Power-law parametrized quintessence model
Rahvar, Sohrab; Movahed, M. Sadegh
2007-01-15
We propose a simple power-law parametrized quintessence model with time-varying equation of state and obtain corresponding quintessence potential of this model. This model is compared with Supernova Type Ia (SNIa) Gold sample data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and structure formation from the 2dFGRS survey and put constrain on the parameters of model. The parameters from the best fit indicates that the equation of state of this model at the present time is w{sub 0}=-1.40{sub -0.65}{sup +0.40} at 1{sigma} confidence level. Finally we calculate the age of universe in this model and compare it with the age of old cosmological objects.
Power law models of stock indices
NASA Astrophysics Data System (ADS)
Tse, Man Kit
Viewing the stock market as a self-organized system, Sornette and Johansen introduced physics-based models to study the dynamics of stock market crashes from the perspective of complex systems. This involved modeling stock market Indices using a mathematical power law exhibiting log-periodicity as the system approaches a market crash, which acts like a critical point in a thermodynamic system. In this dissertation, I aim to investigate stock indices to determine whether or not they exhibit log-periodic oscillations, according to the models proposed by Sornette, as they approach a crash. In addition to analyzing stock market crashes in the frequency domain using the discrete Fourier transform and the Lomb-Scargle periodogram, I perform a detailed analysis of the stock market crash models through parameter estimation and model testing. I find that the probability landscapes have a complex topography and that there is very little evidence that these phase transition-based models accurately describe stock market crashes.
Power-Law entropy corrected holographic dark energy model
NASA Astrophysics Data System (ADS)
Sheykhi, Ahmad; Jamil, Mubasher
2011-10-01
Among various scenarios to explain the acceleration of the universe expansion, the holographic dark energy (HDE) model has got a lot of enthusiasm recently. In the derivation of holographic energy density, the area relation of the black hole entropy plays a crucial role. Indeed, the power-law corrections to entropy appear in dealing with the entanglement of quantum fields in and out the horizon. Inspired by the power-law corrected entropy, we propose the so-called "power-law entropy-corrected holographic dark energy" (PLECHDE) in this Letter. We investigate the cosmological implications of this model and calculate some relevant cosmological parameters and their evolution. We also briefly study the so-called "power-law entropy-corrected agegraphic dark energy" (PLECADE).
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
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
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
Model selection for identifying power-law scaling.
Ton, Robert; Daffertshofer, Andreas
2016-08-01
Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present. PMID:26774613
Singularity problems of the power law for modeling creep compliance
NASA Technical Reports Server (NTRS)
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
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.
A consistency relation for power law inflation in DBI models
NASA Astrophysics Data System (ADS)
Spaliński, Michał
2007-07-01
Brane inflation in string theory leads to a new realization of power law inflation which can give rise to significant non-gaussianity. This can happen for any throat geometry if the scalar potential is appropriate. This Letter presents a consistency relation connecting the running of the nonlinearity parameter characterizing the non-gaussianity and the scalar and tensor indices. The relationship is valid assuming that the throat geometry and scalar potential support power law inflation, regardless of the level of non-gaussianity.
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
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. PMID:26937967
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
An exact thermodynamical model of power-law temperature time scaling
NASA Astrophysics Data System (ADS)
Zingales, Massimiliano
2016-02-01
In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t) ∝tβ with β ∈ R shows a different evolution of the temperature time rate T ˙ (t) with respect to the temperature time-dependence T(t) . Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the thermal energy flux as soon as the distance increases. In this paper this idea has been exploited showing that such thermodynamical system is represented by an heterogeneous one-dimensional distributed mass one with power-law spatial scaling of its physical properties. The model yields, exactly a power-law evolution (decay) of the temperature field in terms of a real exponent as T ∝tβ (or T ∝t-β) that is related to the power-law spatial scaling of the thermodynamical property of the system. The obtained relation yields a physical ground to the formulation of fractional-order generalization of the Fourier diffusion equation.
Power-law and intermediate inflationary models in f( T)-gravity
NASA Astrophysics Data System (ADS)
Rezazadeh, K.; Abdolmaleki, A.; Karami, K.
2016-01-01
We study inflation in the framework of f( T)-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in f( T)-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law f( T) function and investigate the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, the power-law and intermediate inflationary models in f( T)-gravity can be compatible with the observational results of Planck 2015 at 68% CL. We find that in our f( T) setting, the potentials responsible for the both power-law and intermediate inflationary models have the power-law form V( ϕ) ∝ ϕ m but the power m is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of f( T)-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, is that the self-interacting quartic potential V( ϕ) ∝ ϕ 4 which has special reheating properties, can be consistent with the Planck 2015 data in our f( T) scenario while it is ruled out in the standard inflationary scenario.
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.
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.
NASA Astrophysics Data System (ADS)
Di Mauro, B.; Fava, F.; Frattini, P.; Camia, A.; Colombo, R.; Migliavacca, M.
2015-11-01
Monthly wildfire burned area frequency is here modeled with a power law distribution and scaling exponent across different European biomes are estimated. Data sets, spanning from 2000 to 2009, comprehend the inventory of monthly burned areas from the European Forest Fire Information System (EFFIS) and simulated monthly burned areas from a recent parameterization of a Land Surface Model (LSM), that is the Community Land Model (CLM). Power law exponents are estimated with a Maximum Likelihood Estimation (MLE) for different European biomes. The characteristic fire size (CFS), i.e. the area that most contributes to the total burned area, was also calculated both from EFFIS and CLM data set. We used the power law fitting and the CFS analysis to benchmark CLM model against the EFFIS observational wildfires data set available for Europe. Results for the EFFIS data showed that power law fittings holds for 2-3 orders of magnitude in the Boreal and Continental ecoregions, whereas the distribution of the Alpine, Atlantic are fitted only in the upper tail. Power law instead is not a suitable model for fitting CLM simulations. CLM benchmarking analysis showed that the model strongly overestimates burned areas and fails in reproducing size-frequency distribution of observed EFFIS wildfires. This benchmarking analysis showed that some refinements in CLM structure (in particular regarding the anthropogenic influence) are needed for predicting future wildfires scenarios, since the low spatial resolution of the model and differences in relative frequency of small and large fires can affect the reliability of the predictions.
Holographic f(T)-gravity model with power-law entropy correction
NASA Astrophysics Data System (ADS)
Karami, K.; Asadzadeh, S.; Abdolmaleki, A.; Safari, Z.
2013-10-01
Using the correspondence between the f(T)-gravity model and the holographic dark energy model with the power-law entropy correction, we reconstruct the holographic f(T)-gravity model with the power-law entropy correction. We fit the model parameters by using the latest observational data including type Ia supernovae, baryon acoustic oscillations, cosmic microwave background, and Hubble parameter data. We also check the viability of our model using a cosmographic analysis approach. Using the best-fit values of the model, we obtain the evolutionary behavior of the effective torsion equation-of-state parameter of the power-law entropy-corrected holographic f(T)-gravity model, as well as the deceleration parameter of the Universe. We also investigate different energy conditions in our model. Furthermore, we examine the validity of the generalized second law of gravitational thermodynamics. Finally, we point out the growth rate of the matter density perturbation in our model. We conclude that in the power-law entropy-corrected holographic f(T)-gravity model, the Universe begins a matter-dominated phase and approaches a de Sitter regime at late times, as expected. It also can justify the transition from the quintessence state to the phantom regime in the near past, as indicated by recent observations. Moreover, this model is consistent with current data, it passes the cosmographic test, and it fits the data of the growth factor as well as the ΛCDM model.
Hysteresis and creep: Comparison between a power-law model and Kuhnen's model
NASA Astrophysics Data System (ADS)
Oliveri, Alberto; Stellino, Flavio; Parodi, Mauro; Storace, Marco
2016-04-01
In this paper we analyze some properties of a recently proposed model of hysteresis and creep (related to a circuit model, whose only nonlinear element is based on a power law) and compare it with the well-known Kuhnen's model. A first qualitative comparison relies on the analysis of the behavior of the elementary cell of each model. Their responses to step inputs (which allow to better evidence the creep effect) are analyzed and compared. Then, a quantitative comparison is proposed, based on the fitting performances of the two models on experimental data measured from a commercial piezoelectric actuator.
Stochastic Mixing Model with Power Law Decay of Variance
NASA Technical Reports Server (NTRS)
Fedotov, S.; Ihme, M.; Pitsch, H.
2003-01-01
Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.
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.
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
Stochastic modeling of aphid population growth with nonlinear, power-law dynamics.
Matis, James H; Kiffe, Thomas R; Matis, Timothy I; Stevenson, Douglass E
2007-08-01
This paper develops a deterministic and a stochastic population size model based on power-law kinetics for the black-margined pecan aphid. The deterministic model in current use incorporates cumulative-size dependency, but its solution is symmetric. The analogous stochastic model incorporates the prolific reproductive capacity of the aphid. These models are generalized in this paper to include a delayed feedback mechanism for aphid death. Whereas the per capita aphid death rate in the current model is proportional to cumulative size, delayed feedback is implemented by assuming that the per capita rate is proportional to some power of cumulative size, leading to so-called power-law dynamics. The solution to the resulting differential equations model is a left-skewed abundance curve. Such skewness is characteristic of observed aphid data, and the generalized model fits data well. The assumed stochastic model is solved using Kolmogrov equations, and differential equations are given for low order cumulants. Moment closure approximations, which are simple to apply, are shown to give accurate predictions of the two endpoints of practical interest, namely (1) a point estimate of peak aphid count and (2) an interval estimate of final cumulative aphid count. The new models should be widely applicable to other aphid species, as they are based on three fundamental properties of aphid population biology. PMID:17306309
Protein family and fold occurrence in genomes: power-law behaviour and evolutionary model.
Qian, J; Luscombe, N M; Gerstein, M
2001-11-01
Global surveys of genomes measure the usage of essential molecular parts, defined here as protein families, superfamilies or folds, in different organisms. Based on surveys of the first 20 completely sequenced genomes, we observe that the occurrence of these parts follows a power-law distribution. That is, the number of distinct parts (F) with a given genomic occurrence (V) decays as F=aV(-b), with a few parts occurring many times and most occurring infrequently. For a given organism, the distributions of families, superfamilies and folds are nearly identical, and this is reflected in the size of the decay exponent b. Moreover, the exponent varies between different organisms, with those of smaller genomes displaying a steeper decay (i.e. larger b). Clearly, the power law indicates a preference to duplicate genes that encode for molecular parts which are already common. Here, we present a minimal, but biologically meaningful model that accurately describes the observed power law. Although the model performs equally well for all three protein classes, we focus on the occurrence of folds in preference to families and superfamilies. This is because folds are comparatively insensitive to the effects of point mutations that can cause a family member to diverge beyond detectable similarity. In the model, genomes evolve through two basic operations: (i) duplication of existing genes; (ii) net flow of new genes. The flow term is closely related to the exponent b and can accommodate considerable gene loss; however, we demonstrate that the observed data is reproduced best with a net inflow, i.e. with more gene gain than loss. Moreover, we show that prokaryotes have much higher rates of gene acquisition than eukaryotes, probably reflecting lateral transfer. A further natural outcome from our model is an estimation of the fold composition of the initial genome, which potentially relates to the common ancestor for modern organisms. Supplementary material pertaining to this work
NASA Astrophysics Data System (ADS)
Pasqua, Antonio; Assaf, Khudhair A.; Aly, Ayman A.
2013-10-01
In this work, we study the power-law and the logarithmic entropy corrected versions of the Ricci Dark Energy (RDE) model in the framework of the Brans-Dicke cosmology non-minimally coupled with a chameleon scalar field ϕ. Considering the presence of interaction between Dark Energy (DE) and Dark Matter (DM), we derived the expressions of some relevant cosmological parameters, i.e. the equation of state parameter ω D , the deceleration parameter q and the evolution of the energy density parameter \\varOmega'D.
Validation of a power-law noise model for simulating small-scale breast tissue
Reiser, I.; Edwards, A.; Nishikawa, R. M.
