they uniquely generate a span of important applications. In this paper we apply three different methods—oligarchic analysis, Lorenzian analysis and heterogeneity analysis—to explore power-law Poissonian ensembles. The amalgamation of these analyses, combined with the topology of power-law Poissonian ensembles, establishes a detailed and multi-faceted picture of the statistical structure and the statistical phase transitions of these elemental ensembles.
NASA Astrophysics Data System (ADS)
Echeverria, J. C.; Rodriguez, E.; Aguilar-Cornejo, M.; Alvarez-Ramirez, J.
2016-10-01
In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
Do wealth distributions follow power laws? Evidence from ‘rich lists’
NASA Astrophysics Data System (ADS)
Brzezinski, Michal
2014-07-01
We use data on the wealth of the richest persons taken from the ‘rich lists’ provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world’s richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012, and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.
Power-Law Template for IR Point Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglass; Spergel, David N.; Staggs,Suzanne T.; Wollack, Edward
2011-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Major power law slip-weakening in laboratory gouge friction
NASA Astrophysics Data System (ADS)
Chambon, G.; Schmittbuhl, J.; Corfdir, A.
2003-04-01
We performed gouge-shearing experiments in a large-displacement ring-shear apparatus. The granular gouge (quartz sand) undergoes significant slip-weakening over seismic-like distances (0.5 m) and minor velocity-weakening over microscopic length scales (100 μm). The reproducible decrease of gouge effective friction μ with shear displacement δ follows a power law: μ = μ_0 + A δ-β, with β = 0.4. Such a slip-weakening process can be accounted for in an extended rate- and state-dependent friction law through a supplementary state variable. However, unlike classical state variables, the evolution law governing this new variable does not involve any characteristic length scale. Accordingly, slip-weakening is found independent of gouge grain size. Careful checks were performed to insure that observed weakening constitutes a real rheological property of the gouge. Moreover, microscopic origin of the slip-weakening has been investigated by means of a Correlation Image Velocimetry (CIV) technique applied to digital pictures of the sample. Most of the deformation appears localized in a 7 grain-wide, comminuted shear band. Nevertheless, CIV also reveals an intermittent, ongoing deformation outside this zone, whose magnitude slowly diminishes as shear displacement increases. This microscopic relaxation denotes a progressive decoupling between the shear zone and the bulk of the sample. Slow decrease of spatially-averaged shear strain <~ngleγrangle is well modeled by a hyperbolic law in displacement δ, without any characteristic length scale: <~ngleγrangle = γ_0 + a δ-1. We interpret the macroscopic slip-weakening as a consequence of the observed decoupling at micro-scale. When extrapolated to faults, this result shows that decimetric weakening distances, frequently reported during earthquakes, can be produced by complex structuring processes inside the gouge layer.
Power-Law Template for Infrared Point-Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark J.; Halpern, Mark; Hincks, Adam D; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglas; Spergel, David N.; Staggs, Suzanne T.; Wollack, Edward
2012-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ?(sup Beta)B(?, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Das, Sudeep; Hincks, Adam D.; Page, Lyman A.; Staggs, Suzanne T.; Viero, Marco; Bond, J. Richard; Devlin, Mark J.; Reese, Erik D.; Halpern, Mark; Scott, Douglas; Hlozek, Renee; Marriage, Tobias A.; Spergel, David N.; Moodley, Kavilan; Wollack, Edward
2012-06-20
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 {approx}< l {approx}< 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 {mu}m; 1000 {approx}< l {approx}< 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C{sup clust}{sub l}{proportional_to}l{sup -n} with n = 1.25 {+-} 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, {nu}{sup {beta}} B({nu}, T{sub eff}), with a single emissivity index {beta} = 2.20 {+-} 0.07 and effective temperature T{sub eff} = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be {alpha}{sub 150-220} = 3.68 {+-} 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Banerjee, Gadadhar; Maitra, Sarit
2015-04-15
Sagdeev's pseudopotential method is used to study small as well as arbitrary amplitude dust acoustic solitons in a dusty plasma with kappa distributed electrons and ions with dust grains having power law size distribution. The existence of potential well solitons has been shown for suitable parametric region. The criterion for existence of soliton is derived in terms of upper and lower limit for Mach numbers. The numerical results show that the size distribution can affect the existence as well as the propagation characteristics of the dust acoustic solitons. The effect of kappa distribution is also highlighted.
NASA Astrophysics Data System (ADS)
Wang, Jianhui; Ma, Yongli; He, Jizhou
2015-07-01
Based on quantum thermodynamic processes, we make a quantum-mechanical (QM) extension of the typical heat engine cycles, such as the Carnot, Brayton, Otto, Diesel cycles, etc., with no introduction of the concept of temperature. When these QM engine cycles are implemented by an ideal gas confined in an arbitrary power-law trap, a relation between the quantum adiabatic exponent and trap exponent is found. The differences and similarities between the efficiency of a given QM engine cycle and its classical counterpart are revealed and discussed.
Simple inflationary quintessential model. II. Power law potentials
NASA Astrophysics Data System (ADS)
de Haro, Jaume; Amorós, Jaume; Pan, Supriya
2016-09-01
The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive
Scale Invariance in Landscape Evolution Models Using Stream Power Laws
NASA Astrophysics Data System (ADS)
Kwang, J. S.; Parker, G.
2014-12-01
Landscape evolution models (LEM) commonly utilize stream power laws to simulate river incision with formulations such as E = KAmSn, where E is a vertical incision rate [L/T], K is an erodibility constant [L1-2m/T], A is an upstream drainage area [L2], S is a local channel gradient [-], and m and n are positive exponents that describe the basin hydrology. In our reduced complexity model, the landscape approached equilibrium by balancing an incision rate with a constant, uniform, vertical rock uplift rate at every location in the landscape. From our simulations, for a combination of m and n, the landscape exhibited scale invariance. That is, regardless of the size and scale of the basin, the relief and vertical structure of the landscape remained constant. Therefore, the relief and elevation profile of the landscape at equilibrium were only dependent on the coefficients for erodibility and uplift and an equation that described how upstream area, A, increased as the length of a stream increased. In our analytical 1D models, we utilized two equations that described upslope area, (a) A = Bl, where B is the profile width [L], and l is the stream length from the ridge [L] and (b) A = Clh, Hack's Law, where C is a constant [L2-h] and h is a positive exponent. With these equations, (a) m = n and (b) hm = n resulted in scale invariance. In our numerical 2D models, the relationship between A and l was inherent in the actual structure of the drainage network. From our numerical 2D results, scale invariance occurred when 2m = n. Additionally, using reasonable values from the literature for exponents, n, m and h, resulted in singularities at the ridges in the landscape, which caused truncation error. In consequence, the elevation of the ridge increased as the number of grid cells in the domain increased in the numerical model, and the model was unable to converge. These singularities at the ridges appeared when (a) m ≥ n and (b) hm ≥ n in the analytical model and 2m ≥ n in
The double power law in human collaboration behavior: The case of Wikipedia
NASA Astrophysics Data System (ADS)
Kwon, Okyu; Son, Woo-Sik; Jung, Woo-Sung
2016-11-01
We study human behavior in terms of the inter-event time distribution of revision behavior on Wikipedia, an online collaborative encyclopedia. We observe a double power law distribution for the inter-editing behavior at the population level and a single power law distribution at the individual level. Although interactions between users are indirect or moderate on Wikipedia, we determine that the synchronized editing behavior among users plays a key role in determining the slope of the tail of the double power law distribution.
Two universal physical principles shape the power-law statistics of real-world networks.
Lorimer, Tom; Gomez, Florian; Stoop, Ruedi
2015-01-01
The study of complex networks has pursued an understanding of macroscopic behaviour by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex network generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State
NASA Astrophysics Data System (ADS)
Stoop, Ruedi; Gomez, Florian
2016-07-01
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
On the origin of power-law X-ray spectra of active galactic nuclei
NASA Technical Reports Server (NTRS)
Schlosman, I.; Shaham, J.; Shaviv, G.
1984-01-01
In the present analytical model for a power law X-ray continuum production in active galactic nuclei, the dissipation of turbulent energy flux above the accretion disk forms an optically thin transition layer with an inverted temperature gradient. The emitted thermal radiation has a power law spectrum in the 0.1-100 keV range, with a photon energy spectral index gamma of about 0.4-1.0. Thermal X-ray contribution from the layer is 5-10 percent of the total disk luminosity. The gamma value of 0.75 is suggested as a 'natural' power law index for Seyfert galaxies and QSOs.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State.
Stoop, Ruedi; Gomez, Florian
2016-07-15
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
Blinking in quantum dots: The origin of the grey state and power law statistics.
Ye, Mao; Searson, Peter C
2011-09-16
Quantum dot (QD) blinking is characterized by switching between an "on" state and an "off" state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
Blinking in quantum dots: The origin of the grey state and power law statistics
NASA Astrophysics Data System (ADS)
Ye, Mao; Searson, Peter C.
2011-09-01
Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State.
Stoop, Ruedi; Gomez, Florian
2016-07-15
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information. PMID:27472144
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
Oliveira, Gilson F. de Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de
2014-03-15
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.
Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems
NASA Astrophysics Data System (ADS)
Rodin, Aleksandr; Fogler, Michael
2011-03-01
Observation of power-law dependence of conductance on temperature and voltage has been reported for a wide variety of low-dimensional systems(nano-wires, nano-tubes, and conducting polymers). This behavior has been attributed to the Luttinger liquid effects expected in a pure one-dimensional wire. However, the systems studied were neither one-dimensional nor defect-free. Using numerical simulations we show that the power-law behavior can arise from variable-range hopping in an ensemble of non-interacting disordered wires connected in parallel. This power-law behavior holds in restricted ranges of voltage and temperature, typical of experimental situations. Physically, it comes from rare, but highly conducting hopping paths that appear by chance in some members of the ensemble. The power-law exponents and their dependence on system parameters are consistent with the great majority of available empirical data. Supported by Grant NSF DMR-0706654.
Research on power-law acoustic transient signal detection based on wavelet transform
NASA Astrophysics Data System (ADS)
Han, Jian-hui; Yang, Ri-jie; Wang, Wei
2007-11-01
Aiming at the characteristics of acoustic transient signal emitted from antisubmarine weapon which is being dropped into water (torpedo, aerial sonobuoy and rocket assisted depth charge etc.), such as short duration, low SNR, abruptness and instability, based on traditional power-law detector, a new method to detect acoustic transient signal is proposed. Firstly wavelet transform is used to de-noise signal, removes random spectrum components and improves SNR. Then Power- Law detector is adopted to detect transient signal. The simulation results show the method can effectively extract envelop characteristic of transient signal on the condition of low SNR. The performance of WT-Power-Law markedly outgoes that of traditional Power-Law detection method.
Exploring the effect of power law social popularity on language evolution.
Gong, Tao; Shuai, Lan
2014-01-01
We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model
Teka, Wondimu; Stockton, David; Santamaria, Fidel
2016-01-01
We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron. PMID:26937967
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.
Teka, Wondimu; Stockton, David; Santamaria, Fidel
2016-03-01
We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.
Tang, Jau; Marcus, R A
2005-09-01
A mechanism involving diffusion-controlled electron transfer processes in Debye and non-Debye dielectric media is proposed to elucidate the power-law distribution for the lifetime of a blinking quantum dot. This model leads to two complementary regimes of power law with a sum of the exponents equal to 2, and to a specific value for the exponent in terms of a distribution of the diffusion correlation times. It also links the exponential bending tail with energetic and kinetic parameters.
Power-law modeling based on least-squares minimization criteria.
Hernández-Bermejo, B; Fairén, V; Sorribas, A
1999-10-01
The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system.
Steady flow of a power-law non-Newtonian fluid across an unconfined square cylinder
NASA Astrophysics Data System (ADS)
Pantokratoras, A.
2016-03-01
A two-dimensional flow of a non-Newtonian power-law fluid directed normally to a horizontal cylinder with a square cross section is considered in the present paper. The problem is investigated numerically with a finite volume method by using the commercial code Ansys Fluent with a very large computational domain so that the flow could be considered unbounded. The investigation covers the power-law index from 0.1 to 2.0 and the Reynolds number range from 0.001 to 45.000. It is found that the drag coefficient for low Reynolds numbers and low power-law index ( n ≤ 0.5) obeys the relationship C D = A/Re. An equation for the quantity A as a function of the power-law index is derived. The drag coefficient becomes almost independent of the power-law index at high Reynolds numbers and the wake length changes nonlinearly with the Reynolds number and power-law index.
Power law scaling in synchronization of brain signals depends on cognitive load
Tinker, Jesse; Velazquez, Jose Luis Perez
2014-01-01
As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors. PMID:24822039
Power law scaling in synchronization of brain signals depends on cognitive load.
Tinker, Jesse; Velazquez, Jose Luis Perez
2014-01-01
As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors.
Constraints on the tensor-to-scalar ratio for non-power-law models
NASA Astrophysics Data System (ADS)
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M. P.
2013-08-01
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: rLD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
Gutiérrez, Ricardo; Garrahan, Juan P; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity. PMID:26764669
Constraints on the tensor-to-scalar ratio for non-power-law models
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M.P. E-mail: mb435@mrao.cam.ac.uk E-mail: mph@mrao.cam.ac.uk
2013-08-01
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby 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.
NASA Astrophysics Data System (ADS)
Park, Simsoo; Lee, Dong-Ryul
2003-09-01
Numerical solutions are presented for fully developed laminar flow for a modified power law fluid (MPL) in a rectangular duct. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian behavior at low shear rates, through a transition region, to power law behavior at higher shear rates. The analysis identified a dimensionless shear rate parameter which, for a given set of operating conditions, specifies where in the shear rate range a particular system is operating, i.e. in the Newtonian, transition, or power law regions. The numerical results of the friction factor times Reynolds number for the Newtonian and power law region are compared with previously published results showing agreement within 0.05% in the Newtonian region, and 0.9% and 5.1% in the power law region. Rheological flow curves were measured for three CMC-7H4 solutions and were found to be well represented by the MPL constitutive equation. The friction factor times Reynolds number values were measured in the transition region for which previous measurements were unavailable. Good agreement was found between experiment and calculation thus confirming the validity of the analysis.
Double Power Laws in the Event-integrated Solar Energetic Particle Spectrum
NASA Astrophysics Data System (ADS)
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K.
2016-04-01
A double power law or a power law with exponential rollover at a few to tens of MeV nucleon-1 of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochastic approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon-1 is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.
Predicting the long tail of book sales: Unearthing the power-law exponent
NASA Astrophysics Data System (ADS)
Fenner, Trevor; Levene, Mark; Loizou, George
2010-06-01
The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.
Study on local resistance of non-Newtonian power law fluid in elbow pipes
NASA Astrophysics Data System (ADS)
Zhang, Hao; Xu, Tiantian; Zhang, Xinxin; Wang, Yuxiang; Wang, Yuancheng; Liu, Xueting
2016-06-01
This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved 90° bend pipe with circular cross-sections, which are widely used in industrial applications. By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained. To explore the change rule the experiment is carried out by changing the Reynolds number, the wall roughness and different diameter ratio of elbow pipe. The variation of the local resistance coefficient with the Reynolds number, the diameter ratio and the wall roughness is presented comprehensively in the paper. The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid; the wall roughness has a significant impact on the local resistance coefficient. As the pipe wall roughness increasing, the coefficient of local resistance force will increase. The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow, which increases the kinetic energy dissipation of the main flow. This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.
Power-law defect energy in a single-crystal gradient plasticity framework: a computational study
NASA Astrophysics Data System (ADS)
Bayerschen, E.; Böhlke, T.
2016-07-01
A single-crystal gradient plasticity model is presented that includes a power-law type defect energy depending on the gradient of an equivalent plastic strain. Numerical regularization for the case of vanishing gradients is employed in the finite element discretization of the theory. Three exemplary choices of the defect energy exponent are compared in finite element simulations of elastic-plastic tricrystals under tensile loading. The influence of the power-law exponent is discussed related to the distribution of gradients and in regard to size effects. In addition, an analytical solution is presented for the single slip case supporting the numerical results. The influence of the power-law exponent is contrasted to the influence of the normalization constant.
Power-law decay of the view times of scientific courses on YouTube
NASA Astrophysics Data System (ADS)
Gao, Lingling
2012-11-01
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.
Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Rashid, Madiha; Imtiaz, Maria; Alsaedi, Ahmed
2015-11-01
This paper deals with the boundary layer flow of nanofluid over power-law stretched surface. Analysis has been carried out in the presence of applied magnetic field and chemical reaction. Heat and mass transfer characteristics are studied using heat and mass convective conditions. The governing partial differential equations are transferred to the nonlinear ordinary differential equations. Convergent series solutions are obtained for fluid velocity, temperature and concentrations fields. Influences of pertinent parameters including Hartman number, thermal and concentration Biot numbers and chemical reaction parameters are discussed on the velocity, temperature and concentration profiles. Graphical result are presented and discussed. Computations for local Nusselt and Sherwood numbers are carried out. It is observed that the heat transfer rate is enhanced by increasing power-law index, thermal Biot number and chemical reaction parameter while mass transfer rate increases for power-law index and chemical reaction parameter.
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
Eliazar, Iddo
2015-04-15
Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.
Pascal (Yang Hui) triangles and power laws in the logistic map
NASA Astrophysics Data System (ADS)
Velarde, Carlos; Robledo, Alberto
2015-04-01
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic-band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.
Power-law X-ray and gamma-ray emission from relativistic thermal plasmas
NASA Technical Reports Server (NTRS)
Zdziarski, A. A.
1985-01-01
A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
The fractal nature of nature: power laws, ecological complexity and biodiversity.
Brown, James H; Gupta, Vijay K; Li, Bai-Lian; Milne, Bruce T; Restrepo, Carla; West, Geoffrey B
2002-01-01
Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science. PMID:12079523
NASA Astrophysics Data System (ADS)
Tippett, Michael K.; Cohen, Joel E.
2016-02-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from `outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.
Heat transfer analysis in an annular cone subjected to power law variations
NASA Astrophysics Data System (ADS)
Salman Ahmed, N. J.; Al-Rashed, Abdullah A. A. A.; Yunus Khan, T. M.; Kamangar, Sarfaraz; Athani, Abdulgaphur; Anjum Badruddin, Irfan
2016-09-01
Present study deals with the analysis of heat transfer and fluid flow behavior in an annular cone fixed with saturated porous medium. The inner surface of the cone is assumed to have power law variable wall temperature. The governing partial differential equations are solved using well known Finite Element Method (FEM). The coupled nonlinear differential equations are converted into the algebraic equations by using Galerkin method. A 3 noded triangular element is used to divide the porous domain into smaller segments. The effects of various geometrical parameters on the cone angle are presented. It is found that the effect of cone angle on the heat transfer characteristics and fluid flow behavior is considerably significant. The fluid moment is found to shift towards the upper side of cone with increase in the power law coefficient. The fluid velocity decreases with increase in the power law coefficient.
Tanner's simple model of crystallization for power-law fluids extended
NASA Astrophysics Data System (ADS)
Mitsoulis, E.; Zisis, Th.
2014-05-01
Tanner et al. (Rheol. Acta, 48, 2009, 499-507) presented a simple model for power-law fluids in which it was possible to derive semi-analytical solutions based on some key simplifying assumptions. These include shear flows in tubes and channels, a 'step function' or 'amorphous-frozen' model of the viscosity changes due to crystallization, and a power-law index of 1/3 valid for a crystallizing poly(butene-1) polymer for which experiments were available. Their work compared favorably with experimental data for the onset of crystallization times. In the present work, we have repeated and verified the Tanner model and extended it to power-law indices from 1 (Newtonian behavior) down to 0 (extreme shear thinning) in order to study the effect of the different problem parameters and place a set of results that will act as reference for future and more detailed computational calculations through the Finite Element Method.
Thermodynamics of Ideal Bose Gas Under Generic Power Law Potential in d-dimensions
NASA Astrophysics Data System (ADS)
Faruk, M. M.
Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.
Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays
NASA Astrophysics Data System (ADS)
Sibatov, R. T.
2011-08-01
A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.
Phase diagram of power law and Lennard-Jones systems: crystal phases.
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed. PMID:25362319
Tippett, Michael K; Cohen, Joel E
2016-02-29
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.
Fouka, M.; Ouichaoui, S. E-mail: souichaoui@usthb.dz
2011-12-10
We have derived asymptotic forms for the degree of polarization of the optically thin synchrotron and for synchrotron self-absorption (SSA) spectra assuming a power-law particle distribution of the form N({gamma}) {approx} {gamma}{sup -p} with {gamma}{sub 1} < {gamma} < {gamma}{sub 2}, especially for a finite high-energy limit, {gamma}{sub 2}, in the case of an arbitrary pitch angle. The new results inferred concern more especially the high-frequency range x >> {eta}{sup 2} with parameter {eta} = {gamma}{sub 2}/{gamma}{sub 1}. The calculated SSA spectra concern instantaneous photon emission where cooling effects are not considered. They have been obtained by also ignoring likely effects such as Comptonization, pair creation and annihilation, as well as magnetic photon splitting. To that aim, in addition to the two usual absorption frequencies, a third possible one has been derived and expressed in terms of the Lambert W function based on the analytical asymptotic form of the absorption coefficient, {alpha}{sub {nu}}, for the high-frequency range {nu} >> {nu}{sub 2} (with {nu}{sub 2} the synchrotron frequency corresponding to {gamma}{sub 2}). We have shown that the latter frequency may not have realistic applications in astrophysics, except in the case of an adequate set of parameters allowing one to neglect Comptonization effects. More detailed calculations and discussions are presented.
Power Law Inflation and the Cosmic No Hair Theorem in Brane World
Paul, B. C.; Beesham, A.
2006-11-03
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.
Gelled propellant flow: Boundary layer theory for power-law fluids in a converging planar channel
NASA Astrophysics Data System (ADS)
Kraynik, Andrew M.; Geller, A. S.; Glick, J. H.
1989-10-01
A boundary layer theory for the flow of power-law fluids in a converging planar channel has been developed. This theory suggests a Reynolds number for such flows, and following numerical integration, a boundary layer thickness. This boundary layer thickness has been used in the generation of a finite element mesh for the finite element code FIDAP. FIDAP was then used to simulate the flow of power-law fluids through a converging channel. Comparison of the analytic and finite element results shows the two to be in very good agreement in regions where entrance and exit effects (not considered in the boundary layer theory) can be neglected.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; Nalewajko, K.; Begelman, M. C.
2015-12-30
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron–positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power law ${\\gamma }^{-\\alpha }$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.
Transport coefficients in Lorentz plasmas with the power-law kappa-distribution
Jiulin, Du
2013-09-15
Transport coefficients in Lorentz plasma with the power-law κ-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient, and thermal conductivity for the power-law κ-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the κ-parameter, and in the limit of the parameter κ→∞ they are reduced to the standard forms for a Maxwellian distribution.
Schlueter, E.M.; Zimmerman, R.W.; Cook, N.G.W.; Witherspoon, P.A.
1994-12-31
Perimeter-area power-law relationships of pores in five sedimentary rocks are determined from scanning electron photomicrographs of thin sections. These relationships for the pores of four sandstones were found to lie between 1.43 and 1.49, while that of an Indiana limestone was found to be 1.67. The authors discuss how the perimeter-area power-law relationship of pores, along with a pore-size distribution, can be used to estimate the hydraulic permeability.
Input-anticipating critical reservoirs show power law forgetting of unexpected input events.
Mayer, Norbert Michael
2015-05-01
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.
NASA Astrophysics Data System (ADS)
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; Nalewajko, K.; Begelman, M. C.
2016-01-01
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron-positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power law {γ }-α , with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. For large L and σ, the power-law index α approaches about 1.2.
Numerical Simulations of Power Law Heating Functions for Quiescent Loops: Stability and Observables
NASA Astrophysics Data System (ADS)
Martens, P. C.; Winter, H. D.; Munetsi-Mugomba, K.
2007-12-01
We present the numerical simulations of quiescent coronal loops with heating functions that are power law functions of pressure and temperature. These simulations are made using a time-dependent, 1D hydrodynamics code with heating functions that are treated as dynamic variables which are constantly re- evaluated during the loops' lifetimes. These numerical simulations provide a stability test for the analytical solutions formulated by Martens (2007, submitted) for the same heating functions. TRACE and XRT datasets are simulated to determine if present observables can provide adequate information to discriminate between power law heating functions.
NASA Astrophysics Data System (ADS)
Mitchell, David L.