2013-01-01
We have validated a small-scale breast tissue model based on power-law noise. A set of 110 patient images served as truth. The statistical model parameters were determined by matching the radially-averaged power-spectrum of the projected simulated tissue with that of the central tomosynthesis patient breast projections. Observer performance in a signal-known exactly detection task in simulated and actual breast backgrounds was compared. Observers included human readers, a pre-whitening observer model and a channelized Hotelling observer model. For all observers, good agreement between performance in the simulated and actual backgrounds was found, both in the tomosynthesis central projections and the reconstructed images. This tissue model can be used for breast x-ray imaging system optimization. The complete statistical description of the model is provided. PMID:23938858
Validation of a power-law noise model for simulating small-scale breast tissue
NASA Astrophysics Data System (ADS)
Reiser, I.; Edwards, A.; Nishikawa, R. M.
2013-09-01
We have validated a small-scale breast tissue model based on power-law noise. A set of 110 patient images served as truth. The statistical model parameters were determined by matching the radially averaged power-spectrum of the projected simulated tissue with that of the central tomosynthesis patient breast projections. Observer performance in a signal-known exactly detection task in simulated and actual breast backgrounds was compared. Observers included human readers, a pre-whitening observer model and a channelized Hotelling observer model. For all observers, good agreement between performance in the simulated and actual backgrounds was found, both in the tomosynthesis central projections and the reconstructed images. This tissue model can be used for breast x-ray imaging system optimization. The complete statistical description of the model is provided.
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.
The MLP distribution: a modified lognormal power-law model for the stellar initial mass function
NASA Astrophysics Data System (ADS)
Basu, Shantanu; Gil, M.; Auddy, Sayantan
2015-05-01
This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modelling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.
Cota, Wesley; Ferreira, Silvio C; Ódor, Géza
2016-03-01
We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space λ(1)<λ<λ(2), suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at λ(2). We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at λ(c)=0. Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems. PMID:27078381
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
Exploring parameter constraints on quintessential dark energy: The inverse power law model
NASA Astrophysics Data System (ADS)
Yashar, Mark; Bozek, Brandon; Abrahamse, Augusta; Albrecht, Andreas; Barnard, Michael
2009-05-01
We report on the results of a Markov chain Monte Carlo analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data sets as a representation of future dark energy experiments. We generate simulated data sets for a ΛCDM background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model, and present our results in the form of likelihood contours generated by these two background cosmologies. We find that the relative constraining power of the various DETF data sets on the IPL model parameters is broadly equivalent to the DETF results for the w0-wa parametrization of dark energy. Finally, we gauge the power of DETF “stage 4” data by demonstrating a specific IPL model which, if realized in the universe, would allow stage 4 data to exclude a cosmological constant at better than the 3σ level.
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<<
Low prevalence, quasi-stationarity and power-law behavior in a model of contagion spreading
NASA Astrophysics Data System (ADS)
Montakhab, Afshin; Manshour, Pouya
2012-09-01
While contagion (information, infection, etc.) spreading has been extensively studied recently, the role of active local agents has not been fully considered. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local probabilistic dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. We study such spreading dynamics on Erdös-Rényi as well as scale free networks. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. These properties, while absent in standard theoretical models, are observed in recent empirical observations.
A growth model for directed complex networks with power-law shape in the out-degree distribution
NASA Astrophysics Data System (ADS)
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.
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
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)
Sachs, M. K.; Yoder, M. R.; Turcotte, D. L.; Rundle, J. B.; Malamud, B. D.
2012-05-01
Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.
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.
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.
A stable and robust calibration scheme of the log-periodic power law model
NASA Astrophysics Data System (ADS)
Filimonov, V.; Sornette, D.
2013-09-01
We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time tc, defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.
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
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
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.
Power Law and Logarithmic Ricci Dark Energy Models in Hořava-Lifshitz Cosmology
NASA Astrophysics Data System (ADS)
Pasqua, Antonio; Chattopadhyay, Surajit; Khurshudyan, Martiros; Myrzakulov, Ratbay; Hakobyan, Margarit; Movsisyan, Artashes
2015-03-01
In this work, we studied the Power Law and the Logarithmic Entropy Corrected versions of the Ricci Dark Energy (RDE) model in a spatially non-flat universe and in the framework of Hořava-Lifshitz cosmology. For the two cases containing non-interacting and interacting RDE and Dark Matter (DM), we obtained the exact differential equation that determines the evolutionary form of the RDE energy density. Moreover, we obtained the expressions of the deceleration parameter q and, using a parametrization of the equation of state (EoS) parameter ω D given by the relation ω D ( z) = ω 0+ ω 1 z, we derived the expressions of both ω 0 and ω 1. We interestingly found that the expression of ω 0 is the same for both non-interacting and interacting case. The expression of ω 1 for the interacting case has strong dependence from the interacting parameter b 2. The parameters derived in this work are done in small redshift approximation and for low redshift expansion of the EoS parameter.
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.
A unified approach to the power law and the critical state modeling of superconductors in 2D
NASA Astrophysics Data System (ADS)
Morandi, Antonio; Fabbri, Massimo
2015-02-01
Two main options exist for modeling the non-linearity of the superconductor: the power law and the critical state model. A vanishing electric field is predicted by the critical state model, which does not take into account relaxation phenomena. The power law model is to be used if flux creep is to be taken into account. However, detectable flux creep may not occur in many operating conditions. In these cases the critical state represents a more accurate modeling option. The existing numerical tools usually incorporate either the power law with a finite n-exponent or the critical state model, not both. A numerical model which incorporates both the power law and the critical state modeling of superconductors in 2D is developed in this paper. The same mathematical formulation and discretization method are used in both of the cases, and the same matrix equation is obtained. The difference between the two models only arises when the solution of the matrix equation is dealt with. The model is implemented by means of one unique computer code. The discretization can be made by means of both triangular and rectangular meshes. A circuit interpretation of the model is also introduced. The equivalence of the proposed method with the variational approach reported in the literature for dealing with the critical state is also discussed in the paper. The numerical results for some cases of practical interest are presented. The difference between the results obtained by means of the two models in terms of current distribution and ac loss is pointed out.
Generalized power-law stiffness model for nonlinear dynamics of in-plane cable networks
NASA Astrophysics Data System (ADS)
Giaccu, Gian Felice; Caracoglia, Luca
2013-04-01
Cross-ties are used for mitigating stay-cable vibration, induced by wind and wind-rain on cable-stayed bridges. In-plane cable networks are obtained by connecting the stays by transverse cross-ties. While taut-cable theory has been traditionally employed for simulating the dynamics of cable networks, the use of a nonlinear restoring-force discrete element in each cross-tie has been recently proposed to more realistically replicate the network vibration when snapping or slackening of the restrainer may be anticipated. The solution to the free-vibration dynamics can be determined by "equivalent linearization method". In an exploratory study by the authors a cubic-stiffness spring element, in parallel with a linear one, was used to analyze the restoring-force effect in a cross-tie on the nonlinear dynamics of two simplified systems. This preliminary investigation is generalized in this paper by considering a power-law stiffness model with a generic integer exponent and applied to a prototype network installed on an existing bridge. The study is restricted to the fundamental mode and some of the higher ones. A time-domain lumped-mass algorithm is used for validating the equivalent linearization method. For the prototype network with quadratic-stiffness spring and a positive stiffness coefficient, a stiffening effect is observed, with a ten percent increment in the equivalent frequency for the fundamental mode. Results also show dependency on vibration amplitude. For higher modes the equivalent nonlinear effects can be responsible for an alteration of the linear mode shapes and a transition from a "localized mode" to a "global mode".
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
A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences
NASA Astrophysics Data System (ADS)
Main, Ian G.
2000-07-01
It is common practice to refer to three independent stages of creep under static loading conditions in the laboratory: namely transient, steady-state, and accelerating. Here we suggest a simple damage mechanics model for the apparently trimodal behaviour of the strain and event rate dependence, by invoking two local mechanisms of positive and negative feedback applied to constitutive rules for time-dependent subcritical crack growth. In both phases, the individual constitutive rule for measured strain ɛ takes the form ɛ(t)=ɛ0[1+t/mτ]m, where τ is the ratio of initial crack length to rupture velocity. For a local hardening mechanism (negative feedback), we find that transient creep dominates, with 0
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)
Cai, Zhenning; Torrilhon, Manuel
2015-08-01
A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence is proven to be convergent to the linearized Boltzmann operator, and it established a connection between the Shakhov model and the linearized collision model. The convergence is demonstrated by solving the spatially homogeneous Boltzmann equation. By observing the magnitudes of the coefficients, simpler models are developed through removing small entries in the coefficient matrices.
Modelling Absorbent Phenomena of Absorbent Structure
NASA Astrophysics Data System (ADS)
Sayeb, S.; Ladhari, N.; Ben Hassen, M.; Sakli, F.
Absorption, retention and strike through time, as evaluating criteria of absorbent structures quality were studied. Determination of influent parameters on these criteria were realized by using the design method of experimental sets. In this study, the studied parameters are: Super absorbent polymer (SAP)/fluff ratio, compression and the porosity of the non woven used as a cover stock. Absorption capacity and retention are mostly influenced by SAP/fluff ratio. However, strike through time is affected by compression. Thus, a modelling of these characteristics in function of the important parameter was established.
Underdamped strain dynamics of a martensitic model with power-law interactions
NASA Astrophysics Data System (ADS)
Shankaraiah, N.; Puri, Sanjay; Shenoy, S. R.
2014-04-01
Focusing on conversion-time delays in athermal martensites, we present our results on underdamped strain dynamics of triple-well Landau free-energies with power-law anisotropic interactions for square-rectangle ferroelastic transition. After a temperature quench of 2% initial martensite seeds, the deterministic underdamped strain dynamics shows, interestingly, both fast conversions below a temperature and incubation delays above it, as in experiment and Monte Carlo simulations. On increasing damping constant, the fast conversions transform to incubation delays. Surprisingly, conversion-time delays have Vogel-Fulcher divergences as in Monte Carlo simulations. Microstructural evolutions are in good agreement with earlier studies.
NASA Astrophysics Data System (ADS)
Dralle, D.; Karst, N.; Thompson, S. E.
2015-12-01
Multiple competing theories suggest that power law behavior governs the observed first-order dynamics of streamflow recessions - the important process by which catchments dry-out via the stream network, altering the availability of surface water resources and in-stream habitat. Frequently modeled as: dq/dt = -aqb, recessions typically exhibit a high degree of variability, even within a single catchment, as revealed by significant shifts in the values of "a" and "b" across recession events. One potential source of this variability lies in underlying, hard-to-observe fluctuations in how catchment water storage is partitioned amongst distinct storage elements, each having different discharge behaviors. Testing this and competing hypotheses with widely available streamflow timeseries, however, has been hindered by a power law scaling artifact that obscures meaningful covariation between the recession parameters, "a" and "b". Here we briefly outline a technique that removes this artifact, revealing intriguing new patterns in the joint distribution of recession parameters. Using long-term flow data from catchments in Northern California, we explore temporal variations, and find that the "a" parameter varies strongly with catchment wetness. Then we explore how the "b" parameter changes with "a", and find that measures of its variation are maximized at intermediate "a" values. We propose an interpretation of this pattern based on statistical mechanics, meaning "b" can be viewed as an indicator of the catchment "microstate" - i.e. the partitioning of storage - and "a" as a measure of the catchment macrostate (i.e. the total storage). In statistical mechanics, entropy (i.e. microstate variance, that is the variance of "b") is maximized for intermediate values of extensive variables (i.e. wetness, "a"), as observed in the recession data. This interpretation of "a" and "b" was supported by model runs using a multiple-reservoir catchment toy model, and lends support to the
Rojas, Clara; Villalba, Victor M.
2007-03-15
The phase-integral approximation devised by Froeman and Froeman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform-approximation methods.
Stochastic modeling of the migration of Cs-137 in the soil considering a power law tailing in space
NASA Astrophysics Data System (ADS)
Oka, Hiroki; Hatano, Yuko
2016-04-01
We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. In our past study, we derived the analytic solution under the generalized Robin boundary condition (Oka-Yamamoto solution). This is a generalization of the He-Walling solution (1996). We compared our solution with the Fukushima soil data of for 3 years after the accident and found that the concentration of Cs-137 has a discrepancy from our solution, specifically in a deep part because the depth profiles have a power law tailing. Therefore, we improved our model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x,t|D) in terms of the diffusion coefficient D and calculate C(x,t)=∫_(0~∞) C(x,t|D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.