1996-06-01
Based on boundary layer theory and a comparison of empirical power laws relating the Reynolds and Best numbers, it was apparent that the primary variables governing a hydrometeor's terminal velocity were its mass, its area projected to the flow, and its maximum dimension. The dependence of terminal velocities on surface roughness appeared secondary, with surface roughness apparently changing significantly only during phase changes (i.e., ice to liquid). In the theoretical analysis, a new, comprehensive expression for the drag force, which is valid for both inertial and viscous-dominated flow, was derived.A hydrometeor's mass and projected area were simply and accurately represented in terms of its maximum dimension by using dimensional power laws. Hydrometeor terminal velocities were calculated by using mass- and area-dimensional power laws to parameterize the Best number, X. Using a theoretical relationship general for all particle types, the Reynolds number, Re, was then calculated from the Best number. Terminal velocities were calculated from Re.Alternatively, four Re-X power-law expressions were extracted from the theoretical Re-X relationship. These expressions collectively describe the terminal velocities of all ice particle types. These were parameterized using mass- and area-dimensional power laws, yielding four theoretically based power-law expressions predicting fall speeds in terms of ice particle maximum dimension. When parameterized for a given ice particle type, the theoretical fall speed power law can be compared directly with empirical fall speed-dimensional power laws in the literature for the appropriate Re range. This provides a means of comparing theory with observations.Terminal velocities predicted by this method were compared with fall speeds given by empirical fall speed expressions for the same ice particle type, which were curve fits to measured fall speeds. Such comparisons were done for nine types of ice particles. Fall speeds predicted
Modified power law equations for vertical wind profiles. [in investigation of windpower plant siting
NASA Technical Reports Server (NTRS)
Spera, D. A.; Richards, T. R.
1979-01-01
In an investigation of windpower plant siting, equations are presented and evaluated for a wind profile model which incorporates both roughness and wind speed effects, while retaining the basic simplicity of the Hellman power law. These equations recognize the statistical nature of wind profiles and are compatible with existing analytical models and recent wind profile data. Predictions of energy output based on the proposed profile equations are 10% to 20% higher than those made with the 1/7 power law. In addition, correlation between calculated and observed blade loads is significantly better at higher wind speeds when the proposed wind profile model is used than when a constant power model is used.
Arbitrary Metrics in Psychology
ERIC Educational Resources Information Center
Blanton, Hart; Jaccard, James
2006-01-01
Many psychological tests have arbitrary metrics but are appropriate for testing psychological theories. Metric arbitrariness is a concern, however, when researchers wish to draw inferences about the true, absolute standing of a group or individual on the latent psychological dimension being measured. The authors illustrate this in the context of 2…
Exponential and power-law contact distributions represent different atmospheric conditions.
Reynolds, A M
2011-12-01
It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions.
Fingering instability in the flow of a power-law fluid on a rotating disc
NASA Astrophysics Data System (ADS)
Arora, Akash; Doshi, Pankaj
2016-01-01
A computational study of the flow of a non-Newtonian power law fluid on a spinning disc is considered here. The main goal of this work is to examine the effect of non-Newtonian nature of the fluid on the flow development and associated contact line instability. The governing mass and momentum balance equations are simplified using the lubrication theory. The resulting model equation is a fourth order non-linear PDE which describes the spatial and temporal evolutions of film thickness. The movement of the contact line is modeled using a constant angle slip model. To solve this moving boundary problem, a numerical method is developed using a Galerkin/finite element method based approach. The numerical results show that the spreading rate of the fluid strongly depends on power law exponent n. It increases with the increase in the shear thinning character of the fluid (n < 1) and decreases with the increase in shear thickening nature of the fluid (n > 1). It is also observed that the capillary ridge becomes sharper with the value of n. In order to examine the stability of these ridges, a linear stability theory is also developed for these power law fluids. The dispersion relationship depicting the growth rate for a given wave number has been reported and compared for different power-law fluids. It is found that the growth rate of the instability decreases as the fluid becomes more shear thinning in nature, whereas it increases for more shear thickening fluids.
NASA Astrophysics Data System (ADS)
Carrano, Charles S.; Rino, Charles L.
2016-06-01
We extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two-component inverse power law spectrum. The two-component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two-dimensional field-aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self-similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large- and small-scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
ERIC Educational Resources Information Center
Thelwall, Mike; Wilkinson, David
2003-01-01
Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)
The effect of a power-law mantle viscosity on trench retreat rate
NASA Astrophysics Data System (ADS)
Holt, Adam F.; Becker, Thorsten W.
2016-10-01
The subduction of lithospheric plates is partitioned between subducting plate motion and lateral slab migration (i.e., trench retreat and advance). We use 3-D, dynamic models of subduction to address the role of a power-law mantle viscosity on subduction dynamics and, in particular, rates of trench retreat. For all numerical models tested, we find that a power-law rheology results in reduced rates of trench retreat, and elevated slab dip angles, relative to the equivalent isoviscous mantle model. We analyze the asthenospheric pressure distribution and the style of mantle flow, which exhibits only limited variability as a function of mantle rheology, in order to compute estimates of the mantle forces associated with subduction. The inclusion of a power-law rheology reduces the mantle shear force (which resists subducting plate motion) to a greater degree than it reduces the dynamic pressure gradient across the slab (which resists trench retreat). Therefore, the inclusion of a power-law mantle rheology favors a shift towards a subduction mode with a reduced trench retreat component, typically a relative reduction of order 25% in our 3-D models. We suggest that this mechanism may be of importance for reducing the high trench retreat rates observed in many previous models to levels more in line with the average subduction partitioning observed on Earth at present (i.e., trench velocity ≤ plate velocity), for most absolute plate motion reference frames.
Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?
ERIC Educational Resources Information Center
Bauer, Ben
2009-01-01
Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less…
Realization of power law inflation & variants via variation of the strong coupling constant
NASA Astrophysics Data System (ADS)
AlHallak, M.; Chamoun, N.
2016-09-01
We present a model of power law inflation generated by variation of the strong coupling constant. We then extend the model to two varying coupling constants which leads to a potential consisting of a linear combination of exponential terms. Some variants of the latter may be self-consistent and can accommodate the experimental data of the Planck 2015 and other recent experiments.
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Channel geometry and hydraulic characteristics of a given river network, i.e., spatio-temporal variability of width, depth, and velocity, can be described as power functional relationships of flow discharge, named 'hydraulic geometry' (Leopold and Maddock, 1953). Many studies have focused on the implication of this power-law itself, i.e., self-similarity, and accordingly its exponents. Coefficients of the power functional relationships, on the contrary, have received little attention. They are often regarded as empirical constants, determined by 'best fitting' to the power-law without significant scientific implications. Here, we investigate and claim that power-law coefficients of hydraulic geometry relationships carry vital information of a given river system. We approach the given problem on the basis of 'basin hydraulic geometry' formulation (Stall and Fok, 1968) which decomposes power-law coefficients into more elementary constants. The linkage between classical power-law relationship (Leopold and Maddock, 1953) and the basin hydraulic geometry is provided by Paik and Kumar (2004). On the basis of this earlier study, it can be shown that coefficients and exponents of power-law hydraulic geometry are interrelated. In this sense, we argue that more elementary constants that constitute both exponents and coefficients carry important messages. In this presentation, we will demonstrate how these elementary constants vary over a wide range of catchments provided from Stall and Fok (1968) and Stall and Yang (1970). Findings of this study can provide new insights on fundamental understanding about hydraulic geometry relationships. Further, we expect that this understanding can help interpretation of hydraulic geometry relationship in the context of flood propagation through a river system as well. Keywords: Hydraulic geometry; Power-law; River network References Leopold, L. B., & Maddock, T. J. (1953). The hydraulic geometry of stream channels and some physiographic
New version of PLNoise: a package for exact numerical simulation of power-law noises
NASA Astrophysics Data System (ADS)
Milotti, Edoardo
2007-08-01
In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0<α⩽2. Here I extend the algorithm to generate 1/f noises with 2<α⩽4 (black noises). The method is exact in the sense that it produces a sampled process with a theoretically guaranteed range-limited power-law spectrum for any arbitrary sequence of sampling intervals, i.e. the sampling times may be unevenly spaced. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v2_0.html Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press
Power-law ansatz in complex systems: Excessive loss of information.
Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming
2015-12-01
The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring. PMID:26764792
Power-law ansatz in complex systems: Excessive loss of information.
Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming
2015-12-01
The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring.
Power-law ansatz in complex systems: Excessive loss of information
NASA Astrophysics Data System (ADS)
Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming
2015-12-01
The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring.
Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.
Casals, Marc; Ottewill, Adrian
2012-09-14
Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.
Deposition from evaporating drops: Power laws and new morphologies in coffee stains
NASA Astrophysics Data System (ADS)
Freed-Brown, Julian E.
We investigate the structure of stains formed through evaporative deposition in sessile drops. Commonly, the deposited stain has a high surface density near the three phase contact line of the drying drop and much less solute in the bulk of the drop. This is known as the ``coffee ring effect'' and primarily arises due to contact line pinning. While many features of the stain depend on subtle physical phenomena within the drop, the coffee ring effect stands out as a robust feature that persists in many varied experimental realizations. In 2009, Witten predicted another robust feature of deposited stains: an asymptotic regime where a robust power law governs the fadeout profile of the stain into the interior of the drop. This power law is only controlled by geometric properties at a single point and the power does not vary along the contact line. We investigate the approach to this power law using numerical methods. For many evaporation profiles (including common experimental ones) the numerics show good agreement with the power law prediction. However, we demonstrate an intuitive scheme to construct evaporation profiles that subvert the power law prediction. We find that, in general, the approach to the power law cannot be known without full knowledge of the evaporation and height profile. We also extend this work in another way. We apply the basic arguments of the coffee ring effect to the case where the drop has a receding contact line. Here, we develop a new theoretical framework for deposition that has not previously been studied. In this context, the surface density profile can be directly calculated. Unlike a pinned contact line, receding contact lines push fluid into the interior of the drop. This effect can be overcome by strong evaporation near the contact line, but in general the intuition from contact line pinning is reversed. Following Witten's example, we find that the surface density of the stain near the center of the drop goes as eta ∝ rnu, where
NASA Astrophysics Data System (ADS)
Brook, Martin; Hebblewhite, Bruce; Mitra, Rudrajit
2016-04-01
The size-scaling of rock fractures is a well-studied problem in geology, especially for permeability quantification. The intensity of fractures may control the economic exploitation of fractured reservoirs because fracture intensity describes the abundance of fractures potentially available for fluid flow. Moreover, in geotechnical engineering, fractures are important for parameterisation of stress models and excavation design. As fracture data is often collected from widely-spaced boreholes where core recovery is often incomplete, accurate interpretation and representation of fracture aperture-frequency relationships from sparse datasets is important. Fracture intensity is the number of fractures encountered per unit length along a sample scanline oriented perpendicular to the fractures in a set. Cumulative frequency of fractures (F) is commonly related to fracture aperture (A) in the form of a power-law (F = aA‑b), with variations in the size of the a coefficient between sites interpreted to equate to fracture frequency for a given aperture (A). However, a common flaw in this approach is that even a small change in b can have a large effect on the response of the fracture frequency (F) parameter. We compare fracture data from the Late Permian Rangal Coal Measures from Australia's Bowen Basin, with fracture data from Jurassic carbonates from the Sierra Madre Oriental, northeastern Mexico. Both power-law coefficient a and exponent b control the fracture aperture-frequency relationship in conjunction with each other; that is, power-laws with relatively low a coefficients have relatively high b exponents and vice versa. Hence, any comparison of different power-laws must take both a and b into consideration. The corollary is that different sedimentary beds in the Sierra Madre carbonates do not show ˜8× the fracture frequency for a given fracture aperture, as based solely on the comparison of coefficient a. Rather, power-law "sensitivity factors" developed from
NASA Astrophysics Data System (ADS)
Otten, Daniel; Rubbert, Sebastian; Ulrich, Jascha; Hassler, Fabian
2016-09-01
Josephson junctions are the most prominent nondissipative and at the same time nonlinear elements in superconducting circuits allowing Cooper pairs to tunnel coherently between two superconductors separated by a tunneling barrier. Due to this, physical systems involving Josephson junctions show highly complex behavior and interesting novel phenomena. Here, we consider an infinite one-dimensional chain of superconducting islands where neighboring islands are coupled by capacitances. We study the effect of Josephson junctions shunting each island to a common ground superconductor. We treat the system in the regime where the Josephson energy exceeds the capacitive coupling between the islands. For the case of two offset charges on two distinct islands, we calculate the interaction energy of these charges mediated by quantum phase slips due to the Josephson nonlinearities. We treat the phase slips in an instanton approximation and map the problem onto a classical partition function of interacting particles. Using the Mayer cluster expansion, we find that the interaction potential of the offset charges decays with a universal inverse-square power-law behavior.
Mobley, Joel
2010-01-01
The Kramers-Kronig (KK) relations are a large class of integral transformations that exploit the broad principle of simple causality in order to link the physical properties of matter and materials. In applications to the complex-valued wavenumber for acoustic propagation, the method of subtractions is used to form convergent integral relations between the phase velocity and the attenuation coefficient. When the method of subtractions is applied in the usual manner, the integrands in the relations become unnecessarily complicated. In this work, an expanded form of the subtracted relations is presented, which is essentially a truncated Taylor series expansion of the Hilbert transforms. The implementation of the relations only requires the explicit evaluation of two simply expressed integrals involving the Hilbert transform kernel. These two integrals determine the values of the other terms in the subtracted relations, demonstrating the computational efficiency of the technique. The method is illustrated analytically through its application to power-law attenuation coefficients and its associated dispersion, which are observed in a wide variety of materials. This approach explicitly shows the central role of the Hilbert transform kernel in the KK relations, which can become obscured in other formulations.
Durand, O.; Soulard, L.
2013-11-21
Large scale molecular dynamics (MD) simulations are performed to study and to model the ejecta production from the dynamic fragmentation of shock-loaded metals under melt conditions. A generic 3D crystal in contact with vacuum containing about 10{sup 8} atoms and with a sinusoidal free surface roughness is shock loaded so as to undergo a solid-liquid phase change on shock. The reflection of the shock wave at the interface metal/vacuum gives rise to the ejection of 2D jets/sheets of atoms (Richtmyer-Meshkov instabilities in the continuum limit), which develop and break up, forming ejecta (fragments) of different volumes (or mass). The fragmentation process is investigated by analyzing the evolution of the resulting volume distribution of the ejecta as a function of time. Two metals are studied (Cu and Sn) and the amplitude of the roughness is varied. The simulations show that the associated distributions exhibit a generic behavior with the sum of two distinct terms of varying weight, following the expansion rate of the jets: in the small size limit, the distribution obeys a power law dependence with an exponent equal to 1.15 ± 0.08; and in the large size limit, it obeys an exponential form. These two components are interpreted, with the help of additional simple simulations, as the signature of two different basic mechanisms of fragmentation. The power law dependence results from the fragmentation of a 2D network of ligaments arranged following a fractal (scale free) geometry and generated when the sheets of liquid metal expand and tear. The exponential distribution results from a 1D Poisson fragmentation process of the largest ligaments previously generated. Unlike the power law distribution, it is governed by a characteristic length scale, which may be provided by energy balance principle.
Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources
NASA Technical Reports Server (NTRS)
Fiorito, Ralph; Titarchuk, Lev
2004-01-01
Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.
Phase diagram of softly repulsive systems: the Gaussian and inverse-power-law potentials.
Prestipino, Santi; Saija, Franz; Giaquinta, Paolo V
2005-10-01
We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction. PMID:16238377
Deviations from uniform power-law scaling due to exposure to high altitude
NASA Astrophysics Data System (ADS)
Posiewnik, A.
2002-12-01
A major challenge in biological physics is the analysis of time series that are typically highly nonstationary. Viswanathan et al. (Phys. Rev. E 55 (1) (1997) 845-899) using techniques based on the Fano factor and the Allan factor functions, as well as on detrended fluctuation analysis showed that the scaling properties of the dynamics of healthy physiological systems in normal conditions are more stable than those of pathological systems-there is underlying loss of uniform power-law scaling in disease. Here we test, using the same techniques as Viswanathan et al. (1997), the hypothesis that deviations from uniform power-law scaling, similar to those seen in heart failure and deep apnea syndrome occur also for healthy subjects under pathological conditions (hypoxaemic stress during exposure to high altitude, over 6000 m).
MHD boundary layer flow of a power-law nanofluid with new mass flux condition
NASA Astrophysics Data System (ADS)
Khan, Masood; Khan, Waqar Azeem
2016-02-01
An analysis is carried out to study the magnetohydrodynamic (" separators=" MHD ) boundary layer flow of power-law nanofluid over a non-linear stretching sheet. In the presence of a transverse magnetic field, the flow is generated due to non-linear stretching sheet. By using similarity transformations, the governing boundary layer equations are reduced into a system of ordinary differential equations. A recently proposed boundary condition requiring zero nanoparticle mass flux is employed in the flow analysis of power-law fluid. The reduced coupled differential equations are then solved numerically by the shooting method. The variations of dimensionless temperature and nanoparticle concentration with various parameters are graphed and discussed in detail. Numerical values of physical quantities such as the skin-friction coefficient and the reduced local Nusselt number are computed in tabular form.
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin
2014-10-10
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ ≡ B(2)/(4πnm(e)c(2))>1 and when the system size is sufficiently large. In the limit σ ≫ 1, the spectral index approaches p = 1 and most of the available energy is converted into nonthermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection. PMID:25375716
Power-law singularities in string theory and M-theory
NASA Astrophysics Data System (ADS)
Papadopoulos, G.
2004-11-01
We extend the definition of the Szekeres Iyer power-law singularities to supergravity, string and M-theory backgrounds, and find that are characterized by Kasner-type exponents. The near singularity geometries of brane and some intersecting brane backgrounds are investigated and the exponents are computed. The Penrose limits of some of these power-law singularities have profiles A ~ u-γ for γ >= 2. We find the range of the exponents for which γ = 2 and the frequency squares are bounded by 1/4. We propose some qualitative tests for deciding whether a null or timelike spacetime singularity can be resolved within string theory and M-theory based on the near singularity geometry and its Penrose limits.
Two-phase power-law modeling of pipe flows displaying shear-thinning phenomena
Ding, Jianmin; Lyczkowski, R.W.; Sha, W.T.
1993-12-31
This paper describes work in modeling concentrated liquid-solids flows in pipes. COMMIX-M, a three-dimensional transient and steady-state computer program developed at Argonne National Laboratory, was used to compute velocities and concentrations. Based on the authors` previous analyses, some concentrated liquid-solids suspension flows display shear-thinning rather than Newtonian phenomena. Therefore, they developed a two-phase non-Newtonian power-law model that includes the effect of solids concentration on solids viscosity. With this new two-phase power-law solids-viscosity model, and with constitutive relationships for interfacial drag, virtual mass effect, shear lift force, and solids partial-slip boundary condition at the pipe walls, COMMIX-M is capable of analyzing concentrated three-dimensional liquid-solids flows.
Finite sample properties of power-law cross-correlations estimators
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2015-02-01
We study finite sample properties of estimators of power-law cross-correlations-detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA)-with a special focus on short-term memory bias as well as power-law coherency. We present a broad Monte Carlo simulation study that focuses on different time series lengths, specific methods' parameter setting, and memory strength. We find that each method is best suited for different time series dynamics so that there is no clear winner between the three. The method selection should be then made based on observed dynamic properties of the analyzed series.
NASA Technical Reports Server (NTRS)
Raj, S. V.; Pharr, G. M.
1989-01-01
Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.
Speed-invariant encoding of looming object distance requires power law spike rate adaptation.
Clarke, Stephen E; Naud, Richard; Longtin, André; Maler, Leonard
2013-08-13
Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.
Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions.
Kuo, Huan-Yu; Wu, Kuo-An
2015-12-01
We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α≤1 is identical to that of the all-to-all coupling case. For α>1, oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations. PMID:26764785
Power-Law Entanglement Spectrum in Many-Body Localized Phases
NASA Astrophysics Data System (ADS)
Serbyn, Maksym; Michailidis, Alexios A.; Abanin, Dmitry A.; Papić, Z.
2016-10-01
The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
Holm, Sverre; Näsholm, Sven Peter
2014-04-01
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
Linking multiple relaxation, power-law attenuation, and fractional wave equations.
Näsholm, Sven Peter; Holm, Sverre
2011-11-01
The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.
Flow of a power-law fluid over a rotating disk revisited
NASA Astrophysics Data System (ADS)
Andersson, H. I.; de Korte, E.; Meland, R.
2001-02-01
The von Kármán swirling flow due to a rotating disk admits similarity solutions even in the case of a power-law fluid. The non-linearities introduced by the rheological model may deteriorate the numerical solutions of the resulting set of ordinary differential equations with increasing departure from Newtonian behaviour. The reliability of earlier numerical results are nevertheless approved, except for highly shear-thinning fluids (the power-law index n<0.5) for which a severe ambiguity in the solutions is revealed and ascribed to a breakdown of the boundary layer approximation. This phenomenon makes it impossible to determine the pumping action of the disk. For highly shear-thickening fluids, on the other hand, new accurate results are provided beyond the parameter range considered earlier, i.e. for 1.5< n⩽2.0.
Hypersonic aerodynamic characteristics of a family of power-law, wing body configurations
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1973-01-01
The configurations analyzed are half-axisymmetric, power-law bodies surmounted by thin, flat wings. The wing planform matches the body shock-wave shape. Analytic solutions of the hypersonic small disturbance equations form a basis for calculating the longitudinal aerodynamic characteristics. Boundary-layer displacement effects on the body and the wing upper surface are approximated. Skin friction is estimated by using compressible, laminar boundary-layer solutions. Good agreement was obtained with available experimental data for which the basic theoretical assumptions were satisfied. The method is used to estimate the effects of power-law, fineness ratio, and Mach number variations at full-scale conditions. The computer program is included.
Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions.
Kuo, Huan-Yu; Wu, Kuo-An
2015-12-01
We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α≤1 is identical to that of the all-to-all coupling case. For α>1, oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations.
Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow
NASA Astrophysics Data System (ADS)
Matsubara, Yoshitsugu; Hieida, Yasuhiro; Tadaki, Shin-ichi
2013-09-01
Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.
Segmentation of genomic DNA through entropic divergence: Power laws and scaling
NASA Astrophysics Data System (ADS)
Azad, Rajeev K.; Bernaola-Galván, Pedro; Ramaswamy, Ramakrishna; Rao, J. Subba
2002-05-01
Genomic DNA is fragmented into segments using the Jensen-Shannon divergence. Use of this criterion results in the fragments being entropically homogeneous to within a predefined level of statistical significance. Application of this procedure is made to complete genomes of organisms from archaebacteria, eubacteria, and eukaryotes. The distribution of fragment lengths in bacterial and primitive eukaryotic DNAs shows two distinct regimes of power-law scaling. The characteristic length separating these two regimes appears to be an intrinsic property of the sequence rather than a finite-size artifact, and is independent of the significance level used in segmenting a given genome. Fragment length distributions obtained in the segmentation of the genomes of more highly evolved eukaryotes do not have such distinct regimes of power-law behavior.
Weighted scale-free networks with variable power-law exponents
NASA Astrophysics Data System (ADS)
Tanaka, Takuma; Aoyagi, Toshio
2008-06-01
We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model.
Universal power-law and partial condensation in aggregation-chipping processes
NASA Astrophysics Data System (ADS)
Yamamoto, Hiroshi; Ohtsuki, Toshiya
2010-06-01
The asymptotic behaviour of a distribution function P(X) for X clusters is investigated in aggregation-chipping processes, where aggregation and chipping off of a finite unit of size less than L take place simultaneously. Numerical simulations show that above a certain threshold ⟨X⟩c of an average cluster size, the system exhibits partial condensation where one condensed cluster coexists with a universal power-law distribution with the exponent -5/2 . The critical value ⟨X⟩c is calculated and turns out to increase monotonously with L . The z -transform technique is used to analyze the case L=2 in detail. Obtained results agree well with numerical ones. Finally, universality of the asymptotic power law is discussed for general cases. It becomes evident that universality holds as long as the size of chipped off unit is finite.
The Power Laws of Violence against Women: Rescaling Research and Policies
Kappler, Karolin E.; Kaltenbrunner, Andreas
2012-01-01
Background Violence against Women –despite its perpetuation over centuries and its omnipresence at all social levels– entered into social consciousness and the general agenda of Social Sciences only recently, mainly thanks to feminist research, campaigns, and general social awareness. The present article analyzes in a secondary analysis of German prevalence data on Violence against Women, whether the frequency and severity of Violence against Women can be described with power laws. Principal Findings Although the investigated distributions all resemble power-law distributions, a rigorous statistical analysis accepts this hypothesis at a significance level of 0.1 only for 1 of 5 cases of the tested frequency distributions and with some restrictions for the severity of physical violence. Lowering the significance level to 0.01 leads to the acceptance of the power-law hypothesis in 2 of the 5 tested frequency distributions and as well for the severity of domestic violence. The rejections might be mainly due to the noise in the data, with biases caused by self-reporting, errors through rounding, desirability response bias, and selection bias. Conclusion Future victimological surveys should be designed explicitly to avoid these deficiencies in the data to be able to clearly answer the question whether Violence against Women follows a power-law pattern. This finding would not only have statistical implications for the processing and presentation of the data, but also groundbreaking consequences on the general understanding of Violence against Women and policy modeling, as the skewed nature of the underlying distributions makes evident that Violence against Women is a highly disparate and unequal social problem. This opens new questions for interdisciplinary research, regarding the interplay between environmental, experimental, and social factors on victimization. PMID:22768348
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W., Jr.
2003-01-01
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
NASA Technical Reports Server (NTRS)
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
Topological and non-topological exact soliton solution of the power law KdV equation
NASA Astrophysics Data System (ADS)
Biswas, Anjan; Petković, Marko D.; Milović, Daniela
2010-11-01
This paper obtains the exact 1-soliton solution of the perturbed Korteweg-de Vries equation with power law nonlinearity. Both topological as well as non-topological soliton solutions are obtained. The solitary wave ansatz is used to carry out this integration. The domain restrictions are identified in the process and the parameter constraints are also obtained. Finally, the numerical simulations are implemented in the paper.
Soloway, Alexander G; Dahl, Peter H; Odom, Robert I
2015-10-01
Experimental measurements of Scholte waves from underwater explosions collected off the coast of Virginia Beach, VA in shallow water are presented. It is shown here that the dispersion of these explosion-generated Scholte waves traveling in the sandy seabed can be modeled using a power-law dependent shear wave speed profile and an empirical source model that determines the pressure time-series at 1 m from the source as a function of TNT-equivalent charge weight.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows
NASA Astrophysics Data System (ADS)
Anbarlooei, H. R.; Cruz, D. O. A.; Ramos, F.; Silva Freire, A. P.
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
NASA Astrophysics Data System (ADS)
Kowser, Md. A.; Mahiuddin, Md.
2014-11-01
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, α . 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, α 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.
Power-law distributions for a trapped ion interacting with a classical buffer gas.
DeVoe, Ralph G
2009-02-13
Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment. PMID:19257583
A power-law distribution for tenure lengths of sports managers
NASA Astrophysics Data System (ADS)
Aidt, Toke S.; Leong, Bernard; Saslaw, William C.; Sgroi, Daniel
2006-10-01
We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows.
Anbarlooei, H R; Cruz, D O A; Ramos, F; Silva Freire, A P
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
Logarithmic and power law input-output relations in sensory systems with fold-change detection.
Adler, Miri; Mayo, Avi; Alon, Uri
2014-08-01
Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.
Frequency variations of solar radio zebras and their power-law spectra
NASA Astrophysics Data System (ADS)
Karlický, M.
2014-01-01
Context. During solar flares several types of radio bursts are observed. The fine striped structures of the type IV solar radio bursts are called zebras. Analyzing them provides important information about the plasma parameters of their radio sources. We present a new analysis of zebras. Aims: Power spectra of the frequency variations of zebras are computed to estimate the spectra of the plasma density variations in radio zebra sources. Methods: Frequency variations of zebra lines and the high-frequency boundary of the whole radio burst were determined with and without the frequency fitting. The computed time dependencies of these variations were analyzed with the Fourier method. Results: First, we computed the variation spectrum of the high-frequency boundary of the whole radio burst, which is composed of several zebra patterns. This power spectrum has a power-law form with a power-law index -1.65. Then, we selected three well-defined zebra-lines in three different zebra patterns and computed the spectra of their frequency variations. The power-law indices in these cases are found to be in the interval between -1.61 and -1.75. Finally, assuming that the zebra-line frequency is generated on the upper-hybrid frequency and that the plasma frequency ωpe is much higher than the electron-cyclotron frequency ωce, the Fourier power spectra are interpreted to be those of the electron plasma density in zebra radio sources.
Decomposition of Heart Rate Variability Spectrum into a Power-Law Function and a Residual Spectrum
Kuo, Jane; Kuo, Cheng-Deng
2016-01-01
The power spectral density (PSD) of heart rate variability (HRV) contains a power-law relationship that can be obtained by plotting the logarithm of PSD against the logarithm of frequency. The PSD of HRV can be decomposed mathematically into a power-law function and a residual HRV (rHRV) spectrum. Almost all rHRV measures are significantly smaller than their corresponding HRV measures except the normalized high-frequency power (nrHFP). The power-law function can be characterized by the slope and Y-intercept of linear regression. Almost all HRV measures except the normalized low-frequency power have significant correlations with the Y-intercept, while almost all rHRV measures except the total power [residual total power (rTP)] do not. Though some rHRV measures still correlate significantly with the age of the subjects, the rTP, high-frequency power (rHFP), nrHFP, and low-/high-frequency power ratio (rLHR) do not. In conclusion, the clinical significances of rHRV measures might be different from those of traditional HRV measures. The Y-intercept might be a better HRV measure for clinical use because it is independent of almost all rHRV measures. The rTP, rHFP, nrHFP, and rLHR might be more suitable for the study of age-independent autonomic nervous modulation of the subjects. PMID:27314001
Comment on ``Time needed to board an airplane: A power law and the structure behind it''
NASA Astrophysics Data System (ADS)
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.011130 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the “back-to-front” strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.
Mobility of power-law and Carreau fluids through fibrous media.
Shahsavari, Setareh; McKinley, Gareth H
2015-12-01
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
Power-law behavior in complex organizational communication networks during crisis
NASA Astrophysics Data System (ADS)
Uddin, Shahadat; Murshed, Shahriar Tanvir Hasan; Hossain, Liaquat
2011-08-01
Communication networks can be described as patterns of contacts which are created due to the flow of messages and information shared among participating actors. Contemporary organizations are now commonly viewed as dynamic systems of adaptation and evolution containing several parts, which interact with one another both in internal and in external environment. Although there is limited consensus among researchers on the precise definition of organizational crisis, there is evidence of shared meaning: crisis produces individual crisis, crisis can be associated with positive or negative conditions, crises can be situations having been precipitated quickly or suddenly or situations that have developed over time and are predictable etc. In this research, we study the power-law behavior of an organizational email communication network during crisis from complexity perspective. Power law simply describes that, the probability that a randomly selected node has k links (i.e. degree k) follows P(k)∼k, where γ is the degree exponent. We used social network analysis tools and techniques to analyze the email communication dataset. We tested two propositions: (1) as organization goes through crisis, a few actors, who are prominent or more active, will become central, and (2) the daily communication network as well as the actors in the communication network exhibit power-law behavior. Our preliminary results support these two propositions. The outcome of this study may provide significant advancement in exploring organizational communication network behavior during crisis.
Kiflawi, Moshe; Mann, Ofri; Meekan, Mark G
2016-10-21
Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes. PMID:27449788
Accuracy analysis of measurements on a stable power-law distributed series of events
NASA Astrophysics Data System (ADS)
Matthews, J. O.; Hopcraft, K. I.; Jakeman, E.; Siviour, G. B.
2006-11-01
We investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined. The model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events. This leads to a scale-free discrete random process where customary measures, such as mean value and variance, do not exist. However, converting the number of events occurring in fixed time intervals to a 1-bit 'clipped' process allows the construction of well-behaved statistics that still retain vestiges of the original power-law and fluctuation properties. These statistics include the clipped mean and correlation function, from measurements of which both the power-law index of the distribution of events and the time constant of its fluctuations can be deduced. We report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process. This indicates that, for a fixed experiment time, the error on measurements of the sample mean is minimized by an optimum choice of the number of samples. It is shown furthermore that this choice is sensitive to the power-law index and that the approach to Poisson statistics is dominated by rare events or 'outliers'. Our results are supported by numerical simulation.
Evidence for intermittency and a truncated power law from highly resolved aphid movement data.
Mashanova, Alla; Oliver, Tom H; Jansen, Vincent A A
2010-01-01
Power laws are increasingly used to describe animal movement. Despite this, the use of power laws has been criticized on both empirical and theoretical grounds, and alternative models based on extensions of conventional random walk theory (Brownian motion) have been suggested. In this paper, we analyse a large volume of data of aphid walking behaviour (65,068 data points), which provides a highly resolved dataset to investigate the pattern of movement. We show that aphid movement is intermittent--with alternations of a slow movement with frequent change of direction and a fast, relatively directed movement--and that the fast movement consists of two phases--a strongly directed phase that gradually changes into an uncorrelated random walk. By measuring the mean-squared displacement and the duration of non-stop movement episodes we found that both spatial and temporal aspects of aphid movement are best described using a truncated power law approach. We suggest that the observed spatial pattern arises from the duration of non-stop movement phases rather than from correlations in turning angles. We discuss the implications of these findings for interpreting movement data, such as distinguishing between movement and non-movement, and the effect of the range of data used in the analysis on the conclusions.
Tippett, Michael K.; Cohen, Joel E.
2016-01-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from ‘outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954–2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210
A generalized power-law detection algorithm for humpback whale vocalizations.
Helble, Tyler A; Ierley, Glenn R; D'Spain, Gerald L; Roch, Marie A; Hildebrand, John A
2012-04-01
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.
Analysis of electroosmotic flow of power-law fluids in a slit microchannel.
Zhao, Cunlu; Zholkovskij, Emilijk; Masliyah, Jacob H; Yang, Chun
2008-10-15
Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids. PMID:18656891
Cyclotron Maser Emission from Power-law Electrons with Strong Pitch-angle Anisotropy
NASA Astrophysics Data System (ADS)
Zhao, G. Q.; Feng, H. Q.; Wu, D. J.; Chen, L.; Tang, J. F.; Liu, Q.
2016-05-01
Energetic electrons with power-law spectra are commonly observed in astrophysics. This paper investigates electron cyclotron maser emission (ECME) from the power-law electrons, in which strong pitch-angle anisotropy is emphasized. The electron distribution function proposed in this paper can describe various types of pitch-angle anisotropy. Results show that the emission properties of ECME, including radiation growth, propagation, and frequency properties, depend considerably on the types of electron pitch-angle anisotropy, and different wave modes show different dependences on the pitch angle of electrons. In particular, the maximum growth rate of the X2 mode rapidly decreases with respect to the electron pitch-angle cosine μ 0 at which the electron distribution peaks, while the growth rates for other modes (X1, O1, O2) initially increase before decreasing as μ 0 increases. Moreover, the O mode, as well as the X mode, can be the fastest growth mode, in terms of not only the plasma parameter but also the type of electron pitch-angle distribution. This result presents a significant extension of the recent researches on ECME driven by the lower energy cutoff of power-law electrons, in which the X mode is generally the fastest growth mode.
NASA Astrophysics Data System (ADS)
Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.
2014-09-01
We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.
Decomposition of Heart Rate Variability Spectrum into a Power-Law Function and a Residual Spectrum.
Kuo, Jane; Kuo, Cheng-Deng
2016-01-01
The power spectral density (PSD) of heart rate variability (HRV) contains a power-law relationship that can be obtained by plotting the logarithm of PSD against the logarithm of frequency. The PSD of HRV can be decomposed mathematically into a power-law function and a residual HRV (rHRV) spectrum. Almost all rHRV measures are significantly smaller than their corresponding HRV measures except the normalized high-frequency power (nrHFP). The power-law function can be characterized by the slope and Y-intercept of linear regression. Almost all HRV measures except the normalized low-frequency power have significant correlations with the Y-intercept, while almost all rHRV measures except the total power [residual total power (rTP)] do not. Though some rHRV measures still correlate significantly with the age of the subjects, the rTP, high-frequency power (rHFP), nrHFP, and low-/high-frequency power ratio (rLHR) do not. In conclusion, the clinical significances of rHRV measures might be different from those of traditional HRV measures. The Y-intercept might be a better HRV measure for clinical use because it is independent of almost all rHRV measures. The rTP, rHFP, nrHFP, and rLHR might be more suitable for the study of age-independent autonomic nervous modulation of the subjects.
NASA Astrophysics Data System (ADS)
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-03-01
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.
Aspects of flow of power-law fluids in porous media
Shah, C.B.; Yortsos, Y.C.
1995-05-01
Non-Newtonian fluid flow in porous media is encountered in a variety of applications. Aspects of single-phase flow of power-law fluids in porous media are examined. First, homogenization theory is used to derive a macroscopic law. It is shown that the single-capillary power law between flow rate and pressure gradient also applies at the macroscopic scale, provided that the Reynolds number is sufficiently small. Homogenization theory confirms the validity of the use of pore network models to describe flow of power-law fluids, although not necessarily of fluids of a more general rheology. Flow in pore networks is next used to explore various pore geometry effects. Numerical simulations show that approaches based on an effective medium or on the existence of a critical path, which carries most of the flow, are valid in narrow- or wide-pore-size distributions, respectively. The corresponding expressions agreed well with the numerical results in the respective ranges. An analysis presented for Bethe lattices leads to closed-form expressions in two limits: for an effective medium and near percolation. The behavior near percolation generalizes the results of Stinchcombe (1974) for the linear (Newtonian) case.
Power-law scaling in daily rainfall patterns and consequences in urban stream discharges
NASA Astrophysics Data System (ADS)
Park, Jeryang; Krueger, Elisabeth H.; Kim, Dongkyun; Rao, Suresh C.
2016-04-01
Poissonian rainfall has been frequently used for modelling stream discharge in a catchment at the daily scale. Generally, it is assumed that the daily rainfall depth is described by memoryless exponential distribution which is transformed to stream discharge, resulting in an analytical pdf for discharge [Gamma distribution]. While it is true that catchment hydrological filtering processes (censored by constant rate ET losses, and first-order recession) increases "memory", reflected in 1/f noise in discharge time series. Here, we show that for urban watersheds in South Korea: (1) the observation of daily rainfall depths follow power-law pdfs, and spectral slopes range between 0.2 ~ 0.4; and (2) the stream discharge pdfs have power-law tails. These observation results suggest that multiple hydro-climatic factors (e.g., non-stationarity of rainfall patterns) and hydrologic filtering (increasing impervious area; more complex urban drainage networks) influence the catchment hydrologic responses. We test the role of such factors using a parsimonious model, using different types of daily rainfall patterns (e.g., power-law distributed rainfall depth with Poisson distribution in its frequency) and urban settings to reproduce patterns similar to those observed in empirical records. Our results indicate that fractality in temporally up-scaled rainfall, and the consequences of large extreme events are preserved as high discharge events in urbanizing catchments. Implications of these results to modeling urban hydrologic responses and impacts on receiving waters are discussed.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws
Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.
2011-01-01
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.
Mobility of power-law and Carreau fluids through fibrous media.
Shahsavari, Setareh; McKinley, Gareth H
2015-12-01
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers. PMID:26764809
Flow of power-law fluids in self-affine fracture channels.
Yan, Yiguang; Koplik, Joel
2008-03-01
The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values zeta=0.5 and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a different technique to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian, and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, are studied, and the non-Newtonian fluids are compared to the (previously studied) Newtonian case. We find a scaling relation between permeability and mean aperture in the low Reynolds number regime, generalizing an earlier result for Newtonian fluids. As the Reynolds number increases, we observe the same sequence of transitions to nonlinearity found in intergranular porous media. Furthermore, the permeability results may be collapsed into a master curve of friction factor vs Reynolds number, using a scaling similar to that employed for power-law fluids in porous media.
High-index asymptotics of spherical Bessel products averaged with modulated Gaussian power laws
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
2014-12-01
Bessel integrals of type are investigated, where the kernel g( k) is a modulated Gaussian power-law distribution , and the jl ( m) are multiple derivatives of spherical Bessel functions. These integrals define the multipole moments of Gaussian random fields on the unit sphere, arising in multipole fits of temperature and polarization power spectra of the cosmic microwave background. Two methods allowing efficient numerical calculation of these integrals are presented, covering Bessel indices l in the currently accessible multipole range 0 ≤ l ≤ 104 and beyond. The first method is based on a representation of spherical Bessel functions by Lommel polynomials. Gaussian power-law averages can then be calculated in closed form as finite Hankel series of parabolic cylinder functions, which allow high-precision evaluation. The second method is asymptotic, covering the high- l regime, and is applicable to general distribution functions g( k) in the integrand; it is based on the uniform Nicholson approximation of the Bessel derivatives in conjunction with an integral representation of squared Airy functions. A numerical comparison of these two methods is performed, employing Gaussian power laws and Kummer distributions to average the Bessel products.
Tippett, Michael K; Cohen, Joel E
2016-01-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210
Mobility of power-law and Carreau fluids through fibrous media
NASA Astrophysics Data System (ADS)
Shahsavari, Setareh; McKinley, Gareth H.
2015-12-01
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ ≃0.65 , the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
Kiflawi, Moshe; Mann, Ofri; Meekan, Mark G
2016-10-21
Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes.
2015-01-01
Background Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. Objectives The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. Methods Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. Results All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R 2 values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). Conclusions This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns
Non-linear power law approach for spatial and temporal pattern analysis of salt marsh evolution
NASA Astrophysics Data System (ADS)
Taramelli, A.; Cornacchia, L.; Valentini, E.; Bozzeda, F.
2013-11-01
Many complex systems on the Earth surface show non-equilibrium fluctuations, often determining the spontaneous evolution towards a critical state. In this context salt marshes are characterized by complex patterns both in geomorphological and ecological features, which often appear to be strongly correlated. A striking feature in salt marshes is vegetation distribution, which can self-organize in patterns over time and space. Self-organized patchiness of vegetation can often give rise to power law relationships in the frequency distribution of patch sizes. In cases where the whole distribution does not follow a power law, the variance of scale in its tail may often be disregarded. To this end, the research aims at how changes in the main climatic and hydrodynamic variables may influence such non-linearity, and how numerical thresholds can describe this. Since it would be difficult to simultaneously monitor the presence and typology of vegetation and channel sinuosity through in situ data, and even harder to analyze them over medium to large time-space scales, remote sensing offers the ability to analyze the scale invariance of patchiness distributions. Here, we focus on a densely vegetated and channelized salt marsh (Scheldt estuary Belgium-the Netherlands) by means of the sub-pixel analysis on satellite images to calculate the non-linearity in the values of the power law exponents due to the variance of scale. The deviation from power laws represents stochastic conditions under climate drivers that can be hybridized on the basis of a fuzzy Bayesian generative algorithm. The results show that the hybrid approach is able to simulate the non-linearity inherent to the system and clearly show the existence of a link between the autocorrelation level of the target variable (i.e. size of vegetation patches), due to its self-organization properties, and the influence exerted on it by the external drivers (i.e. climate and hydrology). Considering the results of the
NASA Astrophysics Data System (ADS)
Stewart, Michael; Morgenstern, Uwe
2013-04-01
Understanding runoff generation is important for management of freshwater systems. Determining transit time distributions of streamwaters and how they change with discharge gives information on the flowpaths and recharge sources of streams - vital information for determining the responses of streams to stressors such as pollution, landuse change, or climate change. This work takes a first look at unique information on how transit time distributions change with discharge in some New Zealand catchments. Transit time distributions of streamwaters have been determined from tritium measurements on single samples in this work. This allows changes with stream discharge to be observed, in contrast to previous isotope studies which have given averaged transit time distributions based on series of samples. In addition, tritium reveals the wide spectrum of ages present in streams whereas oxygen-18 or chloride variations only show the younger ages (Stewart et al., 2010). It was found that the mean transit time (MTT) data could be reasonably represented by straight lines in log-log plots, indicating power law relationships between MTT and discharge. Similar power law behaviour has been observed for the rock forming elements such as silica in streamwaters (Godsey et al., 2009). Case studies are presented for two New Zealand catchments, both with volcanic ash substrates. Toenepi is a dairy catchment near Hamilton, which shows well-constrained power law relationships between MTT and discharge, and between silica concentration and discharge (Morgenstern et al., 2010). Baseflow MTTs vary from 2.5 to 157 years. Tutaeuaua is a pastoral farming catchment near Taupo. Results for nested catchments along the stream also show power law relationships for both MTT and silica with discharge. Streamwater MTTs vary from 1 to 11 years. The results indicate that (1) relatively old waters dominate many streams, (2) streamwater ages vary with discharge, and (3) age, like silica, varies according to
Strain-rate Dependence of Power-law Creep and Folding of Rocks
NASA Astrophysics Data System (ADS)
Ord, A.; Hobbs, B. E.
2011-12-01
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
NASA Astrophysics Data System (ADS)
Blackmon, Fletcher A.
1993-11-01
An arbitrary waveform generator is capable of producing pulse or continuous waveform signals. It utilizes an EPROM that sends out selected stored digital signals under control of a microprocessor and auxiliary equipment comprised of a clock and an address sequencer. A digital to analog converter receives the digital signals from the EPROM and converts them to analog signals.
Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi
2016-01-01
We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria. PMID:27505155
Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi
2016-01-01
We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria. PMID:27505155
On the interplay between short and long term memory in the power-law cross-correlations setting
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2015-03-01
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equal to an average of separate Hurst exponents of the analyzed processes. Strength of short term memory has no effect on these asymptotic properties. Implications of these findings for the power-law cross-correlations concept are further discussed.
Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi
2016-01-01
We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria.
Froese, M. W.; Blaum, K.; Fellenberger, F.; Grieser, M.; Lange, M.; Laux, F.; Menk, S.; Orlov, D. A.; Repnow, R.; Sieber, T.; Hahn, R. von; Wolf, A.; Toker, Y.
2011-02-15
The decay of excited aluminum-cluster anions (Al{sub n}{sup -}, n=4 and 5) has been investigated in a cryogenic linear ion-beam trap. A power-law is found to accurately reproduce the time dependence of the observed decay rates at early storage times, although the exponents are significantly larger than the typically observed 1/t decay. It is shown that the power-law exponent is, at most, weakly dependent on the cluster electron affinity and heat capacity. A previous power-law exponent model for small clusters is also shown to be in disagreement with both investigated species. The attribution of a drop in the decay rate at later times to radiative cooling as observed in larger molecules also does not appear justified in our case. A strong dependence of the power-law exponent on the ambient temperature was observed.
NASA Astrophysics Data System (ADS)
Jiao, Chengru; Zheng, Liancun; Ma, Lianxi
2015-08-01
This paper studies the magnetohydrodynamic (MHD) thermosolutal Marangoni convection heat and mass transfer of power-law fluids driven by a power law temperature and a power law concentration which is assumed that the surface tension varies linearly with both the temperature and concentration. Heat and mass transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection-diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient and the mass diffusion depends non-linearly on both the concentration and the concentration gradient with modified Fourier heat conduction for power law fluid. The governing equations are reduced to nonlinear ordinary differential equations by using suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM). The transport characteristics of velocity, temperature and concentration fields are analyzed in detail.
NASA Astrophysics Data System (ADS)
Liu, Hsing; Chen, Ying-Hsing; Lih, Jiann-Shing
2015-05-01
Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution.
Chomko, R M; Gordon, H R
1998-08-20
When strongly absorbing aerosols are present in the atmosphere, the usual two-step procedure of processing ocean color data-(1) atmospheric correction to provide the water-leaving reflectance (rho(w)), followed by (2) relating rho(w) to the water constituents-fails and simultaneous estimation of the ocean and aerosol optical properties is necessary. We explore the efficacy of using a simple model of the aerosol-a Junge power-law size distribution consisting of homogeneous spheres with arbitrary refractive index-in a nonlinear optimization procedure for estimating the relevant oceanic and atmospheric parameters for case 1 waters. Using simulated test data generated from more realistic aerosol size distributions (sums of log-normally distributed components with different compositions), we show that the ocean's pigment concentration (C) can be retrieved with good accuracy in the presence of weakly or strongly absorbing aerosols. However, because of significant differences in the scattering phase functions for the test and power-law distributions, large error is possible in the estimate of the aerosol optical thickness. The positive result for C suggests that the detailed shape of the aerosol-scattering phase function is not relevant to the atmospheric correction of ocean color sensors. The relevant parameters are the aerosol single-scattering albedo and the spectral variation of the aerosol optical depth. We argue that the assumption of aerosol sphericity should not restrict the validity of the algorithm and suggest an avenue for including colored aerosols, e.g., wind-blown dust, in the procedure. A significant advantage of the new approach is that realistic multicomponent aerosol models are not required for the retrieval of C.
Monaghan, Padraic; Shillcock, Richard C; Christiansen, Morten H; Kirby, Simon
2014-09-19
It is a long established convention that the relationship between sounds and meanings of words is essentially arbitrary--typically the sound of a word gives no hint of its meaning. However, there are numerous reported instances of systematic sound-meaning mappings in language, and this systematicity has been claimed to be important for early language development. In a large-scale corpus analysis of English, we show that sound-meaning mappings are more systematic than would be expected by chance. Furthermore, this systematicity is more pronounced for words involved in the early stages of language acquisition and reduces in later vocabulary development. We propose that the vocabulary is structured to enable systematicity in early language learning to promote language acquisition, while also incorporating arbitrariness for later language in order to facilitate communicative expressivity and efficiency.