NASA Astrophysics Data System (ADS)
AlMuhammad, A. S.; Lopez-Mobilia, R.
2016-03-01
We use the f2FF model to study the generation of primordial magnetic fields (PMF) in the context of large field inflation (LFI), described by the potential, V ˜ M φp. We compute the magnetic and electric spectra for all possible values of the model parameters under de Sitter and power law expansion. We show that scale invariant PMF are not obtained in LFI to first order in the slow roll approximation, if we impose the constraint V(φ=0)˜ 0. Alternatively, if these constraints are relaxed, the scale invariant PMF can be generated. The associated electric field energy can fall below the energy density of inflation, ρInf for the ranges of comoving wavenumbers, k > 8 × 10-7 Mpc-1 and k > 4 × 10-6 Mpc-1 in de Sitter and power law (PL) expansion. Further, it can drop below ρInf on the ranges, e-foldings N > 51, p<1.66, p >2.03, l_0 > 3 × 105 MPl-1 (H_i < 3.3 × 10-6 MPl), and M > 2.8 × 10-3 MPl. All of the above ranges fit with the observational constraints.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Salari, Erfan
2016-09-01
In the present study, thermo-electro-mechanical vibration characteristics of both sigmoid and power-law functionally graded piezoelectric (FGP) nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier-type solution for the first time. Three kinds of thermal loading, namely uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness according to power-law and sigmoid distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as various temperature distributions, external electric voltage, different material compositions, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams. The results should be relevant to the design and application of the piezoelectric nanodevices.
Power law distribution of wealth in population based on a modified Equíluz-Zimmermann model
NASA Astrophysics Data System (ADS)
Xie, Yan-Bo; Wang, Bing-Hong; Hu, Bo; Zhou, Tao
2005-04-01
We propose a money-based model for the power law distribution (PLD) of wealth in an economically interacting population. It is introduced as a modification of the Equíluz and Zimmermann (EZ) model for crowding and information transmission in financial markets. Still, it must be stressed that in the EZ model a PLD without exponential correction is obtained only for a particular parameter, while our pattern will give the exact PLD within a wide range. The PLD exponent depends on the model parameters in a nontrivial way and is exactly calculated in this paper. The numerical results are in excellent agreement with the analytic prediction, and also comparable with empirical data of wealth distribution.
NASA Astrophysics Data System (ADS)
Wang, Shifang; Wu, Tao; Qi, Hongyan; Zheng, Qiusha; Zheng, Qian
2015-11-01
The fractal theory and technology has been applied to determine the flow rate, the average flow velocity, and the effective permeability for the power-law fluid in porous media composed of a number of tortuous capillaries/pores with arbitrary shapes, incorporating the tortuosity characteristic of flow paths. The fractal permeability and average flow velocity expressions are found to be a function of geometrical shape factors of capillaries, material constants, the fractal dimensions, microstructural parameters. The effects of the porosity, the tortuosity fractal dimension, material constants, and geometrical shape factors on the effective permeability are also analyzed in detail. To verify the validity of the present model, our proposed model is compared with the available macroscopic model and experimental data and there is good agreement between them.
Esquivel-Gómez, J.; Arjona-Villicaña, P. D.; Stevens-Navarro, E.; Pineda-Rico, U.; Balderas-Navarro, R. E.; Acosta-Elias, J.
2015-01-01
The out-degree distribution is one of the most reported topological properties to characterize real complex networks. This property describes the probability that a node in the network has a particular number of outgoing links. It has been found that in many real complex networks the out-degree has a behavior similar to a power-law distribution, therefore some network growth models have been proposed to approximate this behavior. This paper introduces a new growth model that allows to produce out-degree distributions that decay as a power-law with an exponent in the range from 1 to ∞. PMID:25765763
NASA Astrophysics Data System (ADS)
Esquivel-Gómez, J.; Arjona-Villicaña, P. D.; Stevens-Navarro, E.; Pineda-Rico, U.; Balderas-Navarro, R. E.; Acosta-Elias, J.
2015-03-01
The out-degree distribution is one of the most reported topological properties to characterize real complex networks. This property describes the probability that a node in the network has a particular number of outgoing links. It has been found that in many real complex networks the out-degree has a behavior similar to a power-law distribution, therefore some network growth models have been proposed to approximate this behavior. This paper introduces a new growth model that allows to produce out-degree distributions that decay as a power-law with an exponent in the range from 1 to ∞.
Esquivel-Gómez, J; Arjona-Villicaña, P D; Stevens-Navarro, E; Pineda-Rico, U; Balderas-Navarro, R E; Acosta-Elias, J
2015-01-01
The out-degree distribution is one of the most reported topological properties to characterize real complex networks. This property describes the probability that a node in the network has a particular number of outgoing links. It has been found that in many real complex networks the out-degree has a behavior similar to a power-law distribution, therefore some network growth models have been proposed to approximate this behavior. This paper introduces a new growth model that allows to produce out-degree distributions that decay as a power-law with an exponent in the range from 1 to ∞. PMID:25765763
NASA Astrophysics Data System (ADS)
Dralle, David; Karst, Nathaniel; Thompson, Sally E.
2015-11-01
The falling limb of the hydrograph—the streamflow recession—is frequently well approximated by power law functions, in the form dq/dt = -aqb, so that recessions are often characterized in terms of their power law parameters (a, b). The empirical determination and interpretation of the parameter a is typically biased by the presence of a ubiquitous mathematical artifact resulting from the scale-free properties of the power law function. This reduces the information available from recession parameter analysis and creates several heretofore unaddressed methodological "pitfalls." This letter outlines the artifact, demonstrates its genesis, and presents an empirical rescaling method to remove artifact effects from fitted recession parameters. The rescaling process reveals underlying climatic patterns obscured in the original data and, we suggest, could maximize the information content of fitted power laws.
Treeby, Bradley E; Cox, B T
2014-10-01
The absorption of compressional and shear waves in many viscoelastic solids has been experimentally shown to follow a frequency power law. It is now well established that this type of loss behavior can be modeled using fractional derivatives. However, previous fractional constitutive equations for viscoelastic media are based on temporal fractional derivatives. These operators are non-local in time, which makes them difficult to compute in a memory efficient manner. Here, a fractional Kelvin-Voigt model is derived based on the fractional Laplacian. This is obtained by splitting the particle velocity into compressional and shear components using a dyadic wavenumber tensor. This allows the temporal fractional derivatives in the Kelvin-Voigt model to be replaced with spatial fractional derivatives using a lossless dispersion relation with the appropriate compressional or shear wave speed. The model is discretized using the Fourier collocation spectral method, which allows the fractional operators to be efficiently computed. The field splitting also allows the use of a k-space corrected finite difference scheme for time integration to minimize numerical dispersion. The absorption and dispersion behavior of the fractional Laplacian model is analyzed for both high and low loss materials. The accuracy and utility of the model is then demonstrated through several numerical experiments, including the transmission of focused ultrasound waves through the skull. PMID:25324054
Pandolfi, Stefania; Giusarma, Elena; Lattanzi, Massimiliano; Melchiorri, Alessandro
2010-05-15
We consider cosmological models with a non-scale-invariant spectrum of primordial perturbations and assess whether they represent a viable alternative to the concordance {Lambda}CDM model. We find that in the framework of a model selection analysis, the WMAP and 2dF data do not provide any conclusive evidence in favor of one or the other kind of model. However, when a marginalization over the entire space of nuisance parameters is performed, models with a modified primordial spectrum and {Omega}{sub {Lambda}=}0 are strongly disfavored.
NASA Astrophysics Data System (ADS)
Jin, Fan; Guo, Xu; Gao, Huajian
2013-12-01
A cohesive zone model of axisymmetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the double-Hertz model of Greenwood and Johnson (1998). Closed-form solutions are obtained analytically for the surface stress, deformation fields and equilibrium relations among applied load, indentation depth, inner and outer radii of the cohesive zone, which include the corresponding solutions for homogeneous isotropic materials and the Gibson solid as special cases. These solutions provide a continuous transition between JKR and DMT type contact models through a generalized Tabor parameter μ. Our analysis reveals that the magnitude of the pull-off force ranges from (3+k)πRΔγ/2 to 2πRΔγ, where k, R and Δγ denote the gradient exponent of the elastic modulus for the half-space, the radius of the sphere and the work of adhesion, respectively. Interestingly, the pull-off force for the Gibson solid is found to be identically equal to 2πRΔγ, independent of the corresponding Tabor parameter. The obtained analytical solutions are validated with finite element simulations.
Power-law Wrinkling Turbulence-Flame Interaction Model for Astrophysical Flames
NASA Astrophysics Data System (ADS)
Jackson, Aaron P.; Townsley, Dean M.; Calder, Alan C.
2014-04-01
We extend a model for turbulence-flame interactions (TFI) to consider astrophysical flames with a particular focus on combustion in Type Ia supernovae. The inertial range of the turbulent cascade is nearly always under-resolved in simulations of astrophysical flows, requiring the use of a model in order to quantify the effects of subgrid-scale wrinkling of the flame surface. We provide implementation details to extend a well-tested TFI model to low-Prandtl number flames for use in the compressible hydrodynamics code FLASH. A local, instantaneous measure of the turbulent velocity is calibrated for FLASH and verification tests are performed. Particular care is taken to consider the relation between the subgrid rms turbulent velocity and the turbulent flame speed, especially for high-intensity turbulence where the turbulent flame speed is not expected to scale with the turbulent velocity. Finally, we explore the impact of different TFI models in full-star, three-dimensional simulations of Type Ia supernovae.
Power-law wrinkling turbulence-flame interaction model for astrophysical flames
Jackson, Aaron P.; Townsley, Dean M.; Calder, Alan C.
2014-04-01
We extend a model for turbulence-flame interactions (TFI) to consider astrophysical flames with a particular focus on combustion in Type Ia supernovae. The inertial range of the turbulent cascade is nearly always under-resolved in simulations of astrophysical flows, requiring the use of a model in order to quantify the effects of subgrid-scale wrinkling of the flame surface. We provide implementation details to extend a well-tested TFI model to low-Prandtl number flames for use in the compressible hydrodynamics code FLASH. A local, instantaneous measure of the turbulent velocity is calibrated for FLASH and verification tests are performed. Particular care is taken to consider the relation between the subgrid rms turbulent velocity and the turbulent flame speed, especially for high-intensity turbulence where the turbulent flame speed is not expected to scale with the turbulent velocity. Finally, we explore the impact of different TFI models in full-star, three-dimensional simulations of Type Ia supernovae.
NASA Astrophysics Data System (ADS)
Li, Zhijin; Carton, Ann-Katherine; Muller, Serge; Iordache, Rǎzvan; Desolneux, Agnès.
2015-03-01
In breast X-ray imaging, breast texture has been characterized by a radial noise power spectrum (NPS) that has an inverse power-law shape with exponent β. The technique to estimate the radial power-law coefficient β is typically based on averaging 2-dimensional noise power spectra (NPS), calculated from partly overlapping image regions each weighted by a suitable window function. The linear regression applied over a selected frequency range to the logarithm of the 1- dimensional NPS as a function of the logarithm of the radial frequencies, gives β. For each step in this process, several alternative techniques have been proposed. This paper investigates the effect of image region of interest (ROI) size, image data windowing and alternative ways to determine radial frequency in terms of bias, variance and root mean square error (RMSE) in the estimated β. The effects of these three factors were analytically derived and evaluated using synthetic images with known β varying from 1 to 4 to cover the range of textures encountered in 2D and 3D breast X-ray imaging. Our results indicate that the RMSE in estimated β is smallest when the ROIs are multiplied with an appropriate window function and either no radial averaging or radial averaging with small frequency bins is applied. The ROI size yielding the smallest RMSE depends on several factors and needs to be validated with numerical simulations. In clinical practice however, there might be a need to compromise in the choice of the ROI size to balance between the RMSE magnitudes inherent to the applied β estimation technique and encompass the breast texture range so as to obtain an accurate shape of the NPS. When using 2.56 cm x 2.56 cm ROI sizes, applying a 2D Hann window and no radial frequency averaging, the RMSE in the estimated β ranges from 0.04 to 0.1 for true β values equal to 1 and 4. While many subtleties in real images were not modeled to simplify the mathematics in deriving our results, this work is
Power-law exponent of the Bouchaud-Mézard model on regular random networks
NASA Astrophysics Data System (ADS)
Ichinomiya, Takashi
2013-07-01
We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as x→∞. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be in good agreement with those of the numerical simulations.
NASA Astrophysics Data System (ADS)
Thohura, Sharaban; Molla, Md. Mamun; Sarker, M. M. A.
2016-07-01
A study on the natural convection flow of non-Newtonian fluid along a vertical thin cylinder with constant wall temperature using modified power law viscosity model has been done. The basic equations are transformed to non dimensional boundary layer equations and the resulting systems of nonlinear partial differential equations are then solved employing marching order implicit finite difference method. The evolution of the surface shear stress in terms of local skin-friction, the rate of heat transfer in terms of local Nusselt number, velocity and temperature profiles for shear thinning as well as shear-thickening fluid considering the different values of Prandtl number have been focused. For the Newtonian fluids the present numerical results are compared with available published results which show a good agreement indeed. From the results it can be concluded that, at the leading edge, a Newtonian-like solution exists as the shear rate is not large enough to trigger non-Newtonian effects. Non-Newtonian effects can be found when the shear-rate increases beyond a threshold value.
NASA Astrophysics Data System (ADS)
Dexter, Jason; Blaes, Omer
2014-03-01
We propose a new model of the steep power-law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, the inner radii of radiation pressure dominated accretion discs are expected to (i) become effectively optically thin and (ii) produce significant luminosities. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energies. These spectra sum together to form a steep power-law tail to the spectrum. A given photon energy on this tail corresponds to a narrow range in radius, so that local vertical oscillations of the disc naturally produce high-quality high-frequency quasi-periodic oscillations (HFQPOs) in the hard X-ray band. The two lowest order modes have a robust frequency ratio of sqrt{7/3}˜eq 1.53. This model explains the appearance of steep power-law spectra and HFQPOs at high luminosity, the 3:2 HFQPO frequency ratios, and their association with the power-law spectral component. We predict an increase in QPO quality factor when the power spectrum is restricted to a narrower photon energy band, and an increase in HFQPO frequency at higher X-ray energies or lower luminosities. Future X-ray telescopes could detect additional HFQPOs from higher order modes. We demonstrate how this model could be used to measure black hole spin from HFQPOs, and qualitatively estimate the spin of GRO J1655-40 as a/M ˜ 0.4-0.7.
Modeling the Absorbing Aerosol Index
NASA Technical Reports Server (NTRS)
Penner, Joyce; Zhang, Sophia
2003-01-01
We propose a scheme to model the absorbing aerosol index and improve the biomass carbon inventories by optimizing the difference between TOMS aerosol index (AI) and modeled AI with an inverse model. Two absorbing aerosol types are considered, including biomass carbon and mineral dust. A priori biomass carbon source was generated by Liousse et al [1996]. Mineral dust emission is parameterized according to surface wind and soil moisture using the method developed by Ginoux [2000]. In this initial study, the coupled CCM1 and GRANTOUR model was used to determine the aerosol spatial and temporal distribution. With modeled aerosol concentrations and optical properties, we calculate the radiance at the top of the atmosphere at 340 nm and 380 nm with a radiative transfer model. The contrast of radiance at these two wavelengths will be used to calculate AI. Then we compare the modeled AI with TOMS AI. This paper reports our initial modeling for AI and its comparison with TOMS Nimbus 7 AI. For our follow-on project we will model the global AI with aerosol spatial and temporal distribution recomputed from the IMPACT model and DAO GEOS-1 meteorology fields. Then we will build an inverse model, which applies a Bayesian inverse technique to optimize the agreement of between model and observational data. The inverse model will tune the biomass burning source strength to reduce the difference between modelled AI and TOMS AI. Further simulations with a posteriori biomass carbon sources from the inverse model will be carried out. Results will be compared to available observations such as surface concentration and aerosol optical depth.
Gragert, Loren; Maiers, Martin; Chatterjee, Ansu; Albrecht, Mark
2015-01-01
Measures of allele and haplotype diversity, which are fundamental properties in population genetics, often follow heavy tailed distributions. These measures are of particular interest in the field of hematopoietic stem cell transplant (HSCT). Donor/Recipient suitability for HSCT is determined by Human Leukocyte Antigen (HLA) similarity. Match predictions rely upon a precise description of HLA diversity, yet classical estimates are inaccurate given the heavy-tailed nature of the distribution. This directly affects HSCT matching and diversity measures in broader fields such as species richness. We, therefore, have developed a power-law based estimator to measure allele and haplotype diversity that accommodates heavy tails using the concepts of regular variation and occupancy distributions. Application of our estimator to 6.59 million donors in the Be The Match Registry revealed that haplotypes follow a heavy tail distribution across all ethnicities: for example, 44.65% of the European American haplotypes are represented by only 1 individual. Indeed, our discovery rate of all U.S. European American haplotypes is estimated at 23.45% based upon sampling 3.97% of the population, leaving a large number of unobserved haplotypes. Population coverage, however, is much higher at 99.4% given that 90% of European Americans carry one of the 4.5% most frequent haplotypes. Alleles were found to be less diverse suggesting the current registry represents most alleles in the population. Thus, for HSCT registries, haplotype discovery will remain high with continued recruitment to a very deep level of sampling, but population coverage will not. Finally, we compared the convergence of our power-law versus classical diversity estimators such as Capture recapture, Chao, ACE and Jackknife methods. When fit to the haplotype data, our estimator displayed favorable properties in terms of convergence (with respect to sampling depth) and accuracy (with respect to diversity estimates). This
Slater, Noa; Louzoun, Yoram; Gragert, Loren; Maiers, Martin; Chatterjee, Ansu; Albrecht, Mark
2015-04-01
Measures of allele and haplotype diversity, which are fundamental properties in population genetics, often follow heavy tailed distributions. These measures are of particular interest in the field of hematopoietic stem cell transplant (HSCT). Donor/Recipient suitability for HSCT is determined by Human Leukocyte Antigen (HLA) similarity. Match predictions rely upon a precise description of HLA diversity, yet classical estimates are inaccurate given the heavy-tailed nature of the distribution. This directly affects HSCT matching and diversity measures in broader fields such as species richness. We, therefore, have developed a power-law based estimator to measure allele and haplotype diversity that accommodates heavy tails using the concepts of regular variation and occupancy distributions. Application of our estimator to 6.59 million donors in the Be The Match Registry revealed that haplotypes follow a heavy tail distribution across all ethnicities: for example, 44.65% of the European American haplotypes are represented by only 1 individual. Indeed, our discovery rate of all U.S. European American haplotypes is estimated at 23.45% based upon sampling 3.97% of the population, leaving a large number of unobserved haplotypes. Population coverage, however, is much higher at 99.4% given that 90% of European Americans carry one of the 4.5% most frequent haplotypes. Alleles were found to be less diverse suggesting the current registry represents most alleles in the population. Thus, for HSCT registries, haplotype discovery will remain high with continued recruitment to a very deep level of sampling, but population coverage will not. Finally, we compared the convergence of our power-law versus classical diversity estimators such as Capture recapture, Chao, ACE and Jackknife methods. When fit to the haplotype data, our estimator displayed favorable properties in terms of convergence (with respect to sampling depth) and accuracy (with respect to diversity estimates). This
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.
Resurrecting power law inflation in the light of Planck results
Unnikrishnan, Sanil; Sahni, Varun E-mail: varun@iucaa.ernet.in
2013-10-01
It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter f{sub N{sub L}{sup equil}} are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our model is structurally similar to that of a canonical scalar field and has a power law form for the kinetic term. A simple extension of our model resolves the graceful exit problem which usually afflicts models of power law inflation.
Power Law Distribution in Education
NASA Astrophysics Data System (ADS)
Gupta, Hari M.; Campanha, José R.; Chavarette, Fábio R.
We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study-day versus night period (ii) teaching conditions - private versus public school (iii) economical conditions - high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects are due to the nature of the subjects themselves. Further and better study, teaching and economical conditions are more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.
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.
NASA Astrophysics Data System (ADS)
Hong, Byoung Hee; Lee, Kyoung Eun; Lee, Jae Woo
2007-01-01
We consider the scaling behaviors for fluctuations of the number of Korean firms bankrupted in the period from 1 August 2002 to 28 October 2003. We observe a power law for the distribution of the number of the bankrupted firms. The Pareto exponent is close to unity. We also consider the daily increments of the number of firms bankrupted. The probability distribution of the daily increments for the firms bankrupted follows the Gaussian distribution in central part and has a fat tail. The tail parts of the probability distribution of the daily increments for the firms bankrupted follow a power law.
NASA Astrophysics Data System (ADS)
Olin, Miska; Anttila, Tatu; Dal Maso, Miikka
2016-06-01
We present the combined power law and log-normal distribution (PL+LN) model, a computationally efficient model to be used in simulations where the particle size distribution cannot be accurately represented by log-normal distributions, such as in simulations involving the initial steps of aerosol formation, where new particle formation and growth occur simultaneously, or in the case of inverse modeling. The model was evaluated against highly accurate sectional models using input parameter values that reflect conditions typical to particle formation occurring in the atmosphere and in vehicle exhaust. The model was tested in the simulation of a particle formation event performed in a mobile aerosol chamber at Mäkelänkatu street canyon measurement site in Helsinki, Finland. The number, surface area, and mass concentrations in the chamber simulation were conserved with the relative errors lower than 2 % using the PL+LN model, whereas a moment-based log-normal model and sectional models with the same computing time as with the PL+LN model caused relative errors up to 17 and 79 %, respectively.
Power laws and macroeconomic fluctuations
NASA Astrophysics Data System (ADS)
Gaffeo, Edoardo; Gallegati, Mauro; Giulioni, Gianfranco; Palestrini, Antonio
2003-06-01
We study the duration distribution of recessions and recoveries occurred in a pool of industrialized countries during the last 120 years. We find that for recessions the duration is distributed according to a power law, and that the power exponent is virtually invariant as we split up the time span into sub-periods. The evidence regarding the duration of recoveries is mixed, however.
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.
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.
Chakraborti, Anirban; Patriarca, Marco
2009-11-27
A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system. PMID:20366128
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.
Power laws governing epidemics in isolated populations
NASA Astrophysics Data System (ADS)
Rhodes, C. J.; Anderson, R. M.
1996-06-01
TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1-11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12-14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16-19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.
Carloni, Sante; Chaichian, Masud; Tureanu, Anca; Nojiri, Shin'ichi; Odintsov, Sergei D.; Oksanen, Markku
2010-09-15
We propose the most general modified first-order Horava-Lifshitz gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat Friedmann-Robertson-Walker (FRW) space-time, demonstrating many of the features of the general theory. It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent. As a large class of such theories, the modified Horava-Lifshitz F(R) gravity is introduced. The study of its ultraviolet properties shows that its z=3 version seems to be renormalizable in the same way as the original Horava-Lifshitz proposal. The Hamiltonian analysis of the modified Horava-Lifshitz F(R) gravity shows that it is in general a consistent theory. The F(R) gravity action is also studied in the fixed-gauge form, where the appearance of a scalar field is particularly illustrative. Then the spatially-flat FRW cosmology for this F(R) gravity is investigated. It is shown that a special choice of parameters for this theory leads to the same equations of motion as in the case of traditional F(R) gravity. Nevertheless, the cosmological structure of the modified Horava-Lifshitz F(R) gravity turns out to be much richer than for its traditional counterpart. The emergence of multiple de Sitter solutions indicates the possibility of unification of early-time inflation with late-time acceleration within the same model. Power-law F(R) theories are also investigated in detail. It is analytically shown that they have a quite rich cosmological structure: early-/late-time cosmic acceleration of quintessence, as well as of phantom types. Also it is demonstrated that all the four known types of finite-time future singularities may occur in the power-law Horava-Lifshitz F(R) gravity. Finally, a covariant proposal for (renormalizable) F(R) gravity within the Horava-Lifshitz spirit is presented.