NASA Astrophysics Data System (ADS)
Saha, Pameli; Debnath, Ujjal
2016-09-01
Here, we peruse cosmological usage of the most promising candidates of dark energy in the framework of f( T) gravity theory where T represents the torsion scalar teleparallel gravity. We reconstruct the different f( T) modified gravity models in the spatially flat Friedmann-Robertson-Walker universe according to entropy-corrected versions of the holographic and new agegraphic dark energy models in power-law and logarithmic corrections, which describe an accelerated expansion history of the universe. We conclude that the equation of state parameter of the entropy-corrected models can transit from the quintessence state to the phantom regime as indicated by recent observations or can lie entirely in the phantom region. Also, using these models, we investigate the different areas of the stability with the help of the squared speed of sound.
Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators
NASA Astrophysics Data System (ADS)
Casteels, W.; Storme, F.; Le Boité, A.; Ciuti, C.
2016-03-01
We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states; in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a nonadiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in the presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.
Power-Law Modeling of Cancer Cell Fates Driven by Signaling Data to Reveal Drug Effects
Zhang, Fan; Wu, Min; Kwoh, Chee Keong; Zheng, Jie
2016-01-01
Extracellular signals are captured and transmitted by signaling proteins inside a cell. An important type of cellular responses to the signals is the cell fate decision, e.g., apoptosis. However, the underlying mechanisms of cell fate regulation are still unclear, thus comprehensive and detailed kinetic models are not yet available. Alternatively, data-driven models are promising to bridge signaling data with the phenotypic measurements of cell fates. The traditional linear model for data-driven modeling of signaling pathways has its limitations because it assumes that the a cell fate is proportional to the activities of signaling proteins, which is unlikely in the complex biological systems. Therefore, we propose a power-law model to relate the activities of all the measured signaling proteins to the probabilities of cell fates. In our experiments, we compared our nonlinear power-law model with the linear model on three cancer datasets with phosphoproteomics and cell fate measurements, which demonstrated that the nonlinear model has superior performance on cell fates prediction. By in silico simulation of virtual protein knock-down, the proposed model is able to reveal drug effects which can complement traditional approaches such as binding affinity analysis. Moreover, our model is able to capture cell line specific information to distinguish one cell line from another in cell fate prediction. Our results show that the power-law data-driven model is able to perform better in cell fate prediction and provide more insights into the signaling pathways for cancer cell fates than the linear model. PMID:27764199
Power-law dynamics in neuronal and behavioral data introduce spurious correlations.
Schaworonkow, Natalie; Blythe, Duncan A J; Kegeles, Jewgeni; Curio, Gabriel; Nikulin, Vadim V
2015-08-01
Relating behavioral and neuroimaging measures is essential to understanding human brain function. Often, this is achieved by computing a correlation between behavioral measures, e.g., reaction times, and neurophysiological recordings, e.g., prestimulus EEG alpha-power, on a single-trial-basis. This approach treats individual trials as independent measurements and ignores the fact that data are acquired in a temporal order. It has already been shown that behavioral measures as well as neurophysiological recordings display power-law dynamics, which implies that trials are not in fact independent. Critically, computing the correlation coefficient between two measures exhibiting long-range temporal dependencies may introduce spurious correlations, thus leading to erroneous conclusions about the relationship between brain activity and behavioral measures. Here, we address data-analytic pitfalls which may arise when long-range temporal dependencies in neural as well as behavioral measures are ignored. We quantify the influence of temporal dependencies of neural and behavioral measures on the observed correlations through simulations. Results are further supported in analysis of real EEG data recorded in a simple reaction time task, where the aim is to predict the latency of responses on the basis of prestimulus alpha oscillations. We show that it is possible to "predict" reaction times from one subject on the basis of EEG activity recorded in another subject simply owing to the fact that both measures display power-law dynamics. The same is true when correlating EEG activity obtained from different subjects. A surrogate-data procedure is described which correctly tests for the presence of correlation while controlling for the effect of power-law dynamics.
Power-law Growth and Punctuated Equilibrium Dynamics in Water Resources Systems
NASA Astrophysics Data System (ADS)
Parolari, A.; Katul, G. G.; Porporato, A. M.
2015-12-01
The global rise in population-driven water scarcity and recent appreciation of strong dynamic coupling between human and natural systems has called for new approaches to predict the future sustainability of regional and global water resources systems. The dynamics of coupled human-water systems are driven by a complex set of social, environmental, and technological factors. Present projections of water resources systems range from a finite carrying capacity regulated by accessible freshwater, or `peak renewable water,' to punctuated evolution with new supplied and improved efficiency gained from technological and social innovation. However, these projections have yet to be quantified from observations or in a comprehensive theoretical framework. Using data on global water withdrawals and storage capacity of regional water supply systems, non-trivial dynamics are identified in water resources systems development over time, including power-law growth and punctuated equilibria. Two models are introduced to explain this behavior: (1) a delay differential equation and (2) a power-law with log-periodic oscillations, both of which rely on past conditions (or system memory) to describe the present rate of growth in the system. In addition, extension of the first model demonstrates how system delays and punctuated equilibria can emerge from coupling between human population growth and associated resource demands. Lastly, anecdotal evidence is used to demonstrate the likelihood of power-law growth in global water use from the agricultural revolution 3000 BC to the present. In a practical sense, the presence of these patterns in models with delayed oscillations suggests that current decision-making related to water resources development results from the historical accumulation of resource use decisions, technological and social changes, and their consequences.
An Evaluation of Power Law Breakdown in Metals, Alloys, Dispersion Hardened Materials and Compounds
Lesuer, D.R.; Syn, C.K.; Sherby, O.D.
1999-10-20
Creep at high stresses often produces strain rates that exceed those that would be predicted by a power law relationship. In this paper, we examine available high stress creep data for pure metals, solid solution alloys, dispersion strengthened powder metallurgy materials and compounds for power law breakdown (PLB). The results show that, if PLB is observed, then the onset of PLB is generally observed at about {epsilon}/D{sub eff} = 10{sup 13} m{sup -2}, where D{sub eff} is the effective diffusion coefficient incorporating lattice and dislocation pipe diffusion. The common origins of PLB for the various systems studied can be found in the production of excess vacancies by plastic deformation. Anomalous behavior in two pure metals (nickel and tungsten) and a solid solution alloy (Fe-25Cr and Fe-26Cr-1Mo) has been analyzed and provides insight into this excess vacancy mechanism. In metal systems, the onset of PLB is related to a change in the nature of the subgrain structure developed. In the PLB region, subgrains become imperfect containing dislocation tangles adjacent to the sub-boundary, and dislocation cells are evident. The dislocation tangles and cells are the source of excess vacancies and increase the creep rate above that predicted from power law creep. If subgrains do not form then PLB is not observed. In solid solution alloys, in which the dominant deformation resistance results from the interaction of solute atoms with moving dislocations, excess vacancies influence the diffusion of these solute atoms. PLB is not observed in many systems. This is attributed either to the presence of a high equilibrium vacancy concentration (because of a low activation energy for vacancy formation) or to the inability to form subgrains.
Keil, Petr; Herben, Tomás; Rosindell, James; Storch, David
2010-07-01
There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed 'pink noise': a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.
Saichev, A; Sornette, D
2010-01-01
Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law approximately 1/t(alpha) with 0
Effects of diversity and procrastination in priority queuing theory: The different power law regimes
NASA Astrophysics Data System (ADS)
Saichev, A.; Sornette, D.
2010-01-01
Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law ˜1/tα with 0<α≤1 over a time scale of years. We present a simple model for this persistence phenomenon, framed within the standard priority queuing theory, of a target task which has the lowest priority compared to all other tasks that flow on the computer of an individual. We identify a “time deficit” control parameter β and a bifurcation to a regime where there is a nonzero probability for the target task to never be completed. The distribution of waiting time T until the completion of the target task has the power law tail ˜1/t1/2 , resulting from a first-passage solution of an equivalent Wiener process. Taking into account a diversity of time deficit parameters in a population of individuals, the power law tail is changed into 1/tα , with αɛ(0.5,∞) , including the well-known case 1/t . We also study the effect of “procrastination,” defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks. This regime provides an explanation for even slower apparent decay and longer persistence.
Optimal numerical flux of power-law fluids in some partially full pipes
NASA Astrophysics Data System (ADS)
Lefton, Lew; Wei, Dongming; Liu, Yu
2014-07-01
Consider the steady state pressure driven flow of a power-law fluid in a partially filled straight pipe. It is known that an increase in flux can be achieved for a fixed pressure by partially filling the pipe and having the remaining volume either void or filled with a less viscous, lubricating fluid. If the pipe has circular cross section, the fluid level which maximizes flux is the level which avoids contact with exactly 25% of the boundary. This result can be proved analytically for Newtonian fluids and has been verified numerically for certain non-Newtonian models. This paper provides a generalization of this work numerically to pipes with non-circular cross sections which are partially full with a power-law fluid. A simple and physically plausible geometric condition is presented which can be used to approximate the fluid level that maximizes flux in a wide range of pipe geometries. Additional increases in flux for a given pressure can be obtained by changing the shape of the pipe but leaving the perimeter fixed. This computational analysis of flux as a function of both fluid level and pipe geometry has not been considered to our knowledge. Fluxes are computed using a special discretization scheme, designed to uncover general properties which are only dependent on fluid level and/or pipe cross-sectional geometry. Computations use finite elements and take advantage of the variational structure inherent in the power-law model. A minimization technique for approximating the critical points of the associated non-linear energy functional is used. In particular, the numerical scheme for the non-linear partial differential equation has been proved to be convergent with known error estimates. The numerical results obtained in this work can be useful for designing pipes and canals for transportation of non-Newtonian fluids, such as those in chemical engineering and food processing engineering.
On the power-law distributions of X-ray fluxes from solar flares observed with GOES
NASA Astrophysics Data System (ADS)
Li, You-Ping; Feng, Li; Zhang, Ping; Liu, Si-Ming; Gan, Wei-Qun
2016-10-01
The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality (SOC). In this paper, we first show that, so long as the shape of the normalized light curve is not correlated with the peak flux, the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the power-law frequency distribution of the peak flux, which may partially explain why power-law distributions are ubiquitous in the Universe. We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different: the higher energy channel has a harder distribution than the lower energy channel, which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites. The temperature (T) distribution, on the other hand, approaches a power-law distribution with an index of 2 for high values of T. Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.
Langlois, Dominic; Cousineau, Denis; Thivierge, J P
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
NASA Astrophysics Data System (ADS)
Boutelier, D.; Schrank, C.; Cruden, A.
2008-03-01
The selection of appropriate analogue materials is a central consideration in the design of realistic physical models. We investigate the rheology of highly-filled silicone polymers in order to find materials with a power-law strain-rate softening rheology suitable for modelling rock deformation by dislocation creep and report the rheological properties of the materials as functions of the filler content. The mixtures exhibit strain-rate softening behaviour but with increasing amounts of filler become strain-dependent. For the strain-independent viscous materials, flow laws are presented while for strain-dependent materials the relative importance of strain and strain rate softening/hardening is reported. If the stress or strain rate is above a threshold value some highly-filled silicone polymers may be considered linear visco-elastic (strain independent) and power-law strain-rate softening. The power-law exponent can be raised from 1 to ˜3 by using mixtures of high-viscosity silicone and plasticine. However, the need for high shear strain rates to obtain the power-law rheology imposes some restrictions on the usage of such materials for geodynamic modelling. Two simple shear experiments are presented that use Newtonian and power-law strain-rate softening materials. The results demonstrate how materials with power-law rheology result in better strain localization in analogue experiments.
NASA Astrophysics Data System (ADS)
Langlois, Dominic; Cousineau, Denis; Thivierge, J. P.
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
NASA Astrophysics Data System (ADS)
Wang, Q.; Yang, M.; Song, X. L.; Jia, J.; Xiang, Z. D.
2016-07-01
The conventional power law creep equation (Norton equation) relating the minimum creep rate to creep stress and temperature cannot be used to predict the long-term creep strengths of creep-resistant steels if its parameters are determined only from short-term measurements. This is because the stress exponent and activation energy of creep determined on the basis of this equation depend on creep temperature and stress and these dependences cannot be predicted using this equation. In this work, it is shown that these problems associated with the conventional power law creep equation can be resolved if the new power law equation is used to rationalize the creep data. The new power law creep equation takes a form similar to the conventional power law creep equation but has a radically different capability not only in rationalizing creep data but also in predicting the long-term creep strengths from short-term test data. These capabilities of the new power law creep equation are demonstrated using the tensile strength and creep test data measured for both pipe and tube grades of the creep-resistant steel 9Cr-1.8W-0.5Mo-V-Nb-B (P92 and T92).
On global minimizers of repulsive–attractive power-law interaction energies
Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong
2014-01-01
We consider the minimization of the repulsive–attractive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations. PMID:25288810
Solitary and shock waves in discrete strongly nonlinear double power-law materials
NASA Astrophysics Data System (ADS)
Herbold, E. B.; Nesterenko, V. F.
2007-06-01
A laminar metamaterial supporting strongly nonlinear solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. The force-displacement relationship of a compressed o-ring is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into three separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.
Transition in the Flow of Power-Law Fluids through Isotropic Porous Media.
Zami-Pierre, F; de Loubens, R; Quintard, M; Davit, Y
2016-08-12
We use computational fluid dynamics to explore the creeping flow of power-law fluids through isotropic porous media. We find that the flow pattern is primarily controlled by the geometry of the porous structure rather than by the nonlinear effects in the rheology of the fluid. We further highlight a macroscale transition between a Newtonian and a non-Newtonian regime, which is the signature of a coupling between the viscosity of the fluid and the structure of the porous medium. These complex features of the flow can be condensed into an effective length scale, which defines both the non-Newtonian transition and the Newtonian permeability. PMID:27563969
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
Bakalis, Evangelos E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco E-mail: francesco.zerbetto@unibo.it; Venturini, Alessandro
2015-06-07
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; Nalewajko, K.; Begelman, M. C.
2015-12-30
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron–positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power lawmore » $${\\gamma }^{-\\alpha }$$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.« less
Waters; Hughes; Mobley; Brandenburger; Miller
2000-08-01
In the recent literature concern has been raised regarding the validity of Kramers-Kronig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers-Kronig dispersion relations for application to these types of media are available. The developed dispersion relations are compared with measurements on several liquids, and agreement is found to better than 1 m/s over the experimentally available bandwidth. A discussion regarding the validity of these dispersion relations, in particular how the dispersion relations relate to the so-called Paley-Wiener conditions, forms the conclusion.
Numerical study of forced convective power law fluid flow through an annulus sector duct
NASA Astrophysics Data System (ADS)
Ahmed, Farhan; Iqbal, Mazhar; Sher Akbar, Noreen
2016-09-01
This study investigates the forced convection flow of power law fluid through an annulus sector duct. The governing dimensionless form of momentum and energy equations is discretized by using a control volume-based method. Numerical solutions of the system of algebraic equations are obtained for different values of flow behaviour index, n, both for shear thinning fluids ( 0.3≤ n < 1) and shear thickening fluids ( 1 < n ≤ 2). Results for the quantities of interest both for the fluid flow and forced convection are discussed numerically and graphically for different values of n.
An explanation for the universal 3.5 power-law observed in currency markets
NASA Astrophysics Data System (ADS)
Johnson, Nicholas A.; Johnson, Neil F.
We present a mathematical theory to explain a recent empirical finding in the Physics literature (Zhao et al., 2013) in which the distributions of waiting-times between discrete events were found to exhibit power-law tails with an apparent universal exponent: α ∼ 3.5 . This new theory provides the first ever qualitative and quantitative explanation of Zhao et al.'s surprising finding. It also provides a mechanistic description of the origin of the observed universality, assigning its cause to the emergence of dynamical feedback processes between evolving clusters of like-minded agents.
Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids
NASA Astrophysics Data System (ADS)
Maloney, C. E.; Robbins, M. O.
2009-06-01
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.
Laboratory constraints on chameleon dark energy and power-law fields
Steffen, Jason H.; Upadhye, Amol; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; Weltman, Amanda; Wester, William; /Fermilab
2010-10-01
We report results from the GammeV Chameleon Afterglow Search - a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Thermodynamics of Ideal Fermi Gas Under Generic Power Law Potential in d-dimensions
NASA Astrophysics Data System (ADS)
Faruk, M. M.; Bhuiyan, G. M.
Thermodynamics of ideal Fermi gas trapped in an external generic power law potential $U=\\sum_{i=1} ^d c_i |\\frac{x_i}{a_i}|^{n_i}$ are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. These properties are explored deeply in the degenerate limit ($\\mu>> K_BT$), where the thermodynamic properties are greatly dominated by Pauli exclusion principle. Pressure and energy along with the isothermal compressibilty is non zero at $T=0K$, denoting trapped Fermi system is quite live even at absolute zero temperature. The nonzero value of compressibilty denotes zero point pressure is not just a constant but depends on volume.
Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps.
Grossmann, S; Holthaus, M
1997-11-10
After discussing the idea underlying the Maxwell's Demon ensemble, we employ this ensemble for calculating fluctuations of ideal Bose gas condensates in traps with power-law single-particle energy spectra. Two essentially different cases have to be distinguished. If the heat capacity is continuous at the condensation point, the fluctuations of the number of condensate particles vanish linearly with temperature, independent of the trap characteristics. In this case, microcanonical and canonical fluctuations are practically indistinguishable. If the heat capacity is discontinuous, the fluctuations vanish algebraically with temperature, with an exponent determined by the trap, and the micro-canonical fluctuations are lower than their canonical counterparts. PMID:19373412
NASA Astrophysics Data System (ADS)
Mercan, Kadir; Demir, Çiǧdem; Civalek, Ömer
2016-01-01
In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.
Truncation of power law behavior in "scale-free" network models due to information filtering.
Mossa, Stefano; Barthélémy, Marc; Eugene Stanley, H; Nunes Amaral, Luís A
2002-04-01
We formulate a general model for the growth of scale-free networks under filtering information conditions-that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the distribution of the number of incoming links to a node follows a universal scaling form, i.e., that it decays as a power law with an exponential truncation controlled not only by the system size but also by a feature not previously considered, the subset of the network "accessible" to the node. We test our model with empirical data for the World Wide Web and find agreement.
Transition in the Flow of Power-Law Fluids through Isotropic Porous Media.
Zami-Pierre, F; de Loubens, R; Quintard, M; Davit, Y
2016-08-12
We use computational fluid dynamics to explore the creeping flow of power-law fluids through isotropic porous media. We find that the flow pattern is primarily controlled by the geometry of the porous structure rather than by the nonlinear effects in the rheology of the fluid. We further highlight a macroscale transition between a Newtonian and a non-Newtonian regime, which is the signature of a coupling between the viscosity of the fluid and the structure of the porous medium. These complex features of the flow can be condensed into an effective length scale, which defines both the non-Newtonian transition and the Newtonian permeability.
Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids
Maloney, C. E.; Robbins, M. O.
2009-06-05
The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.
Transition in the Flow of Power-Law Fluids through Isotropic Porous Media
NASA Astrophysics Data System (ADS)
Zami-Pierre, F.; de Loubens, R.; Quintard, M.; Davit, Y.
2016-08-01
We use computational fluid dynamics to explore the creeping flow of power-law fluids through isotropic porous media. We find that the flow pattern is primarily controlled by the geometry of the porous structure rather than by the nonlinear effects in the rheology of the fluid. We further highlight a macroscale transition between a Newtonian and a non-Newtonian regime, which is the signature of a coupling between the viscosity of the fluid and the structure of the porous medium. These complex features of the flow can be condensed into an effective length scale, which defines both the non-Newtonian transition and the Newtonian permeability.
So You Think the Crab is Described by a Power-Law Spectrum
NASA Technical Reports Server (NTRS)
Weisskopf, Martin C.
2008-01-01
X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.
Power-law scaling during shadowing growth of nanocolumns by oblique angle deposition
Tang, F.; Karabacak, T.; Li, L.; Pelliccione, M.; Wang, G.-C.; Lu, T.-M.
2007-01-15
The authors have investigated the power-law behaviors of various morphological parameters during the shadowing growth of ruthenium (Ru) nanocolumns by an oblique angle sputter deposition technique with substrate rotation. Particularly, wavelength and column number density were measured at different column heights (h). The exponents associated with the wavelength (p{sub {lambda}}) and column number density (p{sub n}), correlated by the geometrical relationship p{sub {lambda}}{approx_equal}-(1/2)p{sub n}, were measured by atomic force microscopy to be {approx}0.5 and {approx}-1.0, respectively. Using a one-dimensional facet growth model based upon the principle of evolutionary selection under oblique angle deposition, they showed that the exponents associated with the column number density and wavelength can be predicted. The authors also illustrated that the exponent value associated with column number density originates from the competitive growth among columns that have different vertical growth rates. The simulated exponent values are independent of the shape of the facet, which indicates the universality of these power-law exponents.
Power law scaling and ``Dragon-Kings'' in distributions of intraday financial drawdowns
NASA Astrophysics Data System (ADS)
Filimonov, Vladimir; Sornette, Didier
2015-05-01
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of epsilon-drawdowns and epsilon-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (dragon-kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.
Spectral function of the Tomonaga-Luttinger model revisited: Power laws and universality
NASA Astrophysics Data System (ADS)
Markhof, L.; Meden, V.
2016-02-01
We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum dependence of the two-particle interaction V (q ) . Usually, V (q ) is assumed to be a constant and integrals are regularized in the ultraviolet "by hand" employing an ad hoc procedure. As the momentum dependence of the interaction is irrelevant in the renormalization group sense, this does not affect the universal low-energy properties of the model, e.g., exponents of power laws, if all energy scales are sent to zero. If, however, the momentum k is fixed away from the Fermi momentum kF, with |k - kF| setting a nonvanishing energy scale, the details of V (q ) start to matter. We provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys power-law scaling of the momentum-resolved spectral function as a function of energy. Even for |k - kF| much smaller than the momentum-space range of the interaction the spectral line shape depends on the details of V (q ) . The significance of our results for universality in the Luttinger liquid sense, for experiments on quasi-one-dimensional metals, and for recent results on the spectral function of one-dimensional correlated systems taking effects of the curvature of the single-particle dispersion into account ("nonlinear LL phenomenology") is discussed.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.
2002-01-01
The method of Maximum Likelihood (ML) is used to estimate the spectral parameters of an assumed broken power law energy spectrum from simulated detector responses. This methodology, which requires the complete specificity of all cosmic-ray detector design parameters, is shown to provide approximately unbiased, minimum variance, and normally distributed spectra information for events detected by an instrument having a wide range of commonly used detector response functions. The ML procedure, coupled with the simulated performance of a proposed space-based detector and its planned life cycle, has proved to be of significant value in the design phase of a new science instrument. The procedure helped make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope. This ML methodology is then generalized to estimate broken power law spectral parameters from real cosmic-ray data sets.
Bose-Einstein condensation in dark power-law laser traps
NASA Astrophysics Data System (ADS)
Jaouadi, A.; Gaaloul, N.; Viaris de Lesegno, B.; Telmini, M.; Pruvost, L.; Charron, E.
2010-08-01
We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order ℓ allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a “finger” or of a “hockey puck” in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.
NASA Astrophysics Data System (ADS)
Hong, S. Lee; Bodfish, James W.; Newell, Karl M.
2006-03-01
We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Beyond power laws: a new approach for analyzing single molecule photoluminescence intermittency.
Riley, E A; Hess, C M; Whitham, P J; Reid, P J
2012-05-14
The photoluminescence intermittency (PI) exhibited by single emitters has been studied for over a decade. To date, the vast majority of PI analyses involve parsing the data into emissive and non-emissive events, constructing histograms of event durations, and fitting these histograms to either exponential or power law probability distributions functions (PDFs). Here, a new method for analyzing PI data is presented where the data are used directly to construct a cumulative distribution function (CDF), and maximum-likelihood estimation techniques are used to determine the best fit of a model PDF to the CDF. Statistical tests are then employed to quantitatively evaluate the hypothesis that the CDF (data) is represented by the model PDF. The analysis method is outlined and applied to PI exhibited by single CdSe∕CdS core-shell nanocrystals and the organic chromophore violamine R isolated in single crystals of potassium-acid phthalate. Contrary to previous studies, the analysis presented here demonstrates that the PI exhibited by these systems is not described by a power law. The analysis developed here is also used to quantify heterogeneity within PI data obtained from a collection of CdSe/CdS nanocrytals, and for the determination of statistically significant changes in PI accompanying perturbation of the emitter. In summary, the analysis methodology presented here provides a more statistically robust approach for analyzing PI data.