NASA Astrophysics Data System (ADS)
Khodam-Mohammadi, A.
In this work, the PLECHDE model with Granda-Oliveros (G-O) IR-cutoff is studied. The evolution of dark energy density, deceleration and EoS parameters are calculated. I demonstrate that under a condition, our universe can accelerate near the phantom barrier at present time. We calculate these parameters also in PLECHDE at Ricci scale, when α = 2 and β = 1, and a comparison between Ricci scale, G-O cutoff and non-corrected HDE without matter field with G-O cutoff is done. The correspondence between this model and some scalar field of dark energy models is established. By this method, the evolutionary treatment of kinetic energy and potential for quintessence, tachyon, K-essence and dilaton fields, are obtained. I show that the results has a good compatibility with previous work in the limiting case of flat, dark dominated and non-corrected holographic dark energy.
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.
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.
PLMaddon: a power-law module for the Matlab SBToolbox.
Vera, Julio; Sun, Cheng; Oertel, Yvonne; Wolkenhauer, Olaf
2007-10-01
PLMaddon is a General Public License (GPL) software module designed to expand the current version of the SBToolbox (a Matlab toolbox for systems biology; www.sbtoolbox.org) with a set of functions for the analysis of power-law models, a specific class of kinetic models, set in ordinary differential equations (ODE) and in which the kinetic orders can have positive/negative non-integer values. The module includes functions to generate power-law Taylor expansions of other ODE models (e.g. Michaelis-Menten type models), as well as algorithms to estimate steady-states. The robustness and sensitivity of the models can also be analysed and visualized by computing the power-law's logarithmic gains and sensitivities. PMID:17495997
Acoustical model of a Shoddy fibre absorber
NASA Astrophysics Data System (ADS)
Manning, John Peter
Shoddy fibres or "Shoddies" are a mixture of post-consumer and post-industrial fibres diverted from textile waste streams and recycled into their raw fibre form. They have found widespread use as a raw material for manufacturing sound absorbers that include, but are not limited to: automotive, architectural and home appliance applications. The purpose of this project is to develop a simple acoustic model to describe the acoustic behaviour of sound absorbers composed primarily of Shoddy fibres. The model requires knowledge of the material's bulk density only. To date, these materials have not been the focus of much published research and acoustical designers must rely on models that were developed for other materials or are overly complex. For modelling purposes, an equivalent fluid approach is chosen to balance complexity and accuracy. In deriving the proposed model, several popular equivalent fluid models are selected and the required input parameters for each model identified. The models are: the model of Delaney and Bazley, two models by Miki, the model of Johnson in conjunction with the model of Champoux and Allard and the model of Johnson in conjunction with the model of Lafarge. Characterization testing is carried out on sets of Shoddy absorbers produced using three different manufacturing methods. The measured properties are open porosity, tortuosity, airflow resistivity, the viscous and thermal characteristic lengths and the static thermal permeability. Empirical relationships between model parameters and bulk density are then derived and used to populate the selected models. This yields several 'simplified' models with bulk density as the only parameter. The most accurate model is then selected by comparing each model's prediction to the results of normal incidence sound absorption tests. The model of Johnson-Lafarge populated with the empirical relations is the most accurate model over the range of frequencies considered (approx. 300 Hz - 4000 Hz
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
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 .
Vibration absorber modeling for handheld machine tool
NASA Astrophysics Data System (ADS)
Abdullah, Mohd Azman; Mustafa, Mohd Muhyiddin; Jamil, Jazli Firdaus; Salim, Mohd Azli; Ramli, Faiz Redza
2015-05-01
Handheld machine tools produce continuous vibration to the users during operation. This vibration causes harmful effects to the health of users for repeated operations in a long period of time. In this paper, a dynamic vibration absorber (DVA) is designed and modeled to reduce the vibration generated by the handheld machine tool. Several designs and models of vibration absorbers with various stiffness properties are simulated, tested and optimized in order to diminish the vibration. Ordinary differential equation is used to derive and formulate the vibration phenomena in the machine tool with and without the DVA. The final transfer function of the DVA is later analyzed using commercial available mathematical software. The DVA with optimum properties of mass and stiffness is developed and applied on the actual handheld machine tool. The performance of the DVA is experimentally tested and validated by the final result of vibration reduction.
The power laws of nanoscale forces in ambient conditions
NASA Astrophysics Data System (ADS)
Chiesa, Matteo; Santos, Sergio; Lai, Chia-Yun
Power laws are ubiquitous in the physical sciences and indispensable to qualitatively and quantitatively describe physical phenomena. A nanoscale force law that accurately describes the phenomena observed in ambient conditions at several nm or fractions of a nm above a surface however is still lacking. Here we report a power law derived from experimental data and describing the interaction between an atomic force microscope AFM tip modelled as a sphere and a surface in ambient conditions. By employing a graphite surface as a model system the resulting effective power is found to be a function of the tip radius and the distance. The data suggest a nano to mesoscale transition in the power law that results in relative agreement with the distance-dependencies predicted by the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only
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 laws and fragility in flow networks☆
Shore, Jesse; Chu, Catherine J.; Bianchi, Matt T.
2015-01-01
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence. PMID:26082568
Power-law hereditariness of hierarchical fractal bones.
Deseri, Luca; Di Paola, Mario; Zingales, Massimiliano; Pollaci, Pietro
2013-12-01
In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law. PMID:23836622
MHD micropumping of power-law fluids: A numerical solution
NASA Astrophysics Data System (ADS)
Moghaddam, Saied
2013-02-01
The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.
Power-law creep from discrete dislocation dynamics.
Keralavarma, Shyam M; Cagin, T; Arsenlis, A; Benzerga, A Amine
2012-12-28
We report two-dimensional discrete dislocation dynamics simulations of combined dislocation glide and climb leading to "power-law" creep in a model aluminum crystal. The approach fully accounts for matter transport due to vacancy diffusion and its coupling with dislocation motion. The existence of quasiequilibrium or jammed states under the applied creep stresses enables observations of diffusion and climb over time scales relevant to power-law creep. The predictions for the creep rates and stress exponents fall within experimental ranges, indicating that the underlying physics is well captured. PMID:23368581
Power-law distributions in noisy dynamical systems
NASA Astrophysics Data System (ADS)
Wilkinson, Michael; Guichardaz, Robin; Pradas, Marc; Pumir, Alain
2015-09-01
We consider a dynamical system which is non-autonomous, has a stable attractor and which is perturbed by an additive noise. We establish that under some quite typical conditions, the intermittent fluctuations from the attractor have a probability distribution with power-law tails. We show that this results from a stochastic cascade of amplification of fluctuations due to transient periods of instability. The exponent of the power-law is interpreted as a negative fractal dimension, and is explicitly determined, using numerics or perturbation expansion, in the case of a model of colloidal particles in one-dimension.
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.
Competing reaction model with many absorbing configurations.
de Andrade, M F; Figueiredo, W
2010-02-01
We study a competitive reaction model between two monomers A and B on a linear lattice. We assume that monomer A can react with a nearest-neighbor monomer A or B , but reactions between monomers of type B are prohibited. We include in our model lateral interactions between monomers as well as the effects of temperature of the catalyst. The model is considered in the adsorption controlled limit, where the reaction rate is infinitely larger than the adsorption rate of the monomers. We employ site and pair mean-field approximations as well as static Monte Carlo simulations. We determine the phase diagram of the model in the plane y_{A} versus temperature, where y_{A} is the probability that a monomer of the type A arrives at the surface. This phase diagram shows regions of active and absorbing states separated by a line of continuous phase transitions. Despite the absorbing state of the model to be strongly dependent on temperature, we show that the static critical exponents of the model belong to the same universality class of the directed percolation. PMID:20365537
Power law in random multiplicative processes with spatio-temporal correlated multipliers
NASA Astrophysics Data System (ADS)
Morita, Satoru
2016-02-01
It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time correlation: the local environment and the global environment. In addition, we introduce two simple models through which we analytically and numerically show that the local and global environments yield different trends in the power-law exponent.
Power Law Decay in High Intensity Turbulence
NASA Astrophysics Data System (ADS)
Koster, Timothy; Puga, Alejandro; Nguyen, Baolong; Larue, John
2015-11-01
In the study reported herein, the region where the power decay law is applicable for active grid generated turbulence is found by an iterative approach which determines the largest range where the ratio of the dissipation from the power law and the dissipation from the temporal velocity derivative are unity. The square of the Taylor microscale, as noted by Batchelor (1953), is linearly related to downstream distance relative to the virtual origin and can be used in a straightforward manner to find the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for various mean velocities to show the decay exponent as a function of the Taylor Reynolds number.
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
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).
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.
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.
A shock absorber model for structure-borne noise analyses
NASA Astrophysics Data System (ADS)
Benaziz, Marouane; Nacivet, Samuel; Thouverez, Fabrice
2015-08-01
Shock absorbers are often responsible for undesirable structure-borne noise in cars. The early numerical prediction of this noise in the automobile development process can save time and money and yet remains a challenge for industry. In this paper, a new approach to predicting shock absorber structure-borne noise is proposed; it consists in modelling the shock absorber and including the main nonlinear phenomena responsible for discontinuities in the response. The model set forth herein features: compressible fluid behaviour, nonlinear flow rate-pressure relations, valve mechanical equations and rubber mounts. The piston, base valve and complete shock absorber model are compared with experimental results. Sensitivity of the shock absorber response is evaluated and the most important parameters are classified. The response envelope is also computed. This shock absorber model is able to accurately reproduce local nonlinear phenomena and improves our state of knowledge on potential noise sources within the shock absorber.
Power law distribution of dividends in horse races
NASA Astrophysics Data System (ADS)
Park, K.; Domany, E.
2001-02-01
We discovered that the distribution of dividends in Korean horse races follows a power law. A simple model of betting is proposed, which reproduces the observed distribution. The model provides a mechanism to arrive at the true underlying winning probabilities, which are initially unknown, in a self-organized collective fashion, through the dynamic process of betting. Numerical simulations yield excellent agreement with the empirical data.
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
Lee, Sang Bub
2015-12-01
The absorbing phase transition of the modified conserved lattice gas (m-CLG) model was investigated in one dimension. The m-CLG model was modified from the conserved lattice gas (CLG) model in such a way that each active particle hops to one of the nearest-neighbor and next-nearest-neighbor empty sites. The order parameter exponent, the dynamic exponent, and the correlation length exponent were estimated from the power-law behavior and finite-size scaling of the active particle densities. The exponents were found to differ considerably from those of the ordinary CLG model and were also distinct from those of the Manna model, suggesting that next-nearest-neighbor hopping is a relevant factor that alters the critical behavior in the one-dimensional CLG model. PMID:26764627
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.
Power law analysis of the human microbiome.
Ma, Zhanshan Sam
2015-11-01
Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs. PMID:26407082
Anisotropic power-law solutions for a supersymmetry Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Do, Tuan Q.; Kao, W. F.
2016-04-01
A new set of Bianchi type I power-law expanding solutions is obtained for a supersymmetric Dirac-Born-Infeld (SDBI) theory coupled to a gauge field. Stability analysis is also performed to show that this set of power-law expanding solutions is stable. In particular, this set of power-law solutions provides an explicit example to the role played by the supersymmetry correction term. We also show by a general approach that any stable anisotropic solution of SDBI model will turn unstable when a phantom field is introduced. We also show that the result of the scalar perturbation indicates that the SDBI model is a realistic model.
Analysis of Indentation-Derived Power-Law Creep Response
NASA Astrophysics Data System (ADS)
Martinez, Nicholas J.; Shen, Yu-Lin
2016-03-01
The use of instrumented indentation to characterize power-law creep is studied by computational modeling. Systematic finite element analyses were conducted to examine how indentation creep tests can be employed to retrieve the steady-state creep parameters pertaining to regular uniaxial loading. The constant indentation load hold and constant indentation-strain-rate methods were considered, first using tin (Sn)-based materials as a model system. The simulated indentation-strain rate-creep stress relations were compared against the uniaxial counterparts serving as model input. It was found that the constant indentation-strain-rate method can help establish steady-state creep, and leads to a more uniform behavior than the constant-load hold method. An expanded parametric analysis was then performed using the constant indentation-strain-rate method, taking into account a wide range of possible power-law creep parameters. The indentation technique was found to give rise to accurate stress exponents, and a certain trend for the ratio between indentation strain rate and uniaxial strain rate was identified. A contour-map representation of the findings serves as practical guidance for determining the uniaxial power-law creep response based on the indentation technique.