Moduli of curve families and (quasi-)conformality of power-law entropies
NASA Astrophysics Data System (ADS)
Kalogeropoulos, Nikos
2016-03-01
We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the calculations of the moduli of curve families for a cylinder and for an annulus in ℝn. The underlying motivation for these studies is that the definitions and some properties of the modulus of a curve family resembles those of the Tsallis entropy, when the latter is seen from a micro-canonical viewpoint. We comment on the origin of the conjectured invariance of the Tsallis entropy under Möbius transformations of the non-extensive (entropic) parameter. Needing techniques applicable to both locally Euclidean and fractal classes of spaces, we examine the behavior of the Tsallis functional, via the modulus, under quasi-conformal maps. We comment on properties of such maps and their possible significance for the dynamical foundations of power-law entropies.
A power-law model of psychological memory strength in short- and long-term recognition.
Donkin, Chris; Nosofsky, Robert M
2012-06-01
A classic law of cognition is that forgetting curves are closely approximated by power functions. This law describes relations between different empirical dependent variables and the retention interval, and the precise form of the functional relation depends on the scale used to measure each variable. In the research reported here, we conducted a recognition task involving both short- and long-term probes. We discovered that formal memory-strength parameters from an exemplar-recognition model closely followed a power function of the lag between studied items and a test probe. The model accounted for rich sets of response time (RT) data at both individual-subject and individual-lag levels. Because memory strengths were derived from model fits to choices and RTs from individual trials, the psychological power law was independent of the scale used to summarize the forgetting functions. Alternative models that assumed different functional relations or posited a separate fixed-strength working memory store fared considerably worse than the power-law model did in predicting the data. PMID:22527527
Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.
Sasidevan, V
2013-08-01
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-η(sr) whereas they depend on a for a<3-η(sr) where η(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 ν and the percolation threshold. We carry out Monte Carlo simulations and determine the exponent ν as a function of a. The determined values of ν show that it is independent of the parameter a for a>3-η(sr) and is equal to that for the lattice percolation problem, whereas ν varies with a for 2
Double power-law spectra of energetic electrons in the Earth magnetotail
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Hoshino, M.; Lutsenko, V. N.; Petrukovich, A. A.; Imada, S.; Zelenyi, L. M.
2013-01-01
In this paper, we consider electron acceleration in the vicinity of X-line and corresponding formation of energy spectra. We develop an analytical model including the effect of the electron trapping by electrostatic fields and surfing acceleration. Speiser, Fermi and betatron mechanisms of acceleration are also taken into account. Analytical estimates are verified by the numerical integration of electron trajectories. The surfing mechanism and adiabatic heating are responsible for the formation of the double power-law spectrum in agreement with the previous studies. The energy of the spectrum knee is about ~150 keV for typical conditions of the Earth magnetotail. We compare theoretical results with the spacecraft observations of electron double power-law spectra in the magnetotail and demonstrate that the theory is able to describe typical energy of the spectra knee. We also estimate the role of relativistic effects and magnetic field fluctuations on the electron acceleration: the acceleration is more stable for relativistic electrons, while fluctuations of the magnetic field cannot significantly decrease the gained energy for typical magnetospheric conditions.
Universal correlations and power-law tails in financial covariance matrices
NASA Astrophysics Data System (ADS)
Akemann, G.; Fischmann, J.; Vivo, P.
2010-07-01
We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.
Transition from Exponential to Power Law Income Distributions in a Chaotic Market
NASA Astrophysics Data System (ADS)
Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.
Keeping the edge: an accurate numerical method to solve the stream power law
NASA Astrophysics Data System (ADS)
Campforts, B.; Govers, G.
2015-12-01
Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.
Lifetimes of metastable ion clouds in a Paul trap: Power-law scaling
NASA Astrophysics Data System (ADS)
Weiss, D. K.; Nam, Y. S.; Blümel, R.
2016-04-01
It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime τ¯m of the metastable cloud follows a power law, τ¯m˜(γ-γc) -β , where γc is the value of the damping constant at which the transition occurs. The exponent β depends on the trap control parameter q , but is independent of both the number of particles N stored in the trap and the trap control parameter a , which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given a and q , γc scales approximately like γc=C ln[ln(N ) ] +D as a function of N , where C and D are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.
Ruling out the power-law form of the scalar primordial spectrum
Hazra, Dhiraj Kumar; Shafieloo, Arman; Smoot, George F.; Starobinsky, Alexei A. E-mail: arman@apctp.org E-mail: alstar@landau.ac.ru
2014-06-01
Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3σ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large r and at the same time provide suppression in scalar primordial spectrum at large scales.
“Slimming” of power-law tails by increasing market returns
NASA Astrophysics Data System (ADS)
Sornette, D.
2002-06-01
We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r> rδ corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power-law exponent and thus the thinner is the tail of the distribution of price returns.
A power-law model of psychological memory strength in short- and long-term recognition.
Donkin, Chris; Nosofsky, Robert M
2012-06-01
A classic law of cognition is that forgetting curves are closely approximated by power functions. This law describes relations between different empirical dependent variables and the retention interval, and the precise form of the functional relation depends on the scale used to measure each variable. In the research reported here, we conducted a recognition task involving both short- and long-term probes. We discovered that formal memory-strength parameters from an exemplar-recognition model closely followed a power function of the lag between studied items and a test probe. The model accounted for rich sets of response time (RT) data at both individual-subject and individual-lag levels. Because memory strengths were derived from model fits to choices and RTs from individual trials, the psychological power law was independent of the scale used to summarize the forgetting functions. Alternative models that assumed different functional relations or posited a separate fixed-strength working memory store fared considerably worse than the power-law model did in predicting the data.
THE POWER-LAW SPECTRA OF ENERGETIC PARTICLES DURING MULTI-ISLAND MAGNETIC RECONNECTION
Drake, J. F.; Swisdak, M.; Fermo, R. E-mail: swisdak@umd.edu
2013-01-20
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.
Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales
NASA Technical Reports Server (NTRS)
Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.
2006-01-01
The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.
Couette flow of non-Newtonian power-law fluids in narrow eccentric annuli
Yang, L.; Chukwu, G.A.
1995-03-01
The analysis of the steady laminar Couette flow of non-Newtonian power-law fluids in a narrow eccentric cannulus is employed in this study to compute the surge or swab pressure encountered when running or pulling tubular goods in a liquid-filled borehole, respectively. Excessive surge pressure can fracture the formation, while uncontrolled swab pressure can result in well blowout. In this study, the eqs of motion are analytically solved and the solution of these eqs is presented in both dimensionless and graphical forms for a more general application to computing the surge or swab pressure. The family of curves is presented for different pipe/borehole eccentricity ratios and power-law fluid index values which span the range of typical drilling fluids. By employing the computed surge pressures, in combination with the family of curves, the maximum velocity at which the casing can be run in the hole without the danger of fracturing the formation can be obtained. The expected error in surge computation for a narrow concentric annulus represented by a slot, as a result of eccentricity, is evaluated. The results obtained from the these analyses will aid in proper design and optimization of drilling programs, especially in deviated holes.
Peterson, Jeffrey J; Nesbitt, David J
2009-01-01
Single photon detection methods are used to acquire fluorescence trajectories from single CdSe/ZnS colloidal quantum dots (QDs) and analyze their blinking behavior. Although the "off-time" distributions follow ideal power law behavior at all wavelengths and intensities, significant deviations from power law behavior are observed for the "on-times". Specifically, with improved time resolution, trajectory durations, and photon statistics, we report a near-exponential falloff of on-time probability distributions at long times. Investigation of this falloff behavior as a function of laser wavelength and power demonstrate that these deviations originate from multiexciton dynamics, whose formation probabilities can be very low on a "per laser pulse" basis, but become nearly unity on the time scales of the longest on-times. The near quadratic, power-dependent results indicate the predominant role of biexcitons in the long time on-to-off blinking dynamics, which can be interpreted in terms of an Auger ionization event. In conjunction with Poisson modeling of the photon statistics, the data is consistent with QD ionization efficiencies of order approximately 10(-5) and highlight a novel role for biexcitons and Auger ionization in QD blinking.
The US business cycle: power law scaling for interacting units with complex internal structure
NASA Astrophysics Data System (ADS)
Ormerod, Paul
2002-11-01
In the social sciences, there is increasing evidence of the existence of power law distributions. The distribution of recessions in capitalist economies has recently been shown to follow such a distribution. The preferred explanation for this is self-organised criticality. Gene Stanley and colleagues propose an alternative, namely that power law scaling can arise from the interplay between random multiplicative growth and the complex structure of the units composing the system. This paper offers a parsimonious model of the US business cycle based on similar principles. The business cycle, along with long-term growth, is one of the two features which distinguishes capitalism from all previously existing societies. Yet, economics lacks a satisfactory theory of the cycle. The source of cycles is posited in economic theory to be a series of random shocks which are external to the system. In this model, the cycle is an internal feature of the system, arising from the level of industrial concentration of the agents and the interactions between them. The model-in contrast to existing economic theories of the cycle-accounts for the key features of output growth in the US business cycle in the 20th century.
Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses
NASA Technical Reports Server (NTRS)
Wijers, Ralph A. M. J.; Lubin, Lori M.
1994-01-01
We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.
From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies
NASA Astrophysics Data System (ADS)
Soesoo, Alvar; Bons, Paul D.
2015-07-01
Magma is generated by partial melting from micrometre-scale droplets at the source and may accumulate to form >100 km-scale plutons. Magma accumulation thus spans well over ten orders of magnitude in scale. Here we provide measurements of migmatitic leucosomes and granitic veins in drill cores from the Estonian Proterozoic basement and outcrops at Masku in SW Finland and Montemor-o-Novo, central Portugal. Despite the differences in size and number of measured leucosomes and magmatic veins, differences in host rock types and metamorphic grades, the cumulative width distribution of the studied magmatic leucosomes/veins follows a power law with exponents usually between 0.7 and 1.8. Published maps of the SE Australian Lachlan Fold Belt were used to investigate the distribution of granitoid pluton sizes. The granites occupy ca. 22 % of the 2.6 × 105 km2 area. The cumulative pluton area distributions show good power law distributions with exponents between 0.6 and 0.8 depending on pluton area group. Using the self-affine nature of pluton shapes, it is possible to estimate the total volume of magma that was expelled from the source in the 2.6 × 105 km2 map area, giving an estimated 0.8 km3 of magma per km2. It has been suggested in the literature that magma batches in the source merge to form ever-bigger batches in a self-organized way. This leads to a power law for the cumulative distribution of magma volumes, with an exponent m V between 1 for inefficient melt extraction, and 2/3 for maximum accumulation efficiency as most of the volume resides in the largest batches that can escape from the source. If m V ≥ 1, the mass of the magma is dominated by small batches; in case m = 2/3, about 50 % of all magma in the system is placed in a single largest batch. Our observations support the model that the crust develops a self-organized critical state during magma generation. In this state, magma batches accumulate in a non-continuous, step-wise manner to form ever
Investigating dynamics of inhibitory and feedback loops in ERK signalling using power-law models.
Vera, Julio; Rath, Oliver; Balsa-Canto, Eva; Banga, Julio R; Kolch, Walter; Wolkenhauer, Olaf
2010-11-01
The investigation of the structure and dynamics of signal transduction systems through data-based mathematical models in ordinary differential equations or other paradigms has proven to be a successful approach in recent times. Extending this concept, we here analysed the use of kinetic models based on power-law terms with non-integer kinetic orders in the validation of hypotheses concerning regulatory structures in signalling systems. We integrated pre-existent biological knowledge, hypotheses and experimental quantitative data into a power-law model to validate the existence of certain regulatory loops in the Ras/Raf-1/MEK/ERK pathway, a MAPK pathway involved in the transduction of mitogenic and differentiation signals. Towards this end, samples of a human mammary epithelial cell line (MCF-10A) were used to obtain time-series data, characterising the behaviour of the system after epidermal growth factor stimulation in different scenarios of expression for the critical players of the system regarding the investigated loops (e.g., the inhibitory protein RKIP). The mathematical model was calibrated using a computational procedure that included: analysis of structural identifiability, global ranking of parameters to detect the most sensitivity ones towards the experimental setup, model calibration using global optimization methods to find the parameter values that better fit the data, and practical identifiability analysis to estimate the confidence in the estimated values for the parameters. The obtained model was used to perform computational simulations concerning the role of the investigated regulatory loops in the time response of the signalling pathway. Our findings suggest that the special regularity in the structure of the power-law terms make them suitable for a data-based validation of regulatory loops in signalling pathways. The model-based analysis performed identified RKIP as an actual inhibitor of the activation of the ERK pathway, but also suggested
Dipole transition matrix elements for systems with power-law potentials
Grant, A.K.; Rosner, J.L. )
1992-11-01
We study the behavior of dipole matrix elements for systems bound by power-law potentials of the form {ital V}({ital r}){similar to}{ital r}{sup {alpha}}, which are useful in the descriptions of quarkonium systems. The experimental feature for which further understanding is sought is the apparent suppression of the transition {Upsilon}(3{ital S}){r arrow}{chi}{sub {ital b}}{gamma}. We find that this matrix element actually vanishes in a power-law potential {ital r}{sup {alpha}} for a certain power {alpha}{sub 0}{approx}{minus}0.4. The suppression of transitions between states with different numbers of nodes in their radial wave functions is a universal property of most physically interesting power-law potentials. We derive results in the limit of large orbital angular momenta {ital l}, checking that they agree with the known answers for the Coulomb and spherical oscillator potentials. For states with {ital n}{sub {ital r}} nodes in their radial wave functions, we find that the matrix elements {l angle}{ital n}{sub {ital r}},{ital l}{vert bar}{ital r}{vert bar}{ital n}{sub {ital r}},{ital l}+1{r angle} behave as {ital l}{sup 2/(2+{alpha})} for small {ital n}{sub {ital r}} and large {ital l}. Transitions with {Delta}{ital n}{sub {ital r}}={plus minus}1 behave with respect to those with {Delta}{ital n}{sub {ital r}}=0 as const/ {radical}{ital l}, with constants calculated for each {ital n}{sub {ital r}}. Moreover, we find that {l angle}{ital n}{sub {ital r}}=0,{ital l}{vert bar}{ital r}{vert bar}{ital n}{sub {ital r}}=2,{ital l}{minus}1{r angle}/{l angle}{ital n}{sub {ital r}}=0, {ital l}{vert bar}{ital r}{vert bar}{ital n}{sub {ital r}}=0,{ital l}+1{r angle}{r arrow}{Phi}({alpha})/{ital l} as {ital l}{r arrow}{infinity}, where {Phi}({alpha}) is calculated explicitly.
NASA Astrophysics Data System (ADS)
Akiba, M.; Tsujino, K.
2016-08-01
This paper offers a theoretical explanation of the temperature and temporal dependencies of transient dark count rates (DCRs) measured for a linear-mode silicon avalanche photodiode (APD) and the dependencies of afterpulsing that were measured in Geiger-mode Si and InGaAs/InP APDs. The temporal dependencies exhibit power-law behavior, at least to some extent. For the transient DCR, the value of the DCR for a given time period increases with decreases in temperature, while the power-law behavior remains unchanged. The transient DCR is attributed to electron emissions from traps in the multiplication layer of the APD with a high electric field, and its temporal dependence is explained by a continuous change in the electron emission rate as a function of the electric field strength. The electron emission rate is calculated using a quantum model for phonon-assisted tunnel emission. We applied the theory to the temporal dependence of afterpulsing that was measured for Si and InGaAs/InP APDs. The power-law temporal dependence is attributed to the power-law function of the electron emission rate from the traps as a function of their position across the p-n junction of the APD. Deviations from the power-law temporal dependence can be derived from the upper and lower limits of the electric field strength.
Zhao, Xiaofeng; McGough, Robert J
2016-05-01
The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations. PMID:27250193
Lee, S.R.; Irvine, T.F. Jr.; Greene, G.A.
1998-04-01
An implicit finite difference method was applied to analyze laminar natural convection in a vertical channel with a modified power law fluid. This fluid model was chosen because it describes the viscous properties of a pseudoplastic fluid over the entire shear rate range likely to be found in natural convection flows since it covers the shear rate range from Newtonian through transition to simple power law behavior. In addition, a dimensionless similarity parameter is identified which specifies in which of the three regions a particular system is operating. The results for the average channel velocity and average Nusselt number in the asymptotic Newtonian and power law regions are compared with numerical data in the literature. Also, graphical results are presented for the velocity and temperature fields and entrance lengths. The results of average channel velocity and Nusselt number are given in the three regions including developing and fully developed flows. As an example, a pseudoplastic fluid (carboxymethyl cellulose) was chosen to compare the different results of average channel velocity and Nusselt number between a modified power law fluid and the conventional power law model. The results show, depending upon the operating conditions, that if the correct model is not used, gross errors can result.
Zhao, Xiaofeng; McGough, Robert J
2016-05-01
The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations.
On syntheses of the X-ray background with power-law sources
NASA Technical Reports Server (NTRS)
De Zotti, G.; Boldt, E. A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.; Cavaliere, A.; Danese, L.; Franceschini, A.
1982-01-01
The conditions under which the combined emission from power-law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low-luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit steeper spectra at higher energies.
The power law relation of spiral waves in the Belousov-Zhabotinsky reaction
NASA Astrophysics Data System (ADS)
Li, Yan; Bai, Shufeng; Ouyang, Qi
2000-12-01
The relationship of the period Ts and the wavelength λs of spiral waves with the control parameters is systematically studied with the Belousov-Zhabotinksy (BZ) reaction in a spatially extended quasi-two-dimensional system. Our experiments indicate that Ts and λs not only rely on the concentrations of sulfuric acid and sodium bromate, as indicated in the previous work [A. L. Belmonte, Q. Ouyang, and J. M. Flesselles, J. Phys. II 7, 1425 (1997)] but also have strong relation with the concentration of malonic acid (MA). With the influence of the concentration of MA taken into consideration, a revised power law of spiral waves is suggested, which is qualitatively in agreement with early works of numerical simulations and theoretical analysis.
Dominance of the suppressed: Power-law size structure in tropical forests.
Farrior, C E; Bohlman, S A; Hubbell, S; Pacala, S W
2016-01-01
Tropical tree size distributions are remarkably consistent despite differences in the environments that support them. With data analysis and theory, we found a simple and biologically intuitive hypothesis to explain this property, which is the foundation of forest dynamics modeling and carbon storage estimates. After a disturbance, new individuals in the forest gap grow quickly in full sun until they begin to overtop one another. The two-dimensional space-filling of the growing crowns of the tallest individuals relegates a group of losing, slow-growing individuals to the understory. Those left in the understory follow a power-law size distribution, the scaling of which depends on only the crown area-to-diameter allometry exponent: a well-conserved value across tropical forests.
NASA Technical Reports Server (NTRS)
Choi, Sung R.; Gyekenyesi, John P.
2002-01-01
The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The maximum likelihood procedure is developed for estimating the three spectral parameters of an assumed broken power law energy spectrum from simulated detector responses and their statistical properties investigated. The estimation procedure is then generalized for application to real cosmic-ray data. To illustrate the procedure and its utility, analytical methods were developed in conjunction with a Monte Carlo simulation to explore the combination of the expected cosmic-ray environment with a generic space-based detector and its planned life cycle, allowing us to explore various detector features and their subsequent influence on estimating the spectral parameters. This study permits instrument developers to make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope.
Vertical-channel free convection with a power-law fluid
Irvine, T.F. Jr.; Wu, K.C.; Schneider, W.J.
1982-01-01
A finite-difference solution is presented of the velocity and temperature fields for the flow of an Ostwald-de-Waele (power law) fluid between two vertical isothermal parallel plates under the influence of free convection. Two quantities are of particular interest: the total heat transferred from the plates and the average velocity between the plates. Although these quantities can be presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers, there is an important difference compared to the similar problem involving Newtonian fluids. In the present case, the generalized Prandtl number is not a fluid property but contains a geometric factor and thus the geometry of the system must be specified before the Prandtl number is fixed. The results and the manner in which they can be used are illustrated by a numerical example.
NASA Astrophysics Data System (ADS)
Fan, Qingju; Wu, Yonghong
2015-08-01
In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.
Chaube, M. K.; Tripathi, D.; Bég, O. Anwar; Sharma, Shashi; Pandey, V. S.
2015-01-01
A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth. PMID:27057132
Semiclassical trace formula for the two-dimensional radial power-law potentials.
Magner, A G; Vlasenko, A A; Arita, K
2013-06-01
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate up to a constant shift the radial dependence of the Woods-Saxon potential and its quantum spectra in a bound region, was derived by the improved stationary phase method. The specific analytical results are obtained for the powers α=4 and 6. The enhancement of periodic-orbit contribution to the level density near the bifurcations are found to be significant for the description of the fine shell structure. The semiclassical trace formulas for the shell corrections to the level density and the energy of many-fermion systems reproduce the quantum results with good accuracy through all the bifurcation (symmetry breaking) catastrophe points, where the standard stationary-phase method breaks down. Various limits (including the harmonic oscillator and the spherical billiard) are obtained from the same analytical trace formula.
Slow synaptic dynamics in a network: from exponential to power-law forgetting.
Luck, J M; Mehta, A
2014-09-01
We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√[t] relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations. PMID:25314475
Overall potentials and extremal surfaces of power law or ideally plastic composites
NASA Astrophysics Data System (ADS)
Suquet, P. M.
1993-06-01
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.
Metastable state dynamics and power law relaxation in a supercooled liquid.
Srivastava, S; Das, S P
2001-01-01
We consider glassy relaxation by using a model for supercooled liquid where the usual set of hydrodynamic variables is extended to include the presence of very slowly decaying defect densities. The long time limit of the density correlation function, the nonergodicity parameter, is studied in the vicinity of the dynamic transition point, and scaling exponents with respect to the distance from the critical point are obtained. In addition to the usual square root cusp, we also see a linear dependence on distance from transition with respect to the metastability parameters. We analyze the power law relaxation of the density correlation function at the initial stage of the dynamics, and obtain an exponent dependent on temperature. Results are compared with data obtained from light scattering experiments.
Dominance of the suppressed: Power-law size structure in tropical forests.
Farrior, C E; Bohlman, S A; Hubbell, S; Pacala, S W
2016-01-01
Tropical tree size distributions are remarkably consistent despite differences in the environments that support them. With data analysis and theory, we found a simple and biologically intuitive hypothesis to explain this property, which is the foundation of forest dynamics modeling and carbon storage estimates. After a disturbance, new individuals in the forest gap grow quickly in full sun until they begin to overtop one another. The two-dimensional space-filling of the growing crowns of the tallest individuals relegates a group of losing, slow-growing individuals to the understory. Those left in the understory follow a power-law size distribution, the scaling of which depends on only the crown area-to-diameter allometry exponent: a well-conserved value across tropical forests. PMID:26744402
Collision-dependent power law scalings in two dimensional gyrokinetic turbulence
Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.
2014-08-15
Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.
Power law X- and gamma-ray emission from relativistic thermal plasmas
NASA Technical Reports Server (NTRS)
Zdziarski, A. A.
1984-01-01
Pair equilibrium in thermal plasmas emitting power law photon spectra by repeated Compton scatterings of a soft photon source active galactic nuclei was studied. Dependence of the spectral index on optical thickness and on temperature of the plasma is discussed. The equation for pair equilibrium is solved for the maximum steady luminosity. Analytical solutions for the subrelativistic region, and for the ultrarelativistic region are found. In the transrelativistic region the solutions are expressed by single integrals over the pair production cross sections, performed numerically. The constraints on soft photon source imposed by the condition that the soft photon flux cannot exceed the black-body flux are considered. For the Comptonized synchrotron radiation model a relation between magnetic field strength and output luminosity is found.
Slow synaptic dynamics in a network: From exponential to power-law forgetting
NASA Astrophysics Data System (ADS)
Luck, J. M.; Mehta, A.
2014-09-01
We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√t relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.
A comment on power-law inflation with a dark radiation component
NASA Astrophysics Data System (ADS)
Di Valentino, Eleonora; Bouchet, François R.
2016-10-01
Tram et al. 2016 recently pointed out in [1] that power-law inflation in presence of a dark radiation component may relieve the 3.3 σ tension which exists within standard ΛCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) [2] and the value derived from CMB anisotropy data [3] by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the σ8 tension between the Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from Planck HFI data [4] are included in the analysis, the H0 tension reappears and this scenario looses appeal.
Scalar field probes of power-law space-time singularities
NASA Astrophysics Data System (ADS)
Blau, Matthias; Frank, Denis; Weiss, Sebastian
2006-08-01
We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x-2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x-2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
On syntheses of the X-ray background with power-law sources
NASA Astrophysics Data System (ADS)
De Zotti, G.; Boldt, E. A.; Cavaliere, A.; Danese, L.; Franceschini, A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.
1981-08-01
The conditions under which the combined emission from power law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit sleeper spectra at higher energies.