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.
Diffusion with stochastic resetting at power-law times.
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. PMID:27415186
On estimating the exponent of power-law frequency distributions.
White, Ethan P; Enquist, Brian J; Green, Jessica L
2008-04-01
Power-law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning-based methods traditionally used in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation outperforms other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited. PMID:18481513
Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media
NASA Astrophysics Data System (ADS)
Tan, Xiao-Hua; Li, Xiao-Ping; Zhang, Lie-Hui; Liu, Jian-Yi; Cai, Jianchao
2015-09-01
A transient flow model for power-law fluid in fractal porous media is derived by combining transient flow theory with the fractal properties of tortuous capillaries. Pressure changes of transient flow for power-law fluid in fractal porous media are related to pore fractal dimension, tortuosity fractal dimension and the power-law index. Additionally, the starting pressure gradient model of power-law fluid in fractal porous media is established. Good agreement between the predictions of the present model and that of the traditional empirical model is obtained, the sensitive parameters that influence the starting pressure gradient are specified and their effects on the starting pressure gradient are discussed.
Estimation of shear modulus in media with power law characteristics.
Zhang, Wei; Holm, Sverre
2016-01-01
Shear wave propagation in tissue generated by the radiation force is usually modeled by either a lossless or a classical viscoelastic equation. However, experimental data shows power law behavior which is not consistent with those approaches. It is well known that fractional derivatives results in power laws, therefore a time fractional wave equation, the Caputo equation, which can be derived from the fractional Kelvin-Voigt stress and strain relation is tested. This equation is solved using the finite difference method with experimental parameters obtained from the existing literature. The equation is characterized by a fractional order which is also the power law exponent of the frequency dependent shear modulus. It is shown that for fractional order between 0 and 1, the equation gives smaller shear modulus than the classical model. The opposite situation applies for fractional order greater than 1. The numerical simulation also shows that the shear wave velocity method is only reliable for small losses. In our case, this is only for a small fractional order. Based on the published values of fractional order from other studies, there is therefore a chance for biased estimation of the shear modulus. PMID:26385841
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
Non-power law behavior in fragmentation cascades
NASA Astrophysics Data System (ADS)
Belyaev, Mikhail A.; Rafikov, Roman R.
2011-07-01
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper Belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for the particle mass distribution is a power law in the mass. However, previous studies have typically assumed that the mass of the largest fragment produced in a collision with just enough energy to shatter the target and disperse half its mass to infinity is directly proportional to the target mass. We show that if this assumption is not satisfied, then the power law solution for the steady-state particle mass distribution is modified by a multiplicative factor, which is a slowly varying function of the mass. We derive analytic solutions for this correction factor and confirm our results numerically. We find that this correction factor proves important when extrapolating over many orders of magnitude in mass, such as when inferring the number of large objects in a system based on infrared observations. In the course of our work, we have also discovered an unrelated type of non-power law behavior: waves can persist in the mass distribution of objects even in the absence of upper or lower cutoffs to the mass distribution or breaks in the strength law.
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
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.
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
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.
Inflation in the generalized inverse power law scenario
Lu, Zhun
2013-11-01
We propose a single field inflationary model by generalizing the inverse power law potential from the intermediate model. We study the implication of our model on the primordial anisotropy of cosmological microwave background radiation. Specifically, we apply the slow-roll approximation to calculate the scalar spectral tilt n{sub s} and the tensor-to-scalar ratio r. The results are compared with the recent data measured by the Planck satellite. We find that by choosing proper values for the parameters, our model can well describe the Planck data.
Microscopic modeling of nitride intersubband absorbance
NASA Astrophysics Data System (ADS)
Montano, Ines; Allerman, A. A.; Wierer, J. J.; Moseley, M.; Skogen, E. J.; Tauke-Pedretti, A.; Vawter, G. A.
III-nitride intersubband structures have recently attracted much interest because of their potential for a wide variety of applications ranging from electro-optical modulators to terahertz quantum cascade lasers. To overcome present simulation limitations we have developed a microscopic absorbance simulator for nitride intersubband devices. Our simulator calculates the band structure of nitride intersubband systems using a fully coupled 8x8 k.p Hamiltonian and determines the material response of a single period in a density-matrix-formalism by solving the Heisenberg equation including many-body and dephasing contributions. After calculating the polarization due to intersubband transitions in a single period, the resulting absorbance of a superlattice structure including radiative coupling between the different periods is determined using a non-local Green's-function formalism. As a result our simulator allows us to predict intersubband absorbance of superlattice structures with microscopically determined lineshapes and linewidths accounting for both many-body and correlation contributions. This work is funded by Sandia National Laboratories Laboratory Directed Research and Development program. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin.
Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping
NASA Astrophysics Data System (ADS)
Lobos, Alejandro M.; Tezuka, Masaki; García-García, Antonio M.
2013-10-01
In a one-dimensional (1D) superconductor, zero-temperature quantum fluctuations destroy phase coherence. Here we put forward a mechanism which can restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard model with power-law hopping using Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, noninteger spatial dimensionality deff. For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppresses fluctuations and restores superconducting long-range order for any deff>1, at zero temperature. A detailed DMRG analysis fully supports these findings. These results are also of direct relevance to quantum magnetism as our model can be mapped onto an S=1/2 XXZ spin chain with power-law decaying couplings, which can be studied experimentally with cold-ion-trap techniques.
Hill, Steven C.; Williamson, Chatt C.; Doughty, David C.; Pan, Yong-Le; Santarpia, Joshua L.; Hill, Hanna H.
2015-02-02
This paper uses a mathematical model of fluorescent biological particles composed of bacteria and/or proteins (mostly as in Hill et al., 2013 [23]) to investigate the size-dependence of the total fluorescence emitted in all directions. The model applies to particles which have negligible reabsorption of fluorescence within the particle. The specific particles modeled here are composed of ovalbumin and of a generic Bacillus. The particles need not be spherical, and in some cases need not be homogeneous. However, the results calculated in this paper are for spherical homogeneous particles. Light absorbing and fluorescing molecules included in the model are amino acids, nucleic acids, and several coenzymes. Here the excitation wavelength is 266 nm. The emission range, 300 to 370 nm, encompasses the fluorescence of tryptophan. The fluorescence cross section (C_{F}) is calculated and compared with one set of published measured values. We investigate power law (Ad^{y}) approximations to C_{F}, where d is diameter, and A and y are parameters adjusted to fit the data, and examine how y varies with d and composition, including the fraction as water. The particle's fluorescence efficiency (Q_{F}=C_{F}/geometric-cross-section) can be written for homogeneous particles as Q_{abs}R_{F}, where Q_{abs} is the absorption efficiency, and R_{F}, the fraction of the absorbed light emitted as fluorescence, is independent of size and shape. When Q_{F} is plotted vs. m_{i}d or mi(m_{r}-1)d, where m=m_{r}+im_{i} is the complex refractive index, the plots for different fractions of water in the particle tend to overlap.
Hill, Steven C.; Williamson, Chatt C.; Doughty, David C.; Pan, Yong-Le; Santarpia, Joshua L.; Hill, Hanna H.
2015-02-02
This paper uses a mathematical model of fluorescent biological particles composed of bacteria and/or proteins (mostly as in Hill et al., 2013 [23]) to investigate the size-dependence of the total fluorescence emitted in all directions. The model applies to particles which have negligible reabsorption of fluorescence within the particle. The specific particles modeled here are composed of ovalbumin and of a generic Bacillus. The particles need not be spherical, and in some cases need not be homogeneous. However, the results calculated in this paper are for spherical homogeneous particles. Light absorbing and fluorescing molecules included in the model are aminomore » acids, nucleic acids, and several coenzymes. Here the excitation wavelength is 266 nm. The emission range, 300 to 370 nm, encompasses the fluorescence of tryptophan. The fluorescence cross section (CF) is calculated and compared with one set of published measured values. We investigate power law (Ady) approximations to CF, where d is diameter, and A and y are parameters adjusted to fit the data, and examine how y varies with d and composition, including the fraction as water. The particle's fluorescence efficiency (QF=CF/geometric-cross-section) can be written for homogeneous particles as QabsRF, where Qabs is the absorption efficiency, and RF, the fraction of the absorbed light emitted as fluorescence, is independent of size and shape. When QF is plotted vs. mid or mi(mr-1)d, where m=mr+imi is the complex refractive index, the plots for different fractions of water in the particle tend to overlap.« less
NASA Astrophysics Data System (ADS)
Hill, Steven C.; Williamson, Chatt C.; Doughty, David C.; Pan, Yong-Le; Santarpia, Joshua L.; Hill, Hanna H.
2015-05-01
This paper uses a mathematical model of fluorescent biological particles composed of bacteria and/or proteins (mostly as in Hill et al., 2013 [23]) to investigate the size-dependence of the total fluorescence emitted in all directions. The model applies to particles which have negligible reabsorption of fluorescence within the particle. The specific particles modeled here are composed of ovalbumin and of a generic Bacillus. The particles need not be spherical, and in some cases need not be homogeneous. However, the results calculated in this paper are for spherical homogeneous particles. Light absorbing and fluorescing molecules included in the model are amino acids, nucleic acids, and several coenzymes. Here the excitation wavelength is 266 nm. The emission range, 300 to 370 nm, encompasses the fluorescence of tryptophan. The fluorescence cross section (CF) is calculated and compared with one set of published measured values. We investigate power law (Ady) approximations to CF, where d is diameter, and A and y are parameters adjusted to fit the data, and examine how y varies with d and composition, including the fraction as water. The particle's fluorescence efficiency (QF=CF/geometric-cross-section) can be written for homogeneous particles as QabsRF, where Qabs is the absorption efficiency, and RF, the fraction of the absorbed light emitted as fluorescence, is independent of size and shape. When QF is plotted vs. mid or mi(mr-1)d, where m=mr+imi is the complex refractive index, the plots for different fractions of water in the particle tend to overlap.
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
Emergence of Power-Law in Spatial Epidemics Using Cellular Automation
NASA Astrophysics Data System (ADS)
Li, Li; Sun, Gui-Quan; Jin, Zhen
We analyze a spatial susceptible-infected epidemic model using cellular automata and investigate the relations between the power-law distribution of patch sizes and the regime of invasion. The obtained results show that, when the invasion is in the form of coexistence of stable target and spiral wave, power-law will emerge, which may provide a new insight into the control of disease.
The use of models for estimating emissions from products beyond the timeframe of an emissions test is a means of managing the time and expenses associated with product emissions certification. This paper presents a discussion of (1) the impact of uncertainty in test chamber emiss...
Ho, Chih-Hsiang
1994-10-17
Much of the ongoing debate on the use of nuclear power plants in U.S.A. centers on the safe disposal of the radioactive waste. Congress, aware of the importance of the waste issue, passed the Nuclear Waste Policy Act of 1982, requiring the federal government to develop a geologic repository for the permanent disposal of high level radioactive wastes from civilian nuclear power plants. The Department of Energy (DOE) established the Office of Civilian Radioactive Waste Management (OCRWM) in 1983 to identify potential sites. When OCRWM had selected three potential sites to study, Congress enacted the Nuclear Waste Policy Amendments Act of 1987, which directed the DOE to characterize only one of those sites, Yucca Mountain, in southern Nevada. For a site to be acceptable, theses studies must demonstrate that the site could comply with regulations and guidelines established by the federal agencies that will be responsible for licensing, regulating, and managing the waste facility. Advocates and critics disagree on the significance and interpretation of critical geological features which bear on the safety and suitability of Yucca Mountain as a site for the construction of a high-level radioactive waste repository. Recent volcanism in the vicinity of Yucca Mountain is readily recognized as an important factor in determining future public and environmental safety because of the possibility of direct disruption of a repository site by volcanism. In particular, basaltic volcanism is regarded as direct and unequivocal evidence of deep-seated geologic instability. In this paper, statistical analysis of volcanic hazard assessment at the Yucca Mountain site is discussed, taking into account some significant geological factors raised by experts. Three types of models are considered in the data analysis. The first model assumes that both past and future volcanic activities follow a homogeneous Poisson process (HPP).
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.
Analytical time-domain Green’s functions for power-law media
Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.
2008-01-01
Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774
An inverse method for rheometry of power-law fluids
NASA Astrophysics Data System (ADS)
Hemaka Bandulasena, H. C.; Zimmerman, William B.; Rees, Julia M.
2011-12-01
This paper is concerned with the determination of the constitutive viscous parameters of dilute solutions of xanthan gum by means of an inverse method used in conjunction with finite element modeling of the governing system of partial differential equations. At low concentrations xanthan gum behaves as a shear-thinning, power-law non-Newtonian fluid. Finite element modeling is used to simulate the pressure-driven flow of xanthan gum solutions in a microchannel T-junction. As the flow is forced to turn the corner of the T-junction a range of shear rates, and hence viscosities, is produced. It is shown that the statistical properties of the velocity field are sensitive to the constitutive parameters of the power-law model. The inverse method is shown to be stable and accurate, with measurement error in the velocity field translating to small errors in the rheological parameter estimation. Due to the particular structure of the inverse map, the error propagation is substantially less than the estimate from the Hadamard criterion.
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.
Power-law distribution of gene expression fluctuations
NASA Astrophysics Data System (ADS)
Nacher, J. C.; Ochiai, T.
2008-09-01
Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.
Power-Law Tails from Dynamical Comptonization in Converging Flows
NASA Astrophysics Data System (ADS)
Turolla, Roberto; Zane, Silvia; Titarchuk, Lev
2002-09-01
The effects of bulk motion Comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semianalytical, diffusion approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates when photon diffusion holds. Our semianalytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method, we find that although the power-law tail at extremely large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Γ=3 at large accretion rates, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft seed photons when the accretion rate is either quite low (<~5 in Eddington units) or sufficiently high (>~10). On the other hand, the spatial distribution of source photons controls the photon index at intermediate accretion rates, when Γ switches from the first to the second mode. Our analysis confirms that a hard tail with photon index Γ<3 is produced by the upscattering of primary photons onto infalling electrons if the central object is a black hole.
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.
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.
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.
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
Power Law Distributions in Two Community Currencies
NASA Astrophysics Data System (ADS)
Kichiji, N.; Nishibe, M.
2007-07-01
The purpose of this paper is to highlight certain newly discovered social phenomena that accord with Zipf's law, in addition to the famous natural and social phenomena including word frequencies, earthquake magnitude, city size, income1 etc. that are already known to follow it. These phenomena have recently been discovered within the transaction amount (payments or receipts) distributions within two different Community Currencies (CC) that had been initiated as social experiments. One is a local CC circulating in a specific geographical area, such as a town. The other is a virtual CC used among members who belong to a certain community of interest (COI) on the Internet. We conducted two empirical studies to estimate the economic vitalization effects they had on their respective local economies. The results we found were that the amount of transactions (payments and receipts) of the two CCs was distributed according to a power-law distribution with a unity rank exponent. In addition, we found differences between the two CCs with regard to the shapes of their distribution over a low-transaction range. The result may originate from the difference in methods of issuing CCs or in the magnitudes of the minimum-value unit; however, this result calls for further investigation.
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.
NASA Astrophysics Data System (ADS)
Rothschild, Richard
observations of Seyferts to create models of clumpy dust and gas, rather than a uniform toroidal distribution surrounding these AGN to explain their spectral and temporal properties at many wavelengths. Our primary goal is therefore to track evolution of the partial absorbing components in the X-ray spectrum of NGC 2110 between 2005 and the present, using two Suzaku observations to allow for direct comparison. Changing covering fractions could indicate unevenness in the clumpy torus and tell us about the distribution of clumps while ionization levels could help us determine how the different absorbers are distributed radially.
Power-law confusion: You say incremental, I say differential
NASA Technical Reports Server (NTRS)
Colwell, Joshua E.
1993-01-01
Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.
NASA Astrophysics Data System (ADS)
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin; Li, Xiaocan
2014-10-01
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 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 and when the system size is sufficiently large. The power law slope approaches ``-1'' for closed systems and gets softer when particle loss from the acceleration region is included. 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. We demonstrate that both continuous inflow and Fermi-type acceleration lead to the power-law distributions. Finally, we discuss the role of particle anisotropy in particle acceleration during magnetic reconnection. The work shows that hard power-law distributions are a common feature in relativistic magnetic reconnection region, which may be important for explaining the high-energy emissions in systems like pulsars, jets from black holes, and gamma-ray bursts.
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.
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
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions
NASA Astrophysics Data System (ADS)
Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.
Application of the double absorbing boundary condition in seismic modeling
NASA Astrophysics Data System (ADS)
Liu, Yang; Li, Xiang-Yang; Chen, Shuang-Quan
2015-03-01
We apply the newly proposed double absorbing boundary condition (DABC) (Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference (FD) modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer (PML), the complexity decreases, and the stability and flexibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton-Engquist boundary condition and nearly the same as that in the PML.
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.
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.
Two-phase flow in porous media: power-law scaling of effective permeability
NASA Astrophysics Data System (ADS)
Grøva, Morten; Hansen, Alex
2011-09-01
A recent experiment has reported power-law scaling of effective permeability of two-phase flow with respect to capillary number for a two-dimensional model porous medium. In this paper, we consider the simultaneous flow of two phases through a porous medium under steady-state conditions, fixed total flow-rate and saturation, using a two-dimensional network simulator. We obtain power-law exponents for the scaling of effective permeability with respect to capillary number. The simulations are performed both for viscosity matched fluids and for a high viscosity ratio resembling that of air and water. Good power-law behaviour is found for both cases. Different exponents are found, depending on saturation.
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.
Power-law defect energy in a single-crystal gradient plasticity framework: a computational study
NASA Astrophysics Data System (ADS)
Bayerschen, E.; Böhlke, T.
2016-03-01
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 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.
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.
Evidence of microstructure evolution in solid elastic media based on a power law analysis
NASA Astrophysics Data System (ADS)
Scalerandi, M.; Idjimarene, S.; Bentahar, M.; El Guerjouma, R.
2015-05-01
Complex and consolidated granular media or microcracked composites and metals usually exhibit a high level of nonlinearity in their elastic response already at low amplitudes of excitation. To quantify it, a proper nonlinear indicator y is introduced and its dependence on the excitation amplitude x is studied. The dependence of y on x is found in experiments to be a power law. Here we show that the different power law exponents measured for different materials could be predicted by proper classes of discrete models. An application is presented to link the exponent evolution and the changes of the microstructure due to the progression of damage mechanically induced.
Thermal distribution in high power optical devices with power-law thermal conductivity
NASA Astrophysics Data System (ADS)
Zhou, Chuanle; Grayson, M.
2012-01-01
We introduce a power-law approximation to model non-linear ranges of the thermal conductivity, and under this approximation derive a simple analytical expression for calculating the temperature profile in high power quantum cascade lasers and light emitting diodes. The thermal conductivity of a type II InAs/GaSb superlattice (T2SL) is used as an example, having negative or positive power-law exponents depending on the thermal range of interest. The result is an increase or decrease in the temperature, respectively, relative to the uniform thermal conductivity assumption.
Bootstrap Percolation in Power-Law Random Graphs
NASA Astrophysics Data System (ADS)
Amini, Hamed; Fountoulakis, Nikolaos
2014-04-01
A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remains so forever. The parameter is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse this process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent , where , then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function such that with the following property. Assuming that is the number of vertices of the underlying random graph, if , then the process does not evolve at all, with high probability as grows, whereas if , then there is a constant such that, with high probability, the final set of infected vertices has size at least . This behaviour is in sharp contrast with the case where the underlying graph is a random graph with . It follows from an observation of Balogh and Bollobás that in this case if the number of initially infected vertices is sublinear, then there is lack of evolution of the process. It turns out that when the maximum degree is , then depends also on . But when the maximum degree is , then.
Power-law distribution of family names in Japanese societies
NASA Astrophysics Data System (ADS)
Miyazima, Sasuke; Lee, Youngki; Nagamine, Tomomasa; Miyajima, Hiroaki
2000-04-01
We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total number of different family names in a society scales as a power law of the population, (ii) the total number of family names of the same size decreases as the size increases with a power law and (iii) the relation between size and rank of a family name also shows a power law. These scaling properties are found to be consistent for five different regional communities in Japan.
Non-power law behavior of the radial profile of phase-space density of halos
Popolo, A. Del
2011-07-01
We study the pseudo phase-space density, ρ(r)/σ{sup 3}(r), of ΛCDM dark matter halos with and without baryons (baryons+DM, and pure DM), by using the model introduced in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay. We examine the radial dependence of ρ(r)/σ{sup 3}(r) over 9 orders of magnitude in radius for structures on galactic and cluster of galaxies scales. We find that ρ(r)/σ{sup 3}(r) is approximately a power-law only in the range of halo radius resolved by current simulations (down to 0.1% of the virial radius) while it has a non-power law behavior below the quoted scale, with inner profiles changing with mass. The non-power-law behavior is more evident for halos constituted both of dark matter and baryons while halos constituted just of dark matter and with angular momentum chosen to reproduce a Navarro-Frenk-White (NFW) density profile, are characterized by an approximately power-law behavior. The results of the present paper lead to conclude that density profiles of the NFW type are compatible with a power-law behavior of ρ(r)/σ{sup 3}(r), while those flattening to the halo center, like those found in Del Popolo (2009) or the Einasto profile, or the Burkert profile, cannot produce radial profile of the pseudo-phase-space density that are power-laws at all radii. The results argue against universality of the pseudo phase-space density and as a consequence argue against universality of density profiles constituted by dark matter and baryons as also discussed in Del Popolo (2009)
NASA Astrophysics Data System (ADS)
Chae, Kyu-Hyun
2002-04-01
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two-power-law ellipsoidal mass distributions are presented. The cusped two-power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and η models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two-power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e.g., 10-5). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two-power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single-power-law mass model are made publicly available.
Liouville-Type Theorems for Steady Flows of Degenerate Power Law Fluids in the Plane
NASA Astrophysics Data System (ADS)
Bildhauer, Michael; Fuchs, Martin; Zhang, Guo
2013-09-01
We extend the Liouville-type theorems of Gilbarg and Weinberger and of Koch, Nadirashvili, Seregin and Sverák valid for the stationary variant of the classical Navier-Stokes equations in 2 D to the degenerate power law fluid model.
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)
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.
Intramolecular vibrational dephasing obeys a power law at intermediate times
Gruebele, M.
1998-01-01
Experimental intramolecular vibrational dephasing transients for several large organic molecules are reanalyzed. Fits to the experimental data, as well as full numerical quantum calculations with a factorized potential surface for all active degrees of freedom of fluorene indicate that power law decays, not exponentials, occur at intermediate times. The results support a proposal that power law decays describe vibrational dephasing dynamics in large molecules at intermediate times because of the local nature of energy flow. PMID:9600900
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.
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.
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}.
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)
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.
Power law distributions and dynamic behaviour of stock markets
NASA Astrophysics Data System (ADS)
Richmond, P.
2001-04-01
A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t' = 2Dδ t-t' and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψ ϕ - ln G(ϕ)} where Ψ ϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ2 - cϕ3 and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ>>ɛ, a distribution function with power law tails, viz: P ϕ = exp{ 2bϕ-cϕ2 /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D | J|.
Material Model Evaluation of a Composite Honeycomb Energy Absorber
NASA Technical Reports Server (NTRS)
Jackson, Karen E.; Annett, Martin S.; Fasanella, Edwin L.; Polanco, Michael A.