Evidence for power-law tail of the wealth distribution in India
NASA Astrophysics Data System (ADS)
Sinha, Sitabhra
2006-01-01
The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-2004. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year under analysis). This provides a comparison with previous studies of wealth distribution, which have all been confined to Western advanced capitalist economies. We conclude with a discussion on the appropriateness of multiplicative stochastic process as a model for asset accumulation, the relation between the wealth and income distributions (we estimate the Pareto exponent for the latter to be around 1.5 for India), as well as possible sources of error in measuring the Pareto exponent for wealth.
Modified Anderson orthogonality catastrophe power law in the presence of shell structure
NASA Astrophysics Data System (ADS)
Bandopadhyay, Swarnali; Hentschel, Martina
2011-01-01
We study Anderson orthogonality catastrophe (AOC) for parabolic quantum dots and focus on the effects of degeneracies, realized through the inherent shell structure of their energy levels that can be lifted through an external magnetic field, on the Anderson overlap. We find rich and interesting behaviors as a function of the strength and position of the perturbation, the system size, and the applied magnetic field. In particular, even for weak perturbations, we observe a pronounced AOC that is related to the degeneracy of energy levels. Most importantly, the power-law decay of the Anderson overlap as a function of the number of particles is modified in comparison to the metallic case due to the rearrangement of the energy-level shell structure. We support our analytical results by numerical calculations and also study the distribution of Anderson overlaps.
Revisiting the Anderson Model with Power-Law Correlated Disorder in 1D and 2D
NASA Astrophysics Data System (ADS)
Petersen, Greg; Sandler, Nancy
2011-03-01
The dimensionality of a disordered system directly affects the critical energy where a localization/delocalization transition occurs. In non-interacting systems with uncorrelated disorder, it is widely known that all states in one-dimension are localized. However, for some correlations there exist transition energies similar to mobility edges or small subsets of extended states that are robust against disorder. In this talk, we will present results on the diffusion of a wavepacket in a power-law correlated random potential of the form < V (r) V (0) > =1/(a + r)α . We also report results for the participation ratio Pr =1/N 2 < |ai |4 > . Preliminary results for 1D chains support the existence of a mobility edge near the band center. Square and graphene lattices will also be discussed. This work has been supported by the NSF-PIRE mwn/ciam and NSF Grant DMR-0710581.
Architectures engender crises: The emergence of power laws in social networks
NASA Astrophysics Data System (ADS)
Tohmé, Fernando; Larrosa, Juan M. C.
2016-05-01
Recent financial crises posed a number of questions. The most salient were related to the cogency of derivatives and other sophisticated hedging instruments. One claim is that all those instruments rely heavily on the assumption that events in the world are guided by normal distributions while, instead, all the evidence shows that they actually follow fat-tailed power laws. Our conjecture is that it is the very financial architecture that engenders extreme events. Not on purpose but just because of its complexity. That is, the system has an internal connection structure that is able to propagate and enhance initially small disturbances. The final outcome ends up not being correlated with its triggering event. To support this claim, we appeal to the intuition drawn from the behavior of social networks. Most of the interesting cases constitute scale-free structures. In particular, we contend, those that arise from strategic decisions of the agents.
Conductance statistics for the power-law banded random matrix model
Martinez-Mendoza, A. J.; Mendez-Bermudez, J. A.; Varga, Imre
2010-12-21
We study numerically the conductance statistics of the one-dimensional (1D) Anderson model with random long-range hoppings described by the Power-law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single-mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT){proportional_to}T{sup M2/2}, for T<<
Unification of Small and Large Time Scales for Biological Evolution: Deviations from Power Law
NASA Astrophysics Data System (ADS)
Chowdhury, Debashish; Stauffer, Dietrich; Kunwar, Ambarish
2003-02-01
We develop a unified model that describes both “micro” and “macro” evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the “microevolution” over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the “macroevolution” over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.
NASA Astrophysics Data System (ADS)
Liu, Chao; Li, Rong
2016-09-01
An evolutionary prisoner's dilemma game (PDG) with players located on Barabási-Albert scale-free networks is studied. The impact of players' heterogeneous temporal activity pattern on the evolution of cooperation is investigated. To this end, the normal procedure that players update their strategies immediately after a round of game is discarded. Instead, players update strategies according to their assigned reproduction time, which follows a power-law distribution. We find that the temporal heterogeneity of players' activities facilitates the prosperity of cooperation, indicating the important role of hubs in the maintenance of cooperation on scale-free networks. When the reproduction time is assigned to individuals negatively related to their degrees, a fluctuation of the cooperation level with the increase of the exponent β is observed.
NASA Technical Reports Server (NTRS)
Beltrametti, M.
1980-01-01
The analytic solutions for radiatively driven winds are given for the case in which the winds are driven by absorption of line and continuum radiation. The wind solutions are analytically estimated for different parameters of the central source and for different power law spectra. For flat spectra, three sonic points can exist; it is shown, however, that only one of these sonic points is physically realistic. Parameters of the central source are given which generate winds of further interest for explaining the narrow and broad absorption lines in quasars. For the quasar model presented here, winds which could give rise to the narrow absorption lines are generated by central sources with parameters which are not realistic for quasars.
NASA Astrophysics Data System (ADS)
Makinde, O. D.
2014-12-01
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.
Effect of acoustic coupling on power-law flame acceleration in spherical confinement
NASA Astrophysics Data System (ADS)
Akkerman, V'yacheslav; Law, Chung K.
2013-01-01
A model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach number flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into an existing theory of self-similar flame acceleration in free space [V. Akkerman, C. K. Law, and V. Bychkov, "Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering," Phys. Rev. E 83, 026305 (2011)], 10.1103/PhysRevE.83.026305. Being reflected from the chamber wall, flame-generated acoustics interact with the flamefront and the attendant hydrodynamic flamefront cellular instability. This in turn affects the subsequent flame morphology and propagation speed. It is shown that the acoustics modify the power-law flame acceleration, concomitantly facilitating or inhibiting the transition to detonation in confinement, which allows reconciliation of a discrepancy in experimental measurements of different groups.
On syntheses of the X-ray background with power-law sources
NASA Technical Reports Server (NTRS)
Dezotti, G.; Boldt, E. A.; Cavaliere, A.; Danese, L.; Franceschini, A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.
1981-01-01
The conditions under which the combined emission from power law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit sleeper spectra at higher energies.
Transport ac loss of elliptical thin strips with a power-law E(J) relation
NASA Astrophysics Data System (ADS)
Jia, Chen-Xi; Chen, Du-Xing; Li, Shuo; Fang, Jin
2015-10-01
The transport ac loss Q of an elliptical thin strip of critical current I c with a power-law relation E\\propto {J}n is accurately computed as a function of current amplitude I m and frequency f. The resulting Q({I}m) is normalized to q({i}m) following the Norris critical-state formula, and converted to {q}*({i}m*) at a critical frequency f c based on a transport scaling law. Having a set of {q}*({i}m*) at several values of n as a base, a general expression of {q}*({i}m*,n) is obtained, which can be used to easily calculate q({i}m) for any practical purposes.
Monaghan, Padraic; Shillcock, Richard C.; Christiansen, Morten H.; Kirby, Simon
2014-01-01
It is a long established convention that the relationship between sounds and meanings of words is essentially arbitrary—typically the sound of a word gives no hint of its meaning. However, there are numerous reported instances of systematic sound–meaning mappings in language, and this systematicity has been claimed to be important for early language development. In a large-scale corpus analysis of English, we show that sound–meaning mappings are more systematic than would be expected by chance. Furthermore, this systematicity is more pronounced for words involved in the early stages of language acquisition and reduces in later vocabulary development. We propose that the vocabulary is structured to enable systematicity in early language learning to promote language acquisition, while also incorporating arbitrariness for later language in order to facilitate communicative expressivity and efficiency. PMID:25092667
Musical rhythm spectra from Bach to Joplin obey a 1/f power law.
Levitin, Daniel J; Chordia, Parag; Menon, Vinod
2012-03-01
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/f(β) power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
NASA Technical Reports Server (NTRS)
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Dipole-dipole interactions in optical lattices do not follow an inverse cube power law
NASA Astrophysics Data System (ADS)
Wall, M. L.; Carr, L. D.
2013-12-01
We study the effective dipole-dipole interactions in ultracold quantum gases on optical lattices as a function of asymmetry in confinement along the principal axes of the lattice. In particular, we study the matrix elements of the dipole-dipole interaction in the basis of lowest band Wannier functions which serve as a set of low-energy states for many-body physics on the lattice. We demonstrate that, for shallow lattices in quasi-reduced dimensional scenarios, the effective interaction between dipoles in an optical lattice is non-algebraic in the inter-particle separation at short to medium distance on the lattice scale and has a long-range power-law tail, in contrast to the pure power-law behavior of the dipole-dipole interaction in free space. The modifications to the free-space interaction can be sizable; we identify differences of up to 36% from the free-space interaction at the nearest-neighbor distance in quasi-one-dimensional arrangements. The interaction difference depends essentially on asymmetry in confinement, due to the d-wave anisotropy of the dipole-dipole interaction. Our results do not depend on statistics, applying to both dipolar Bose-Einstein condensates and degenerate Fermi gases. Using matrix product state simulations, we demonstrate that use of the correct lattice dipolar interaction leads to significant deviations from many-body predictions using the free-space interaction. Our results are relevant to up and coming experiments with ultracold heteronuclear molecules, Rydberg atoms and strongly magnetic atoms in optical lattices.
Caduff, Marloes; Huijbregts, Mark A J; Althaus, Hans-Joerg; Hendriks, A Jan
2011-01-15
To perform life-cycle assessment studies, data on the production and use of the products is required. However, often only few data or measurements are available. Estimation of properties can be performed by applying scaling relationships. In many disciplines, they are used to either predict data or to search for underlying patterns, but they have not been considered in the context of product assessments hitherto. The goal of this study was to explore size scaling for commonly used energy conversion equipment, that is, boilers, engines, and generators. The variables mass M, fuel consumption Q, and costs C were related to power P. The established power-law relationships were M = 10(0.73.. 1.89)P(0.64.. 1.23) (R(2) ≥ 0.94), Q = 10(0.06.. 0.68)P(0.82.. 1.02) (R(2) ≥ 0.98) and C = 10(2.46.. 2.86)P(0.83.. 0.85) (R(2) ≥ 0.83). Mass versus power and costs versus power showed that none of the equipment types scaled isometrically, that is, with a slope of 1. Fuel consumption versus power scaled approximately isometrically for steam boilers, the other equipments scaled significantly lower than 1. This nonlinear scaling behavior induces a significant size effect. The power laws we established can be applied to scale the mass, fuel consumption and costs of energy conversion equipments up or down. Our findings suggest that empirical scaling laws can be used to estimate properties, particularly relevant in studies focusing on early product development for which generally only little information is available. PMID:21133374
Caduff, Marloes; Huijbregts, Mark A J; Althaus, Hans-Joerg; Hendriks, A Jan
2011-01-15
To perform life-cycle assessment studies, data on the production and use of the products is required. However, often only few data or measurements are available. Estimation of properties can be performed by applying scaling relationships. In many disciplines, they are used to either predict data or to search for underlying patterns, but they have not been considered in the context of product assessments hitherto. The goal of this study was to explore size scaling for commonly used energy conversion equipment, that is, boilers, engines, and generators. The variables mass M, fuel consumption Q, and costs C were related to power P. The established power-law relationships were M = 10(0.73.. 1.89)P(0.64.. 1.23) (R(2) ≥ 0.94), Q = 10(0.06.. 0.68)P(0.82.. 1.02) (R(2) ≥ 0.98) and C = 10(2.46.. 2.86)P(0.83.. 0.85) (R(2) ≥ 0.83). Mass versus power and costs versus power showed that none of the equipment types scaled isometrically, that is, with a slope of 1. Fuel consumption versus power scaled approximately isometrically for steam boilers, the other equipments scaled significantly lower than 1. This nonlinear scaling behavior induces a significant size effect. The power laws we established can be applied to scale the mass, fuel consumption and costs of energy conversion equipments up or down. Our findings suggest that empirical scaling laws can be used to estimate properties, particularly relevant in studies focusing on early product development for which generally only little information is available.
A Hard X-Ray Power-law Spectral Cutoff in Centaurus X-4
NASA Astrophysics Data System (ADS)
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
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.
Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons
Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves
2009-01-01
Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it 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
Fatigue crack propagation rates in PMMA bone cement cannot be reduced to a single power law.
Race, Amos; Mann, Kenneth A
2008-07-01
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.
Supernova blast waves in wind-blown bubbles, turbulent, and power-law ambient media
NASA Astrophysics Data System (ADS)
Haid, S.; Walch, S.; Naab, T.; Seifried, D.; Mackey, J.; Gatto, A.
2016-08-01
Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media (densities of 0.1 ≥ n0 [cm- 3] ≥ 100) with uniform (and with stellar wind blown bubbles), power-law, and turbulent (Mach numbers M from 1to100) density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with n(r) ˜ r-2 (for n(r) > nfloor) the amount of momentum injection is solely regulated by the background density nfloor and compares to nuni = nfloor. However, in turbulent ambient media with lognormal density distributions the momentum input can increase by a factor of 2 (compared to the homogeneous case) for high Mach numbers. The average momentum boost can be approximated as p_{turb}/{p_{{0}}} =23.07 (n_{{0,turb}}/1 cm^{-3})^{-0.12} + 0.82 (ln (1+b2{M}2))^{1.49}(n_{{0,turb}}/1 cm^{-3})^{-1.6}. The velocity distributions are broad as gas can be accelerated to high velocities in low-density channels. The model values agree with results from recent, computationally expensive, three-dimensional simulations of SN explosions in turbulent media.
From the Cover: Musical rhythm spectra from Bach to Joplin obey a 1/f power law
NASA Astrophysics Data System (ADS)
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-03-01
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.
Undersampling power-law size distributions: effect on the assessment of extreme natural hazards
Geist, Eric L.; Parsons, Thomas E.
2014-01-01
The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and by attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historic data.
Effective power-law dependence of Lyapunov exponents on the central mass in galaxies
NASA Astrophysics Data System (ADS)
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-04-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L ∝ mp between the mean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p ≈ 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q ≈ 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x1 family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution ofx galaxies are discussed.
A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4
Chakrabarty, Deepto; Nowak, Michael A.; Tomsick, John A.; Boggs, Steven E.; Craig, William W.; Grefenstette, Brian W.; Fürst, Felix; Harrison, Fiona A.; Rana, Vikram; Psaltis, Dimitrios; Bachetti, Matteo; Barret, Didier; Christensen, Finn E.; Hailey, Charles J.; Kaspi, Victoria M.; Miller, Jon M.; Stern, Daniel; Wik, Daniel R.; Zhang, William W.; Wilms, Jörn
2014-12-20
The low-mass X-ray binary (LMXB) Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1×10{sup 33} D{sub kpc}{sup 2} erg s{sup –1}, with ≅60% in the thermal component. We clearly detect a cutoff of the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. We show that thermal Comptonization and synchrotron shock origins for the hard X-ray emission are ruled out on physical grounds. However, the hard X-ray spectrum is well fit by a thermal bremsstrahlung model with kT{sub e} = 18 keV, which can be understood as arising either in a hot layer above the neutron star atmosphere or in a radiatively inefficient accretion flow. The power-law cutoff energy may be set by the degree of Compton cooling of the bremsstrahlung electrons by thermal seed photons from the neutron star surface. Lower thermal luminosities should lead to higher (possibly undetectable) cutoff energies. We compare Cen X-4's behavior with PSR J1023+0038, IGR J18245–2452, and XSS J12270–4859, which have shown transitions between LMXB and radio pulsar modes at a similar X-ray luminosity.
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
El Boustani, Sami; Marre, Olivier; Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves
2009-09-01
Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m) activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m) reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the "effective" connectivity responsible for the dynamical signature of the population signals measured
NASA Astrophysics Data System (ADS)
Takahashi, Ryosuke; Okajima, Takaharu
2016-08-01
We investigated how stress relaxation mapping is quantified compared with the force modulation mapping of confluent epithelial cells using atomic force microscopy (AFM). Using a multi-frequency AFM technique, we estimated the power-law rheological behaviors of cells simultaneously in time and frequency domains. When the power-law exponent α was low (<0.1), the α values were almost the same in time and frequency domains. On the other hand, we found that at the high values (α > 0.1), α in the time domain was underestimated relative to that in the frequency domain, and the difference increased with α, whereas the cell modulus was overestimated in the time domain. These results indicate that power-law rheological parameters estimated by stress relaxation are sensitive to lag time during initial indentation, which is inevitable in time-domain AFM experiments.
A growth model for directed complex networks with power-law shape in the out-degree distribution.
Esquivel-Gómez, J; Stevens-Navarro, E; Pineda-Rico, U; Acosta-Elias, J
2015-01-01
Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141
A growth model for directed complex networks with power-law shape in the out-degree distribution
Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.
2015-01-01
Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141
Gong Jingyu; Du Jiulin
2012-06-15
We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on both the secondary emitted electron flux and the dust charging currents, and this effect depends strongly on the ratio of the electrostatic potential energy of the primary electrons at the dust grain's surface to the thermodynamic energy, implying that a competition in the dusty plasma between these two energies plays a crucial role in this novel effect.
Effect of buoyancy-assisted flow on convection from an isothermal spheroid in power-law fluids
NASA Astrophysics Data System (ADS)
Gupta, Anoop K.; Chhabra, Rajendra Prasad
2016-05-01
In this work, the coupled momentum and energy equations have been solved to elucidate the effect of aiding-buoyancy on the laminar mixed-convection from a spheroidal particle in power-law media over wide ranges of the pertinent parameters: Richardson number, 0≤ Ri≤5; Reynolds number, 1≤ Re≤100; Prandtl number, 1≤ Pr≤100; power-law index, 0.3≤ n≤1.8, and aspect ratio, 0.2≤ e≤5 for the case of constant thermo-physical properties. New results for the velocity and temperature fields are discussed in terms of the streamline and isotherm contours, surface pressure and vorticity contours, drag coefficient, local and surface averaged Nusselt number. The effect of particle shape on the flow is seen to be more pronounced in the case of oblates ( e < 1) than that for prolates ( e > 1). The propensity for wake formation reduces with the rising values of power-law index, Richardson number and slenderness of the body shape ( e > 1). Also, the drag coefficient is seen to increase with the Richardson number and power-law index. All else being equal, the Nusselt number shows a positive dependence on the Richardson number and Reynolds number and an inverse dependence on the power-law index and aspect ratio of the spheroid. Limited results were also obtained by considering the exponential temperature dependence of the power-law consistency index. This factor can increase the values of the average Nusselt number by up to ~10-12% with reference to the corresponding values for the case of the constant thermo-physical properties under otherwise identical conditions. Finally, the present values of the Nusselt number have been consolidated in the form of Colburn j-factor as a function of the modified Reynolds and Prandtl numbers for each value of the aspect ratio ( e). The effect of the temperature dependent viscosity is included in this correlation in terms of a multiplication factor.
A simple marriage model for the power-law behaviour in the frequency distributions of family names
NASA Astrophysics Data System (ADS)
Wu, Hao-Yun; Chou, Chung-I.; Tseng, Jie-Jun
2011-01-01
In many countries, the frequency distributions of family names are found to decay as a power law with an exponent ranging from 1.0 to 2.2. In this work, we propose a simple marriage model which can reproduce this power-law behaviour. Our model, based on the evolution of families, consists of the growth of big families and the formation of new families. Preliminary results from the model show that the name distributions are in good agreement with empirical data from Taiwan and Norway.
NASA Astrophysics Data System (ADS)
Grabski, Jakub Krzysztof; Kołodziej, Jan Adam
2016-06-01
In the paper an analysis of fluid flow and heat transfer of a power-law fluid in an internally finned tube with different fin length is conducted. Nonlinear momentum equation of a power-law fluid flow and nonlinear energy equation are solved using the Picard iteration method. Then on each iteration step the solution of inhomogeneous equation consists of two parts: the general solution and the particular solution. Firstly the particular solution is obtained by interpolation of the inhomogeneous term by means of the radial basis functions and monomials. Then the general solution is obtained using the method of fundamental solutions and by fulfilling boundary conditions.
NASA Astrophysics Data System (ADS)
Garanina, O. S.; Romanovsky, M. Yu.
2015-06-01
A multi-parametric family of exponential distributions with various power law tails is introduced and is shown to describe adequately the known distributions of incomes and wealth as well as the recently measured distributions of new car sales. The three or four-parametric families are characterized by effective temperature in the exponential part, the power exponent in the power-law asymptotic part, the coefficient for the transition between the above two parts, and the starting value, if it is not equal to zero. Since the new car sales distributions are found to correspond to known distributions of incomes, the latter may be inferred from the former.
Evidence for two hard X-ray components in double power-law fits to the 1980 June 7 flare
NASA Technical Reports Server (NTRS)
Smith, Dean F.; Orwig, Larry E.
1988-01-01
The June 7, 1980 flare at 0312 UT was analyzed with double power-law fits on the basis of SMM hard X-ray burst spectrometer data. The flare is found to consist of seven peaks of characteristic time scale of about 8 sec followed by seven valleys which may contain significant peak components because of overlap. It is suggested that the possibility of thermal spectra for the peaks is unlikely. An investigation of the double power-law parameters through the third and fourth peaks revealed a hysteresis effect in the fourth peak. The present results have been interpreted in terms of a trap plus precipitation model.
NASA Astrophysics Data System (ADS)
Arefi, Mohammad; Nahas, Iman; Abedi, Majid
2015-12-01
Thermo-mechanical analysis of the functionally graded orthotropic rotating hollow structures, subjected to thermo-mechanical loadings is studied in this paper. The relations were derived for both plane strain and plane stress conditions as a cylinder and disk, respectively. Non homogeneity was considered arbitrary through thickness direction for all mechanical and thermal properties. The responses of the system including temperature distribution, radial displacement and radial and circumferential stresses were derived in the general state. As case study, power law gradation was assumed for functionally graded cylinder and the mentioned results were evaluated in terms of parameters of the system such as non-homogeneous index and angular velocity.
NASA Astrophysics Data System (ADS)
Blackmon, Fletcher A.
1992-04-01
It is a general purpose and object of the present invention to provide an arbitrary waveform generator. It is a further object that the generator has the ability to produce both pulse waveforms and continuous waveforms. Other objects are that the generator be compact and only require low power for lending itself to battery powered operation. These objects are accomplished with the present invention by providing a system in which digital waveforms are created using a software package such as DADiSP. The software package forms signals that are then transferred to an EPROM. Each signal type occupies a certain block of address space within the EPROM. A great number of signals may be digitally stored in this way. The operator then constructs simple microprocessor computer codes to access any signal, any combination of signals, or all signals to form a unique waveform generation sequence. Therefore the operator selects arbitrarily which of the previously stored signals to generate. Key features include the EPROM storing a single pulse for pulse waveforms and a single period of waveform for continuous waveforms. Other key features are the ability to control the sequence of generation, the number of times each signal is generated, the time between pulses, and the time between the generation of different signal types. These features are controlled by the microprocessor codes residing in a microprocessor.
Spectral methods on arbitrary grids
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Gottlieb, David
1995-01-01
Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.
Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements
Mukherjee, Suvodip; Das, Santanu; Souradeep, Tarun; Joy, Minu E-mail: santanud@iucaa.ernet.in E-mail: tarun@iucaa.ernet.in
2015-01-01
Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m{sub eff} for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation ν{sub t} and change in spectral index for scalar perturbation ν{sub st} to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of n{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.
The Causal Connection Between Disc and Power-Law Variability in Hard State Black Hole X-Ray Binaries
NASA Technical Reports Server (NTRS)
Uttley, P.; Wilkinson, T.; Cassatella, P.; Wilms, J.; Pottschimdt, K.; Hanke, M.; Boeck, M.
2010-01-01
We use the XMM-Newton EPIC-pn instrument in timing mode to extend spectral time-lag studies of hard state black hole X-ray binaries into the soft X-ray band. \\Ve show that variations of the disc blackbody emission substantially lead variations in the power-law emission, by tenths of a second on variability time-scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time-delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time-scales less than a second the disc lags the power-law variations by a few ms, consistent with the disc variations being dominated by X-ray heating by the power-law, with the short lag corresponding to the light-travel time between the power-law emitting region and the disc. Our results indicate that instabilities in the accretion disc are responsible for continuum variability on time-scales of seconds or longer and probably also on shorter time-scales.
NASA Astrophysics Data System (ADS)
Debnath, P. K.; Chakrabarti, Barnali
2010-10-01
We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.80.1576 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of (1-(A)/(Acr)), A is the number of condensate atoms and Acr is the critical number near collapse. We observe that the power-law exponent becomes (1)/(6) in our calculation for the pure harmonic trap and it becomes (1)/(7), for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.
Debnath, P. K.; Chakrabarti, Barnali
2010-10-15
We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett. 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of (1-(A/A{sub cr})), A is the number of condensate atoms and A{sub cr} is the critical number near collapse. We observe that the power-law exponent becomes (1/6) in our calculation for the pure harmonic trap and it becomes (1/7), for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.
EVIDENCE FOR DEPARTURE FROM A POWER-LAW FLARE SIZE DISTRIBUTION FOR A SMALL SOLAR ACTIVE REGION
Wheatland, M. S.
2010-02-20
Active region 11029 was a small, highly flare-productive solar active region observed at a time of extremely low solar activity. The region produced only small flares: the largest of the >70 Geostationary Observational Environmental Satellite (GOES) events for the region has a peak 1-8 A flux of 2.2 x 10{sup -6} W m{sup -2} (GOES C2.2). The background-subtracted GOES peak-flux distribution suggests departure from power-law behavior above 10{sup -6} W m{sup -2}, and a Bayesian model comparison strongly favors a power-law plus rollover model for the distribution over a simple power-law model. The departure from the power law is attributed to this small active region having a finite amount of energy. The rate of flaring in the region varies with time, becoming very high for 2 days coinciding with the onset of an increase in complexity of the photospheric magnetic field. The observed waiting-time distribution for events is consistent with a piecewise-constant Poisson model. These results present challenges for models of flare statistics and of energy balance in solar active regions.
Houel, Julien; Doan, Quang T; Cajgfinger, Thomas; Ledoux, Gilles; Amans, David; Aubret, Antoine; Dominjon, Agnès; Ferriol, Sylvain; Barbier, Rémi; Nasilowski, Michel; Lhuillier, Emmanuel; Dubertret, Benoît; Dujardin, Christophe; Kulzer, Florian
2015-01-27
We present an unbiased and robust analysis method for power-law blinking statistics in the photoluminescence of single nanoemitters, allowing us to extract both the bright- and dark-state power-law exponents from the emitters' intensity autocorrelation functions. As opposed to the widely used threshold method, our technique therefore does not require discriminating the emission levels of bright and dark states in the experimental intensity timetraces. We rely on the simultaneous recording of 450 emission timetraces of single CdSe/CdS core/shell quantum dots at a frame rate of 250 Hz with single photon sensitivity. Under these conditions, our approach can determine ON and OFF power-law exponents with a precision of 3% from a comparison to numerical simulations, even for shot-noise-dominated emission signals with an average intensity below 1 photon per frame and per quantum dot. These capabilities pave the way for the unbiased, threshold-free determination of blinking power-law exponents at the microsecond time scale.
A graph-dynamic model of the power law of practice and the problem-solving fan-effect.
Shrager, J; Hogg, T; Huberman, B A
1988-10-21
Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically. PMID:3175664
NASA Astrophysics Data System (ADS)
Xu, Dandan; Sluse, Dominique; Schneider, Peter; Springel, Volker; Vogelsberger, Mark; Nelson, Dylan; Hernquist, Lars
2016-02-01
A power-law density model, i.e. ρ (r) ∝ r^{-γ ^' }}, has been commonly employed in strong gravitational lensing studies, including the so-called time-delay technique used to infer the Hubble constant H0. However, since the radial scale at which strong lensing features are formed corresponds to the transition from the dominance of baryonic matter to dark matter, there is no known reason why galaxies should follow a power law in density. The assumption of a power law artificially breaks the mass-sheet degeneracy, a well-known invariance transformation in gravitational lensing which affects the product of Hubble constant and time delay and can therefore cause a bias in the determination of H0 from the time-delay technique. In this paper, we use the Illustris hydrodynamical simulations to estimate the amplitude of this bias, and to understand how it is related to observational properties of galaxies. Investigating a large sample of Illustris galaxies that have velocity dispersion σSIE ≥ 160 km s-1 at redshifts below z = 1, we find that the bias on H0 introduced by the power-law assumption can reach 20-50 per cent, with a scatter of 10-30 per cent (rms). However, we find that by selecting galaxies with an inferred power-law model slope close to isothermal, it is possible to reduce the bias on H0 to ≲ 5 per cent and the scatter to ≲ 10 per cent. This could potentially be used to form less biased statistical samples for H0 measurements in the upcoming large survey era.
Arata, Yukinobu; Takagi, Hiroaki; Sako, Yasushi; Sawa, Hitoshi
2015-01-01
Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and <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
2014-01-01
Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and <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.
Higher-order analysis of crack tip fields in elastic power-law hardening materials
NASA Astrophysics Data System (ADS)
Xia, L.; Wang, T. C.; Shih, C. F.
1993-04-01
A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode I. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.
Power-law Optical Conductivity from Unparticles: Application to the Cuprates
NASA Astrophysics Data System (ADS)
Limtragool, Kridsanaphong; Phillips, Philip
We calculate the optical conductivity using several models for unparticle or scale-invariant matter. Within a Gaussian action for unparticles that is gauged with Wilson lines, we find that the conductivity computed from the Kubo formalism with vertex corrections yields no non-trivial deviation from the free-theory result. This result obtains because at the Gaussian level, unparticles are just a superposition of particle fields and hence any transport property must be consistent with free theory. Beyond the Gaussian approach, we adopt the continuous mass formulation of unparticles and calculate the Drude conductivity directly. We show that unparticles in this context can be tailored to yield an algebraic conductivity that scales as ω - 2 / 3 with the associated phase angle between the imaginary and real parts of arctanσ2/σ1 =60° as is seen in the cuprates. Our results indicate that at each frequency in the scaling regime, excitations on all energy scales contribute. Hence, incoherence is at the heart of the power-law in the optical conductivity in strongly correlated systems such as the cuprates. We thank NSF DMR-1461952 for partial funding of this project. KL is supported by a scholarship from the Ministry of Science and Technology, Royal Thai Government. PP thanks the Guggenheim Foundation for a 2015-2016 Fellowship.
Can log-periodic power law structures arise from random fluctuations?
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Leker, Jens
2014-05-01
Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable LPPL structures. To this end, we first estimate the stochastic process underlying the DAX log-returns during the period from mid-1997 until end-2003. The employed data set contains about 3.93ṡ106 intraday DAX quotes at a sampling rate of 15 s. Our results indicate that the DAX log-returns can be described as a Markov process. As a consequence, a Langevin equation is derived. Based on this model equation, we run extensive simulations in order to generate 100 synthetic DAX trajectories each covering 3000 trading days. We find LPPL behavior in ten artificial time series. Moreover, we can establish a link between LPPL patterns and ensuing bubble bursts in seven synthetic 600-week windows. However, the LPPL components in most synthetic trajectories differ fundamentally from those LPPL structures that have previously been detected in real financial time series. Summarized, this paper demonstrates that LPPL structures are not necessarily the signature of imitative behavior among investors but can also stem from noise, even though the likelihood of this is extremely low. Thus, our findings confirm with high statistical confidence that the LPPL structures in the DAX development are rooted deeper than only in the random fluctuations of the German stock market.
A Recommended Procedure for Estimating the Cosmic Ray Spectral Parameter of a Simple Power Law
NASA Technical Reports Server (NTRS)
Howell, Leonard W.; Rose, M. Franklin (Technical Monitor)
2000-01-01
A simple power law model consisting of a single spectral index a(f(sub i)) is believed to be an adequate description of the galactic cosmic ray (GQ proton flux at energies below 1013 eV. Two procedures for estimating a(f(sub i)), referred as (1) the method of moments, and (2) maximum likelihood, are developed and their statistical performance compared. I concluded that the maximum likelihood procedure attains the most desirable statistical properties and is hence the recommended statistic estimation procedure for estimating a1. The maximum likelihood procedure is then generalized for application to a set of real cosmic ray data and thereby makes this approach applicable to existing cosmic ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution, as well as inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic ray detector because they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose practical limits to the design envelope.
Two-dimensional magnetic cluster growth with a power law interaction
NASA Astrophysics Data System (ADS)
Xu, Xiaojun; Wu, Yiqi; Ye, Gaoxiang
2008-03-01
A two-dimensional cluster model in which the morphology of clusters depends on power-law magnetic interactions that decay with distance r as a r- α law is introduced. The growth algorithm is a generalization of diffusion-limited aggregation (DLA) model. The particles with spin degree diffuse on a square lattice and each spin is allowed to flip under a Monte Carlo probability. The simulation shows that, for the antiferromagnetic coupling, the spins of the particles in clusters tend to be oriented alternately. For the ferromagnetic coupling, however, the spin distribution depends on the exponent α: for large value of α, domains with different sizes are observed in the clusters; while for small α, during the earlier stage of the growth process, the clusters exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the clusters, the spin states of all particles are similar. The magnetization and system energy of the clusters as well as their evolutions with the growth parameters are also studied in detail.
Interim Report on the Power Law Index of Interplanetary Suprathermal Ion Spectra
Hill, M. E.; Hamilton, D. C.
2010-12-30
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.
Power-law scaling and fractal nature of medium-range order in metallic glasses.
Ma, D; Stoica, A D; Wang, X-L
2009-01-01
The atomic structure of metallic glasses has been a long-standing scientific problem. Unlike crystalline metals, where long-range ordering is established by periodic stacking of fundamental building blocks known as unit cells, a metallic glass has no long-range translational or orientational order, although some degrees of short- and medium-range order do exist. Previous studies have identified solute- (minority atom)-centred clusters as the fundamental building blocks or short-range order in metallic glasses. Idealized cluster packing schemes, such as efficient cluster packing on a cubic lattice and icosahedral packing as in a quasicrystal, have been proposed and provided first insights on the medium-range order in metallic glasses. However, these packing schemes break down beyond a length scale of a few clusters. Here, on the basis of neutron and X-ray diffraction experiments, we propose a new packing scheme-self-similar packing of atomic clusters. We show that the medium-range order has the characteristics of a fractal network with a dimension of 2.31, and is described by a power-law correlation function over the medium-range length scale. Our finding provides a new perspective of order in disordered materials and has broad implications for understanding their structure-property relationship, particularly those involving a change in length scales.
Apparent power-law distributions in animal movements can arise from intraspecific interactions
Breed, Greg A.; Severns, Paul M.; Edwards, Andrew M.
2015-01-01
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
Observation of a power-law energy distribution in atom-ion hybrid system
NASA Astrophysics Data System (ADS)
Meir, Ziv; Akerman, Nitzan; Sikorsky, Tomas; Ben-Shlomi, Ruti; Dallal, Yehonatan; Ozeri, Roee
2016-05-01
Understanding atom-ion collision dynamics is at the heart of the growing field of ultra-cold atom-ion physics. The naive picture of a hot ion sympathetically-cooled by a cold atomic bath doesn't hold due to the time dependent potentials generated by the ion Paul trap. The energy scale of the atom-ion system is determined by a combination of the atomic bath temperature, the ion's excess micromotion (EMM) and the back action of the atom-ion attraction on the ion's position in the trap. However, it is the position dependent ion's inherent micromotion which acts as an amplifier for the ion's energy during random consecutive collisions. Due to this reason, the ion's energy distribution deviates from Maxwell-Boltzmann (MB) characterized by an exponential tail to one with power-law tail described by Tsallis q-exponential function. Here we report on the observation of a strong deviation from MB to Tsallis energy distribution of a trapped ion. In our experiment, a ground-state cooled 88 Sr+ ion is immersed in an ultra-cold cloud of 87 Rb atoms. The energy scale is determined by either EMM or solely due to the back action on the ion position during a collision with an atom in the trap. Energy distributions are obtained using narrow optical clock spectroscopy.
Slip development and instability on a nonuniformly loaded interface with power-law slip-weakening
NASA Astrophysics Data System (ADS)
Rice, James R.; Uenishi, Koji
2003-03-01
We study rupture instability on a planar interface subjected to a locally peaked stress that increases quasi-statically in time. The interface follows a nonlinear slip-weakening relation where the strength drop is proportional to (slip)^n. Such a form with n 0.2-0.4 has been inferred from seismological observations on the scaling of radiated energy with slip (Abercrombie and Rice, 2001, 2002) and similarly abrupt strength drops are found at slips greater than sub-mm range in experiments involving large rotary shear (Chambon et al., 2002; Tullis and Goldsby, 2002). We use a simple Rayleigh-Ritz method and also full numerical simulations. Results show there is no longer a universal nucleation length when n ne 1 and qualitative features of the slip development are controlled by n. If n < 2/3, instability occurs as soon as the peaked value of the loading reaches the strength. This is a prediction based on the power law starting at (slip) = 0^+ whereas the observational results correspond to slips beyond the sub-mm range.
The profound impact of negative power law noise on statistical estimation.
Reinhardt, Victor S
2010-01-01
This paper investigates the profound impact of negative power law (neg-p) noise - that is, noise with a power spectral density L(p)(f) proportional variant | f |(p) for p < 0 - on the ability of practical implementations of statistical estimation or fitting techniques, such as a least squares fit (LSQF) or a Kalman filter, to generate valid results. It demonstrates that such negp noise behaves more like systematic error than conventional noise, because neg-p noise is highly correlated, non-stationary, non-mean ergodic, and has an infinite correlation time tau(c). It is further demonstrated that stationary but correlated noise will also cause invalid estimation behavior when the condition T > tau(c) is not met, where T is the data collection interval for estimation. Thus, it is shown that neg-p noise, with its infinite Tau(c), can generate anomalous estimation results for all values of T, except in certain circumstances. A covariant theory is developed explaining much of this anomalous estimation behavior. However, simulations of the estimation behavior of neg-p noise demonstrate that the subject cannot be fully understood in terms of covariant theory or mean ergodicity. It is finally conjectured that one must investigate the variance ergodicity properties of neg-p noise through the use of 4th order correlation theory to fully explain such simulated behavior. PMID:20040429
A power-law rheology-based finite element model for single cell deformation.
Zhou, E H; Xu, F; Quek, S T; Lim, C T
2012-09-01
Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.
Cupid is Still Doomed: Overlapping Power Laws and the Stability of the Inner Uranian Satellites
NASA Astrophysics Data System (ADS)
French, Robert S.; Showalter, M. R.
2012-05-01
We have continued our exploration of the stability of the inner Uranian satellites (French & Showalter 2011, DDA abstract) using simulations based on recent observational data. We find that the moon subsets Cressida/Desdemona/Juliet and Cupid/Belinda/Perdita are unstable in isolation, crossing orbits in 106-107 years. The presence of the other inner moons reduces this time to 104-106 years. The stability of the inner moons is not changed by the presence of the five classical satellites but Perdita, a very small moon, has a surprisingly large effect on the stability of Cupid and Belinda. We extend the power law previously discovered by Duncan & Lissauer (1997, Icarus, 125, 1-12), in which the crossing time of a pair of moons can be predicted using multiple simulations with higher moon masses, to the case of two unstable moon pairs. We use this new formalism to predict the lifetimes of Cupid/Belinda and Cressida/Desdemona using a conservative density assumption, ρ=0.5 g/cm3. The inner satellites continue to exhibit instability with crossing times of 105-107 years in this case. Such short crossing times imply the continuing, rapid evolution of the Uranian satellites.
Thermodynamics of charged rotating dilaton black branes with power-law Maxwell field
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Sheykhi, A.; Dehghani, M. H.
2015-10-01
In this paper, we construct a new class of charged rotating dilaton black brane solutions, with a complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime, such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both the canonical and the grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of the Maxwell field on the thermal stability of the solutions. We find that, for α ≤ 1, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For α >1, the solutions can encounter an unstable phase depending on the metric parameters.
Wright, Christopher K
2010-07-01
Although habitat networks show promise for conservation planning at regional scales, their spatiotemporal dynamics have not been well studied, especially in climate-sensitive landscapes. Here I use satellite remote sensing to compile wetland habitat networks from the Prairie Pothole Region (PPR) of North America. An ensemble of networks assembled across a hydrologic gradient from deluge to drought and a range of representative dispersal distances exhibits power-law scaling of important topological parameters. Prairie wetland networks are "meso-worlds" with mean topological distance increasing faster with network size than small-world networks, but slower than a regular lattice (or "large world"). This scaling implies rapid dispersal through wetland networks without some of the risks associated with "small worlds" (e.g., extremely rapid propagation of disease or disturbance). Retrospective analysis of wetland networks establishes a climatic envelope for landscape connectivity in the PPR, where I show that a changing climate might severely impact metapopulation viability and restrict long-distance dispersal and range shifts. More generally, this study demonstrates an efficient approach to conservation planning at a level of abstraction addressing key drivers of the global biodiversity crisis: habitat fragmentation and climatic change.
Cascade model of gamma-ray bursts: Power-law and annihilation-line components
NASA Technical Reports Server (NTRS)
Harding, A. K.; Sturrock, P. A.; Daugherty, J. K.
1988-01-01
If, in a neutron star magnetosphere, an electron is accelerated to an energy of 10 to the 11th or 12th power eV by an electric field parallel to the magnetic field, motion of the electron along the curved field line leads to a cascade of gamma rays and electron-positron pairs. This process is believed to occur in radio pulsars and gamma ray burst sources. Results are presented from numerical simulations of the radiation and photon annihilation pair production processes, using a computer code previously developed for the study of radio pulsars. A range of values of initial energy of a primary electron was considered along with initial injection position, and magnetic dipole moment of the neutron star. The resulting spectra was found to exhibit complex forms that are typically power law over a substantial range of photon energy, and typically include a dip in the spectrum near the electron gyro-frequency at the injection point. The results of a number of models are compared with data for the 5 Mar., 1979 gamma ray burst. A good fit was found to the gamma ray part of the spectrum, including the equivalent width of the annihilation line.
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Denz, Cornelia
2013-09-01
We employ the log-periodic power law (LPPL) to analyze the late-2000 financial crisis from the perspective of critical phenomena. The main purpose of this study is to examine whether LPPL structures in the development of credit default swap (CDS) spreads can be used for default classification. Based on the different triggers of Bear Stearns’ near bankruptcy during the late-2000 financial crisis and Ford’s insolvency in 2009, this study provides a quantitative description of the mechanism behind bank runs. We apply the Johansen-Ledoit-Sornette (JLS) positive feedback model to explain the rise of financial institutions’ CDS spreads during the global financial crisis 2007-2009. This investigation is based on CDS spreads of 40 major banks over the period from June 2007 to April 2009 which includes a significant CDS spread increase. The qualitative data analysis indicates that the CDS spread variations have followed LPPL patterns during the global financial crisis. Furthermore, the univariate classification performances of seven LPPL parameters as default indicators are measured by Mann-Whitney U tests. The present study supports the hypothesis that discrete scale-invariance governs the dynamics of financial markets and suggests the application of new and fast updateable default indicators to capture the buildup of long-range correlations between creditors.
Disorder-driven transition in a chain with power-law hopping
NASA Astrophysics Data System (ADS)
Gärttner, M.; Syzranov, S. V.; Rey, A. M.; Gurarie, V.; Radzihovsky, L.
2015-07-01
We study a one-dimensional (1D) system with a power-law quasiparticle dispersion ∝|k| αs g n k in the presence of a short-range-correlated random potential, and demonstrate that for α <1 /2 it exhibits a disorder-driven quantum phase transition with critical properties similar to those of the localization transition near the edge of the band of a semiconductor in high dimensions, as studied recently [Phys. Rev. Lett. 114, 166601 (2015), 10.1103/PhysRevLett.114.166601; Phys. Rev. B 91, 035133 (2015), 10.1103/PhysRevB.91.035133]. Despite the absence of localization in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of α . The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localization effects and has the potential for experimental realizations in chains of ultracold atoms in optical traps.
Power Law Behavior and Self-Similarity in Modern Industrial Accidents
NASA Astrophysics Data System (ADS)
Lopes, António M.; Tenreiro Machado, J. A.
Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.
Analysis of log-periodic power law singularity patterns in time series related to credit risk
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Sornette, Didier
2015-04-01
The log-periodic (super-exponential) power law singularity (LPPLS) has become a promising tool for predicting extreme behavior of self-organizing systems in natural sciences and finance. Some researchers have recently proposed to employ the LPPLS on credit risk markets. The review article at hand summarizes four papers in this field and shows how they are linked. After structuring the research questions, we collect the corresponding answers from the four articles. This eventually gives us an overall picture of the application of the LPPLS to credit risk data. Our literature review begins with grounding the view that credit default swap (CDS) spreads are hotbeds for LPPLS patterns and it ends up with drawing attention to the recently proposed alarm index for the prediction of institutional bank runs. By presenting a new field of application for the LPPLS, the reviewed strand of literature further substantiates the LPPLS hypothesis. Moreover, the results suggest that CDS spread trajectories belong to a different universality class than, for instance, stock prices.
Vertical channel free convection for a power law fluid with a constant heat flux
Irvine, T.F. Jr.; Schneider, W.J.
1984-08-08
The development of free convection in a purely viscous non-newtonian fluid under the influence of a uniform wall heat flux is investigated. A finite difference solution is presented of the velocity and temperature profiles for the flow of an Ostwald-de Waele (power law) fluid between two symmetrically heated vertical plates. The flow, temperature and heat transfer characteristics of the channel are presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers and the fully developed flow range is established. The numerical solutions for the developing flow are shown to approach two classical asymptotes - fully developed duct free convection at low Rayleigh numbers and two independent vertical plates at high Rayleigh numbers. A comparison is made between the results of this theoretical investigation and previously published analytical and experimental work on newtonian and non-newtonian fluids. The results and their application to engineering problems are discussed. The changes caused by the addition of soluble substances to water cause significant variations in the mean flow between the plates and in the outlet temperature.
Wave-speed dispersion associated with an attenuation obeying a frequency power law.
Buckingham, Michael J
2015-11-01
An attenuation scaling as a power of frequency, |ω|(β), over an infinite bandwidth is neither analytic nor square-integrable, thus calling into question the application of the Kramers-Krönig dispersion relations for determining the frequency dependence of the associated phase speed. In this paper, three different approaches are developed, all of which return the dispersion formula for the wavenumber, K(ω). The first analysis relies on the properties of generalized functions and the causality requirement that the impulse response, k(t), the inverse Fourier transform of -iK(ω), must vanish for t < 0. Second, a wave equation is introduced that yields the phase-speed dispersion associated with a frequency-power-law attenuation. Finally, it is shown that, with minor modification, the Kramers-Krönig dispersion relations with no subtractions (the Plemelj formulas) do in fact hold for an attenuation scaling as |ω|(β), yielding the same dispersion formula as the other two derivations. From this dispersion formula, admissible values of the exponent β are established. Physically, the inadmissible values of β, which include all the integers, correspond to attenuation-dispersion pairs whose Fourier components cannot combine in such a way as to make the impulse response, k(t), vanish for t < 0. There is no upper or lower limit on the value that β may take.
Common origin of power-law tails in income distributions and relativistic gases
NASA Astrophysics Data System (ADS)
Modanese, G.
2016-01-01
Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms ("saving propensity") which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the macroscopic distribution for the income or respectively for the energy.
Electroosmotic Flow of Power-Law Fluids in a Cylindrical Microcapillary
NASA Astrophysics Data System (ADS)
Saidi, M. H.; Babaie, Ashkan; Sadeghi, Arman; Center of Excellence in Energy Conversion Team
2012-11-01
In biological applications where most fluids are considered to be non-Newtonian, Newtonian law of viscosity looks insufficient for describing the flow characteristics. In the present work, the electroosmotic flow of power-law fluids in a circular micro tube is investigated. The Poisson-Boltzmann equation for electrical potential is solved numerically in the complete form without using the Debye-Hückel approximation. The physical model includes the Joule heating and viscous dissipation effects. Once the momentum and energy equations are solved numerically, a parametric study is done to investigate the effects of different parameters such as flow behavior index, wall zeta potential and the Debye-Hückel parameter on thermal and hydrodynamic characteristics of the flow. Results show that based on the value of viscous dissipation and the Debye-Hückel parameter the non-Newtonian characteristics of the flow can lead to significant changes regarding to Newtonian behaviors. The provided results in this study would lead to accurate prediction of temperature of biofluids in Lab-on-a-chip devices which is vital for retaining samples in a healthy condition.
Random sampling of skewed distributions implies Taylor's power law of fluctuation scaling.
Cohen, Joel E; Xu, Meng
2015-06-23
Taylor's law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species' population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)(b), a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared. PMID:25852144
A unified econophysics explanation for the power-law exponents of stock market activity
NASA Astrophysics Data System (ADS)
Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, Eugene
2007-08-01
We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Daboul, Jamil
1995-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Nieto, M.M.; Daboul, J.
1994-07-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = {minus}{gamma}/r{sup {nu}}, {gamma} > 0 and {minus}{infinity} < {nu} < {infinity}. When the angular momentum is non-zero, these solutions lead to the classical orbits {rho}(t) = [cos {mu}({var_phi}(t) {minus} {var_phi}{sub 0}(t))]{sup 1/{mu}}, with {mu} = {nu}/2 {minus} 1 {ne} 0. For {nu} > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when {nu} > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed.
A Simple Arbitrary Solid Slicer
Yao, J
2005-06-23
The intersection of a given plane and an arbitrary (possibly non-convex, with multiple connectivities) meshed solid is exactly expressed by a set of planar cross-sections. A rule for marching on the edges of an arbitrary polyhedron is set for obtaining the topology of the cross-section. The method neither seeks triangulation of the surface mesh nor utilizes look-up tables, therefore it has optimal efficiency.
Slip Development and Instability on a Heterogeneously Loaded Fault with Power-Law Slip-Weakening
NASA Astrophysics Data System (ADS)
Rice, J. R.; Uenishi, K.
2002-12-01
We consider slip initiation and rupture instability on planar faults that follow a non-linear slip-weakening relation and are subjected to a locally peaked loading stress, the level of which changes quasi-statically in time. For the case in which strength weakens linearly with slip, Uenishi and Rice [2002] (http://esag.harvard.edu/uenishi/research/nl/nl.html) have shown there exists a universal length of the slipping region at instability, independent of any length scales entering into the description of the shape of the loading stress distribution. Here we study slip development and its (in)stability for a power-law slip-weakening relation, giving fault strength as τ = τ p - Aδn where τ p is the peak strength at which slip initiates, δ is the slip, and A is a constant. Such a form with n ≈ 0.2-0.4 has been inferred, for slips from 1 to 500 mm, as an interpretation of seismological observations on the scaling of radiated energy with slip [Abercrombie and Rice, EOS, 2001; SCEC, 2002]. It is also consistent with laboratory experiments involving large rotary shear [Chambon et al., GRL, 2002]. We first employed an energy approach to give a Rayleigh-Ritz approximation for the dependence of slipping length and maximum slip on the level and shape of the loading stress distribution. That was done for a loading stress distribution τ p + Rt - κ x2 / 2 where x is distance along the fault, κ is a constant, and Rt is the stress change from that for which the peak in the loading stress distribution equals the strength τ p. Results show there is no longer a universal nucleation length, independent of κ , when n != 1, and that qualitative features of the slip development are significantly controlled by n. We also obtained full numerical solutions for the slip development. Remarkably, predictions of the simple energy approach are in reasonable quantitative agreement with them and give all qualitative features correctly. Principal results are as follows: If n > 2/3, the
PLNoise: a package for exact numerical simulation of power-law noises
NASA Astrophysics Data System (ADS)
Milotti, Edoardo
2006-08-01
Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1<β⩽1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v1_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3
Why credit risk markets are predestined for exhibiting log-periodic power law structures
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Leker, Jens
2014-01-01
Recent research has established the existence of log-periodic power law (LPPL) patterns in financial institutions’ credit default swap (CDS) spreads. The main purpose of this paper is to clarify why credit risk markets are predestined for exhibiting LPPL structures. To this end, the credit risk prediction of two variants of logistic regression, i.e. polynomial logistic regression (PLR) and kernel logistic regression (KLR), are firstly compared to the standard logistic regression (SLR). In doing so, the question whether the performances of rating systems based on balance sheet ratios can be improved by nonlinear transformations of the explanatory variables is resolved. Building on the result that nonlinear balance sheet ratio transformations hardly improve the SLR’s predictive power in our case, we secondly compare the classification performance of a multivariate SLR to the discriminative powers of probabilities of default derived from three different capital market data, namely bonds, CDSs, and stocks. Benefiting from the prompt inclusion of relevant information, the capital market data in general and CDSs in particular increasingly outperform the SLR while approaching the time of the credit event. Due to the higher classification performances, it seems plausible for creditors to align their investment decisions with capital market-based default indicators, i.e., to imitate the aggregate opinion of the market participants. Since imitation is considered to be the source of LPPL structures in financial time series, it is highly plausible to scan CDS spread developments for LPPL patterns. By establishing LPPL patterns in governmental CDS spread trajectories of some European crisis countries, the LPPL’s application to credit risk markets is extended. This novel piece of evidence further strengthens the claim that credit risk markets are adequate breeding grounds for LPPL patterns.
Pulsatile flow of power-law fluid model for blood flow under periodic body acceleration.
Chaturani, P; Palanisamy, V
1990-01-01
A mathematical model has been proposed to study the pulsatile flow of a power-law fluid through rigid circular tubes under the influence of a periodic body acceleration. Numerical solutions have been obtained by using finite difference method. The accuracy of the numerical procedure has been checked by comparing the obtained numerical results with other numerical and analytical solutions. It is found that the agreement between them is quite good. Interaction of non-Newtonian nature of fluid with the body acceleration has been investigated by using the physiological data for two particular cases (coronary and femoral arteries). The axial velocity, fluid acceleration, wall shear stress and instantaneous volume flow rate have been computed and their variations with different parameters have been analyzed. The following important observations have been made: (i) The velocity and acceleration profiles can have more than one maxima, this is in contrast with usual parabolic profiles where they have only one maximum at the axis. As n increases, the maxima shift towards the axis; (ii) For the flow with no body acceleration, the amplitude of both, wall shear and flow rate, increases with n, whereas for the flow with body acceleration, the amplitude of wall shear (flow rate) increases (decreases) as n increases; (iii) In the absence of body acceleration, pseudoplastic (dilatant) fluids, with low frequency pulsations, have higher (lower) value of maximum flow rate Qmax than Newtonian fluids, whereas for high frequencies, opposite behavior has been observed; for flow with body acceleration pulsations gives higher (lower) value of Qmax for pseudoplastic (dilatant) fluids than Newtonian fluids.
Theory of Exploring the Dark Halo with Microlensing. I. Power-Law Models
NASA Astrophysics Data System (ADS)
Alcock, C.; Allsman, R. A.; Axelrod, T. S.; Bennett, D. P.; Cook, K. H.; Evans, N. W.; Freeman, K. C.; Griest, K.; Jijina, J.; Lehner, M.; Marshall, S. L.; Perlmutter, S.; Peterson, B. A.; Pratt, M. R.; Quinn, P. J.; Rodgers, A. W.; Stubbs, C. W.; Sutherland, W.; MACHO Collaboration
1995-08-01
If microlensing of stars by dark matter has been detected, then the way is open for the development of new methods in galactic astronomy. This series of papers investigates what microlensing can teach us about the structure and shape of the dark halo. In this paper we present formulae for the microlensing rate, optical depth, and event duration distributions for a simple set of axisymmetric disk-halo models. The halos are based on the "power-law models" of Evans which have simple velocity distributions. Using these models, we show that there is a large uncertainty in the predicted microlensing rate because of uncertainty in the halo parameters. For example, models which reproduce the measured galactic observables to within their errors still differ in microlensing rate toward the Magellanic Clouds by more than a factor of 10. We find that while the more easily computed optical depth correlates well with microlensing rate, the ratio of optical depth to rate can vary by a factor of 2 (or greater if the disk is maximal). Comparison of microlensing rates toward the Large and Small Magellanic Clouds (LMC and SMC) and M31 can be used to aid determinations of the halo flattening and rotation curve slope. For example, the ratio of microlensing rates toward the LMC and SMC is ˜0.7-0.8 for E0 halos and ˜1.0-1.2 for E7 halos. Once the flattening has been established, the ratio of microlensing rates toward M3 1 and the LMC may help to distinguish between models with rising, flat, or falling rotation curves. Comparison of rates along LMC and galactic bulge lines of sight gives useful information on the halo core radius, although this may not be so easy to extract in practice. Maximal disk models provide substantially smaller halo optical depths, shorter event durations, and even larger model uncertainties.
Propagation of Gravity Currents of non-Newtonian Power-Law Fluids in Porous Media
NASA Astrophysics Data System (ADS)
Di Federico, V.; Longo, S.; Ciriello, V.; Chiapponi, L.
2014-12-01
A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by k; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, α; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters ω and β. Scalings for current length and thickness are derived in self similar form coupling the modified Darcy's law accounting for the fluid rheology with the mass balance equation. The length, thickness, and aspect ratio of the current are studied as functions of model parameters; several different critical values of α emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times.
The origin of tablet boudinage: Results from experiments using power-law rock analogs
NASA Astrophysics Data System (ADS)
Zulauf, J.; Zulauf, G.; Kraus, R.; Gutiérrez-Alonso, G.; Zanella, F.
2011-10-01
We used power-law viscous plasticine ( n = ca. 7) as a rock analog to simulate boudinage of rocks undergoing dislocation creep and brittle fracture. A competent plasticine layer, oriented perpendicular to the main shortening direction, Z, underwent bulk pure flattening inside a less competent plasticine matrix. Computer tomographic analyses of the deformed samples revealed that boudinage results from an initial phase of viscous necking followed by tensile failure along the previously formed necks. The resulting boudins display a polygonal shape in plan-view and are referred to as 'tablet boudins' (in contrast to the square to rectangular shaped chocolate-tablet boudins). The ratio between the plan-view long and short axis, R, ranges from 1.2 to 2.6. The polygonal, non-isometric shape of the tablet boudins can be explained by the strong interaction of concentric and radial tensile fractures. With increasing layer thickness, Hi, the mean diameter of the boudin tablets, Wa, increases, while the number of boudins, N, decreases. Progressive finite strain results in a higher number of the boudins and a smaller mean diameter. The thickness of the boudins, Hf, is almost the same as the initial layer thickness, Hi, while the aspect ratio ( Wd = Wa / Hf) decreases with layer thickness and finite strain. The mean Wd values obtained from all experiments span from ca. 4 to ca. 11. Tablet boudins, described in the present paper, have yet not been described from natural outcrops. The reasons might be that pure flattening strain is not common in nature, and the characterization and evaluation of tablet boudins requires geometrical analysis in three dimensions, which is a difficult task when such structures occur in nature.
Hubble Space Telescope Morphologies of z ~ 2 Dust Obscured Galaxies. I. Power-Law Sources
NASA Astrophysics Data System (ADS)
Bussmann, R. S.; Dey, Arjun; Lotz, J.; Armus, L.; Brand, K.; Brown, M. J. I.; Desai, V.; Eisenhardt, P.; Higdon, J.; Higdon, S.; Jannuzi, B. T.; Le Floc'h, E.; Melbourne, J.; Soifer, B. T.; Weedman, D.
2009-03-01
We present high-spatial resolution optical and near-infrared imaging obtained using the ACS, WFPC2, and NICMOS cameras aboard the Hubble Space Telescope of 31 24 μm bright z ≈ 2 Dust Obscured Galaxies (DOGs) identified in the Boötes Field of the NOAO Deep Wide-Field Survey. Although this subset of DOGs have mid-IR spectral energy distributions dominated by a power-law component suggestive of an AGN, all but one of the galaxies are spatially extended and not dominated by an unresolved component at rest-frame UV or optical wavelengths. The observed V - H and I-H colors of the extended components are 0.2-3 magnitudes redder than normal star-forming galaxies. All but one have axial ratios >0.3, making it unlikely that DOGs are composed of an edge-on star-forming disk. We model the spatially extended component of the surface brightness distributions of the DOGs with a Sérsic profile and find effective radii of 1-6 kpc. This sample of DOGs is smaller than most submillimeter galaxies (SMGs), but larger than quiescent high-redshift galaxies. Nonparametric measures (Gini and M20) of DOG morphologies suggest that these galaxies are more dynamically relaxed than local ULIRGs. We estimate lower limits to the stellar masses of DOGs based on the rest-frame optical photometry and find that these range from ~109-1011 M sun. If major mergers are the progenitors of DOGs, then these observations suggest that DOGs may represent a postmerger evolutionary stage.
Papadopoulos, Anthony
2009-01-01
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
Power laws and self-organized criticality in theory and nature
NASA Astrophysics Data System (ADS)
Marković, Dimitrije; Gros, Claudius
2014-03-01
Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real
Power-driven and adiabatic expansions into vacuum
NASA Astrophysics Data System (ADS)
Farnsworth, A. V., Jr.
1980-08-01
Analytical solutions are obtained for the planar, cylindrical, and spherical expansions into vacuum of matter initially concentrated at a plane, a line, or a point. Both power-driven and adiabatic expansions are considered, where in the power-driven case, the specific power is deposited uniformly in space, but may vary in time according to a power law. These problems are found to be self-similar. The non-self-similar motion of matter during the adiabatic expansion that follows a power pulse of finite duration has also been addressed and a solution has been obtained.
A MODEL FOR THE NON-UNIVERSAL POWER LAW OF THE SOLAR WIND SUB-ION-SCALE MAGNETIC SPECTRUM
Passot, T.; Sulem, P. L. E-mail: sulem@oca.eu
2015-10-20
A phenomenological turbulence model for kinetic Alfvén waves in a magnetized collisionless plasma that is able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere is presented. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition from large-scale weak turbulence to smaller scale strong turbulence is captured and nonlocal interactions, relevant in the case of steep spectra, are accounted for.
Cioslowski, Jerzy; Albin, Joanna
2013-09-14
Energies E(N) of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials vary in a convoluted fashion with the particle totalities N. Accurate rigorous upper bounds to these energies, which are amenable to detailed mathematical analysis, are found to comprise terms with smooth, oscillatory, and fluctuating dependences on N. The smooth energy component is obtained as a power series in N(-2/3) with the first two terms corresponding to the bulk and Madelung energies. The oscillatory component possesses the large-N asymptotics given by a product of N(1/(λ + 1)), where λ is the power-law exponent, and a function periodic in N(1/3). The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy E(Th)(n) on n, also scales like N(1/(λ + 1)).
Brey, J Javier; Ruiz-Montero, M J
2015-01-01
The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power-law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power-law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored.
NASA Astrophysics Data System (ADS)
Dessau, Daniel; Reber, Ted; Zhou, Xiaoqing; Plumb, Nick; Parham, Stephen; Waugh, Justin; Cao, Yue; Sun, Zhe; Li, Haoxiang; Wang, Qiang; Wen, J. S.; Xu, Z. J.; Gu, Genda; Yoshida, Y.; Eiaski, Hiroshi; Arnold, Gerald; University of Colorado, Boulder Team; Brookhaven National Labs Team; AIST, Tsukuba, Japan Team
Based upon detailed ARPES measurements of Bi2Sr2CaCu2O8 + δ over a wide range of doping levels, we present a new unifying phenomenology for the non-Fermi liquid normal-state interactions (scattering rates) in the nodal direction. This new phenomenology has a continuously varying power law exponent (hence named a Power Law Liquid or PLL), which with doping varies smoothly from a quadratic Fermi Liquid to a linear Marginal Fermi Liquid and beyond. Using the extracted PLL parameters we can calculate the optics and resistivity over a wide range of doping and normal-state temperature values, with the results closely matching the experimental curves. This agreement includes the presence of the T* ``pseudogap'' temperature scale observed in the resistivity curves including the apparent quantum critical point.
Freeman; Watkins; Riley
2000-12-01
We calculate the probability density functions P of burst energy e, duration T, and interburst interval tau for a known turbulent system in nature. Bursts in the Earth-Sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organized criticality (SOC). We find also a power-law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence.
Erbas, S.; Ece, M.C.
1999-07-01
Fluids such as molten plastics, polymers, pulps, foodstuffs or slurries exhibit non-Newtonian fluid behavior and are increasingly used in various manufacturing and processing industries. Determination of the friction and heat transfer characteristics of non-Newtonian fluids over heated surfaces is important for the design of industrial equipment working with this type of fluids. Steady free convection laminar boundary-layer flow along a heated vertical plate immersed in a quiescent power-law fluid is investigated. Two heating modes are considered by assuming that either surface temperature or heat flux has a power-law variation. Similarity solutions of the boundary-layer equations are obtained numerically for both heating conditions. The skin friction coefficient and Nusselt number are found to be higher in the prescribed temperature case for large Prandtl numbers and increase with the flow behavior index.
Takahashi, Ryosuke; Okajima, Takaharu
2015-10-26
We present multi-frequency force modulation atomic force microscopy (AFM) for mapping the complex shear modulus G* of living cells as a function of frequency over the range of 50–500 Hz in the same measurement time as the single-frequency force modulation measurement. The AFM technique enables us to reconstruct image maps of rheological parameters, which exhibit a frequency-dependent power-law behavior with respect to G{sup *}. These quantitative rheological measurements reveal a large spatial variation in G* in this frequency range for single cells. Moreover, we find that the reconstructed images of the power-law rheological parameters are much different from those obtained in force-curve or single-frequency force modulation measurements. This indicates that the former provide information about intracellular mechanical structures of the cells that are usually not resolved with the conventional force measurement methods.
Brey, J Javier; Ruiz-Montero, M J
2015-01-01
The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power-law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power-law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored. PMID:25679614
Wang, Zebin; Narsimhan, Ganesan
2006-08-01
A model for drainage of a power-law fluid through a Plateau border is proposed which accounts for the actual Plateau border geometry and interfacial mobility. The non-dimensionalized Navier-Stokes equations have been solved using finite element method to obtain the contours of velocity within the Plateau border cross section and average Plateau border velocity in terms of dimensionless inverse surface viscosity and power-law rheological parameters. The velocity coefficient, the correction for the average velocity through a Plateau border of actual geometry compared to that for a simplified circular geometry of the same area of cross section, was expressed as a function of dimensionless inverse surface viscosity and flow behavior index of the power-law fluid. The results of this improved model for Plateau border drainage were then incorporated in a previously developed foam drainage model [G. Narsimhan, J. Food Eng. 14 (1991) 139] to predict the evolution of liquid holdup profiles in a standing foam. Foam drainage was found to be slower for actual Plateau border cross section compared to circular geometry and faster for higher interfacial mobility and larger bubble size. Evolution of liquid holdup profiles in a standing foam formed by whipping and stabilized by 0.1% beta-lactoglobulin in the presence of xanthan gum when subjected to 16g and 45g centrifugal force fields was measured using magnetic resonance imaging for different xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Measured bubble size, surface shear viscosity of beta-lactoglobulin solutions and literature values of power-law parameters of xanthan gum solution were employed in the current model to predict the evolution of liquid holdup profile which compared well with the experimental data. Newtonian model for foam drainage for zero shear viscosity underpredicted drainage rates and did not agree with the experimental data. PMID
Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
Marshall, Najja; Timme, Nicholas M.; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M.
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of “neural avalanches” (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods—power-law fitting, avalanche shape collapse, and neural complexity—have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox. PMID:27445842
Eigenspectra and orders of stress singularity at a mode I crack tip for a power-law medium
NASA Astrophysics Data System (ADS)
Stepanova, Larisa
2008-01-01
In this Note eigenspectra and orders of singularity of the stress field near a mode I crack tip in a power-law material are discussed. The perturbation theory technique is employed to pose the required asymptotic solution. The whole set of eigenvalues is obtained. It is shown that the eigenvalues of the nonlinear problem are fully determined by the corresponding eigenvalues of the linear problem and by the hardening exponent. To cite this article: L. Stepanova, C. R. Mecanique 336 (2008).
Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox. PMID:27445842
On the extent of size range and power law scaling for particles of natural carbonate fault cores
NASA Astrophysics Data System (ADS)
Billi, Andrea
2007-09-01
To determine the size range and both type and extent of the scaling laws for particles of loose natural carbonate fault rocks, six granular fault cores from Mesozoic carbonate strata of central Italy were sampled. Particle size distributions of twelve samples were determined by combining sieving and sedimentation methods. Results show that, regardless of the fault geometry, kinematics, and tectonic history, the size of fault rock particles respects a power law distribution across approximately four orders of magnitude. The fractal dimension ( D) of the particle size distribution in the analysed samples ranges between ˜2.0 and ˜3.5. A lower bound to the power law trend is evident in all samples except in those with the highest D-values; in these samples, the smallest analysed particles (˜0.0005 mm in diameter) were also included in the power law interval, meaning that the lower size limit of the power law distribution decreases for increasing D-values and that smallest particles start to be comminuted with increasing strain (i.e. increasing fault displacement and D-values). For increasing D-values, also the largest particles tends to decrease in number, but this evidence may be affected by a censoring bias connected with the sample size. Stick-slip behaviour is suggested for the studied faults on the basis of the inferred particle size evolutions. Although further analyses are necessary to make the results of this study more generalizable, the preliminary definition of the scaling rules for fault rock particles may serve as a tool for predicting a large scale of fault rock particles once a limited range is known. In particular, data from this study may result useful as input numbers in numerical models addressing the packing of fault rock particles for frictional and hydraulic purposes.
Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T
2012-06-01
The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe. PMID:22712907
Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Dehghani, M. H.; Sheykhi, A.
2015-11-01
In this paper, we present a new class of higher-dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon.
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.
2015-10-01
We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.
NASA Astrophysics Data System (ADS)
Dorman, L. M.
2015-12-01
The seafloor plays an important role in the propagation ofseafloor noise because its low shear velocity forms a strongwaveguide and the high shear velocity gradient facilitatesconversion processes.In 2001 (JASA), O. A. Godin and D. M.F. Chapman studiedpropagation of interface (Scholte) waves in models with ashear speed profile with a power-law depth dependence.They analyzed of four datasets from shallow-watersites, which they fit well with two-parameter models.Furthermore, they show that for the exponent value of1/2, the mode wavefunctions are self-similar.Data from the deep seafloor from seafloor sources observedby Ocean-Bottom Seismographs frequently exhibit afundamental mode ending in an Airy phase with a frequencyof a few Hertz. This is, of course,, incompatiblewith self-similarity. Adjusting the power-law shear velocityprofile near the water interface, however, improvesthe fit of this simple model with a parsimoniousparameterization to data from the the deep seafloor.Approximation of a power-law model using thin layers ofuniform velocity is eased by using an editor with aninteractive graphical user interface.
Howard, Robert W
2014-09-01
The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development.
Howard, Robert W
2014-09-01
The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. PMID:24915472
Global analysis of the stream power law parameters based on worldwide 10Be denudation rates
NASA Astrophysics Data System (ADS)
Harel, M.-A.; Mudd, S. M.; Attal, M.
2016-09-01
The stream power law, expressed as E = KAmSn - where E is erosion rate [LT - 1], K is an erodibility coefficient [T - 1L (1 - 2m)], A is drainage area [L 2], S is channel gradient [L/L], and m and n are constants - is the most widely used model for bedrock channel incision. Despite its simplicity and limitations, the model has proved useful for topographic evolution, knickpoint migration, palaeotopography reconstruction, and the determination of rock uplift patterns and rates. However, the unknown parameters K, m, and n are often fixed arbitrarily or are based on assumptions about the physics of the erosion processes that are not always valid, which considerably limits the use and interpretation of the model. In this study, we compile a unique global data set of published basin-averaged erosion rates that use detrital cosmogenic 10Be. These data (N = 1457) enable values for fundamental river properties to be empirically constrained, often for the first time, such as the concavity of the river profile (m/n ratio or concavity index), the link between channel slope and erosion rate (slope exponent n), and substrate erodibility (K). These three parameters are calculated for 59 geographic areas using the integral method of channel profile analysis and allow for a global scale analysis in terms of climatic, tectonic, and environmental settings. In order to compare multiple sites, we also normalize n and K using a reference concavity index m/n = 0.5. A multiple regression analysis demonstrates that intuitive or previously demonstrated local-scale trends, such as the correlation between K and precipitation rates, do not appear at a global scale. Our results suggest that the slope exponent is generally > 1, meaning that the relationship between erosion rate and the channel gradient is nonlinear and thus support the hypothesis that incision is a threshold controlled process. This result questions the validity of many regional interpretations of climate and/or tectonics where
Comments regarding the binary power law for heterogeneity of disease incidence.
Turechek, W W; Madden, L V; Gent, D H; Xu, X-M
2011-12-01
The binary power law (BPL) has been successfully used to characterize heterogeneity (overdispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial distribution over the range of incidence values, and the estimated scale (?) and slope (b) parameters provide information on the characteristics of aggregation. When b = 1, the interpretation is that the degree of aggregation remains constant over the range of incidence values observed; otherwise, aggregation is variable. In two articles published in this journal in 2009, Gosme and Lucas used their stochastic simulation model, Cascade, to show a multiphasic (split-line) relationship of the variances, with straight-line (linear) relationships on a log-log scale within each phase. In particular, they showed a strong break point in the lines at very low incidence, with b considerably >1 in the first line segment (corresponding to a range of incidence values usually not observed in the field), and b being ?1 in the next segment (corresponding to the range of incidence values usually observed). We evaluated their findings by utilizing a general spatially explicit stochastic simulator developed by Xu and Ridout in 1998, with a wide range of median dispersal distances for the contact distribution and number of plants in the sampling units (quadrats), and through an assessment of published BPL results. The simulation results showed that the split-line phenomenon can occur, with a break point at incidence values of ?0.01; however, the split is most obvious for short median dispersal distances and large quadrat sizes. However, values of b in the second phase were almost always >1, and only approached 1 with extremely short median dispersal distances and small quadrat sizes. An appraisal of published results showed no evidence of multiple phases (although the minimum incidence may
Scattering theory for arbitrary potentials
Kadyrov, A.S.; Bray, I.; Stelbovics, A.T.; Mukhamedzhanov, A.M.
2005-09-15
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.