2012-01-01
A study was conducted to evaluate four different material models in predicting the dynamic crushing response of solid-element-based models of a composite honeycomb energy absorber, designated the Deployable Energy Absorber (DEA). Dynamic crush tests of three DEA components were simulated using the nonlinear, explicit transient dynamic code, LS-DYNA . In addition, a full-scale crash test of an MD-500 helicopter, retrofitted with DEA blocks, was simulated. The four material models used to represent the DEA included: *MAT_CRUSHABLE_FOAM (Mat 63), *MAT_HONEYCOMB (Mat 26), *MAT_SIMPLIFIED_RUBBER/FOAM (Mat 181), and *MAT_TRANSVERSELY_ANISOTROPIC_CRUSHABLE_FOAM (Mat 142). Test-analysis calibration metrics included simple percentage error comparisons of initial peak acceleration, sustained crush stress, and peak compaction acceleration of the DEA components. In addition, the Roadside Safety Verification and Validation Program (RSVVP) was used to assess similarities and differences between the experimental and analytical curves for the full-scale crash test.
Frequency Integrated Radiation Models for Absorbing and Scattering Media
NASA Technical Reports Server (NTRS)
Ripoll, J. F.; Wray, A. A.
2004-01-01
The objective of this work is to contribute to the simplification of existing radiation models used in complex emitting, absorbing, scattering media. The application in view is the computation of flows occurring in such complex media, such as certain stellar interiors or combusting gases. In these problems, especially when scattering is present, the complexity of the radiative transfer leads to a high numerical cost, which is often avoided by simply neglecting it. The complexity lies partly in the strong dependence of the spectral coefficients on frequency. Models are then needed to capture the effects of the radiation when one cannot afford to directly solve for it. In this work, the frequency dependence will be modeled and integrated out in order retain only the average effects. A frequency-integrated radiative transfer equation (RTE) will be derived.
Modeling the Effect of Polychromatic Light in Quantitative Absorbance Spectroscopy
ERIC Educational Resources Information Center
Smith, Rachel; Cantrell, Kevin
2007-01-01
Laboratory experiment is conducted to give the students practical experience with the principles of electronic absorbance spectroscopy. This straightforward approach creates a powerful tool for exploring many of the aspects of quantitative absorbance spectroscopy.
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}.
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
NASA Astrophysics Data System (ADS)
Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming
2015-12-01
The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring.
Power-Law Entropy-Corrected HDE and NADE in Brans-Dicke Cosmology
NASA Astrophysics Data System (ADS)
Sheykhi, A.; Karami, K.; Jamil, M.; Kazemi, E.; Haddad, M.
2012-06-01
Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution. As a result we find that this model can provide the present cosmic acceleration and even the equation of state parameter of this model can cross the phantom line w D =-1 provided the model parameters are chosen suitably.
Reciprocity and the Emergence of Power Laws in Social Networks
NASA Astrophysics Data System (ADS)
Schnegg, Michael
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.
Folding of a finite length power law layer
NASA Astrophysics Data System (ADS)
Schmid, Daniel W.; Podladchikov, Yuri Y.; Marques, Fernando O.
2004-03-01
Folding of an isolated finite length power law layer embedded in a Newtonian viscous matrix is investigated and compared to conventional folding experiments where the layer is of infinite length or in direct contact with lateral boundaries. The approach employed is a combination of the complex potential method for the basic state and the thin plate approximation for the linear stability analysis and is verified by finite element models. The resulting theory reveals that the aspect ratio of a layer has a first-order influence on the development of folds. The aspect ratio competes with the effective viscosity contrast for dominant influence on the folding process. If the aspect ratio is substantially larger than the effective viscosity contrast, the conventional theories are applicable. In other situations, where the aspect ratio is smaller than the effective viscosity contrast, substantial corrections must be taken into account, which lead to a new folding mode that is mainly characterized by decreasing growth rates with increasing effective viscosity contrast (relative to the far-field shortening rate). This new folding mode helps explain the absence of large wavelength to thickness ratio folds in nature, which may be due to the limitations of aspect ratios rather than large effective viscosity contrasts.
Absorbed Dose and Dose Equivalent Calculations for Modeling Effective Dose
NASA Technical Reports Server (NTRS)
Welton, Andrew; Lee, Kerry
2010-01-01
While in orbit, Astronauts are exposed to a much higher dose of ionizing radiation than when on the ground. It is important to model how shielding designs on spacecraft reduce radiation effective dose pre-flight, and determine whether or not a danger to humans is presented. However, in order to calculate effective dose, dose equivalent calculations are needed. Dose equivalent takes into account an absorbed dose of radiation and the biological effectiveness of ionizing radiation. This is important in preventing long-term, stochastic radiation effects in humans spending time in space. Monte carlo simulations run with the particle transport code FLUKA, give absorbed and equivalent dose data for relevant shielding. The shielding geometry used in the dose calculations is a layered slab design, consisting of aluminum, polyethylene, and water. Water is used to simulate the soft tissues that compose the human body. The results obtained will provide information on how the shielding performs with many thicknesses of each material in the slab. This allows them to be directly applicable to modern spacecraft shielding geometries.
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
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.
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
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.
The power law distribution for lower tail cities in India
NASA Astrophysics Data System (ADS)
Devadoss, Stephen; Luckstead, Jeff; Danforth, Diana; Akhundjanov, Sherzod
2016-01-01
The city size distribution for lower tail cities has received scant attention because a small portion of the population lives in rural villages, particularly in developed countries, and data are not readily available for small cities. However, in developing countries much of the population inhabits rural areas. The purpose of this study is to test whether power law holds for small cities in India by using the most recent and comprehensive Indian census data for the year 2011. Our results show that lower tail cities for India do exhibit a power law.
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. PMID:26764803
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.
A spatial network explanation for a hierarchy of urban power laws
NASA Astrophysics Data System (ADS)
Andersson, Claes; Hellervik, Alexander; Lindgren, Kristian
2005-01-01
Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.
Nonlinear modeling of magnetorheological energy absorbers under impact conditions
NASA Astrophysics Data System (ADS)
Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M.; Browne, Alan L.; Ulicny, John; Johnson, Nancy
2013-11-01
Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s-1. Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R&D Center for nominal drop speeds of up to 6 m s-1.
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
Scalar field reconstruction of power-law entropy-corrected holographic dark energy
NASA Astrophysics Data System (ADS)
Ebrahimi, Esmaeil; Sheykhi, Ahmad
2011-10-01
A so-called 'power-law entropy-corrected holographic dark energy' (PLECHDE) was recently proposed to explain the dark energy (DE)-dominated universe. This model is based on the power-law corrections to black hole entropy that appear when dealing with the entanglement of quantum fields between the inside and the outside of the horizon. In this paper, we suggest a correspondence between the interacting PLECHDE and the tachyon, quintessence, K-essence and dilaton scalar field models of DE in a non-flat Friedmann-Robertson-Walker universe. Then, we reconstruct the potential terms accordingly, and present the dynamical equations that describe the evolution of the scalar field DE models.
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
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 law corrections to BTZ black hole entropy
NASA Astrophysics Data System (ADS)
Singh, Dharm Veer
2015-11-01
We study the quantum scalar field in the background of BTZ black hole and evaluate the entanglement entropy of the nonvacuum states. The entropy is proportional to the area of event horizon for the ground state, but the area law is violated in the case of nonvacuum states (first excited state and mixed states) and the corrections scale as power law.
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
Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources
NASA Technical Reports Server (NTRS)
Fiorito, Ralph; Titarchuk, Lev
2004-01-01
Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.
Power-Law Template for IR Point Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglass; Spergel, David N.; Staggs,Suzanne T.; Wollack, Edward
2011-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
Power-Law Template for Infrared Point-Source Clustering
NASA Technical Reports Server (NTRS)
Addison, Graeme E; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark J.; Halpern, Mark; Hincks, Adam D; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglas; Spergel, David N.; Staggs, Suzanne T.; Wollack, Edward
2012-01-01
We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ?(sup Beta)B(?, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.
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.
The Forbes 400, the Pareto power-law and efficient markets
NASA Astrophysics Data System (ADS)
Klass, O. S.; Biham, O.; Levy, M.; Malcai, O.; Solomon, S.
2007-01-01
Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.
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
Hughes, Timothy; Liberles, David A
2008-05-15
Genome sequencing has shown that the number of homologous gene families of a given size declines rapidly with family size. A power-law has been shown to provide the best mathematical description of this relationship. However, it remains unclear what evolutionary forces drive this observation. We use models of gene duplication, pseudogenisation and accumulation of replacement substitutions, which have been validated and parameterised using genomic data, to build a model of homologous gene evolution. We use this model to simulate the evolution of the distribution of gene family size and show that the power-law distribution is driven by the pseudogenisation rate's heterogeneity across gene families and its correlation within families. Moreover, we show that gene duplication and pseudogenisation are necessary and sufficient for the emergence of the power-law. PMID:18378100
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.
Evidence of power-law flow in the Mojave desert mantle.
Freed, Andrew M; Bürgmann, Roland
2004-07-29
Studies of the Earth's response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress-strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine--the most abundant mineral in the upper mantle--and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust. PMID:15282602
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
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
NASA Astrophysics Data System (ADS)
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin
2014-10-01
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≡B2/(4πnmec2)>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.
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
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.
Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile.
O'Boy, Daniel J; Bowyer, Elizabeth P; Krylov, Victor V
2011-06-01
The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor. PMID:21682374
A robust absorbing layer method for anisotropic seismic wave modeling
Métivier, L.; Brossier, R.; Labbé, S.; Operto, S.; Virieux, J.
2014-12-15
When applied to wave propagation modeling in anisotropic media, Perfectly Matched Layers (PML) exhibit instabilities. Incoming waves are amplified instead of being absorbed. Overcoming this difficulty is crucial as in many seismic imaging applications, accounting accurately for the subsurface anisotropy is mandatory. In this study, we present the SMART layer method as an alternative to PML approach. This method is based on the decomposition of the wavefield into components propagating inward and outward the domain of interest. Only outgoing components are damped. We show that for elastic and acoustic wave propagation in Transverse Isotropic media, the SMART layer is unconditionally dissipative: no amplification of the wavefield is possible. The SMART layers are not perfectly matched, therefore less accurate than conventional PML. However, a reasonable increase of the layer size yields an accuracy similar to PML. Finally, we illustrate that the selective damping strategy on which is based the SMART method can prevent the generation of spurious S-waves by embedding the source in a small zone where only S-waves are damped.
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
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.
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.
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-01-01
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns. PMID:25779306
Comment on "Time needed to board an airplane: a power law and the structure behind it".
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the "back-to-front" strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups. PMID:23005813
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.
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.
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.
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
Lévy flights with power-law absorption
NASA Astrophysics Data System (ADS)
Cattivelli, Luca; Agliari, Elena; Sartori, Fabio; Cassi, Davide
2015-10-01
We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ +1 . Assuming that the walker moves in the presence of a distribution a (x ) of targets (traps) depending on the spatial coordinate x , we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a (x ) ˜x-α and we find that, as long as μ <α , there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
Power-law distribution in Japanese racetrack betting
NASA Astrophysics Data System (ADS)
Ichinomiya, Takashi
2006-08-01
Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)∝1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.
Universal power law for the spectrum of breaking Riemann waves
NASA Astrophysics Data System (ADS)
Pelinovsky, Dmitry; Pelinovsky, Efim; Kartashova, Elena; Talipova, Tatiana
2014-05-01
The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation with arbitrary nonlinearity. This equation describe the long surface and internal wave in the coastal zone. The spectrum of spatial amplitudes at the breaking time has an power asymptotic decay with exponent - 4/3. This spectrum is formed by the singularity of the form like x1/3 in the wave shape at the breaking time. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg-de Vries equations.
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.
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.
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
Decay Power Law in, High Intensity, Isotropic Turbulent Flow
NASA Astrophysics Data System (ADS)
Koster, Timothy; Puga, Alejandro; Larue, John
2014-11-01
In the study reported here, isotropy is determined using the measure proposed by George (1992), where isotropy corresponds to those downstream positions where the product of the Taylor Reynolds number and the skewness of the velocity derivative is a constant. Straight forward approach can be used which is based on the observation of Batchelor (1953), that the square of the Talor micorscale is linearly related to downstream distance relative to the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for mean velocities of 6 and 8 m/s for the downstream decay of the parameters listed in the preceding. The corresponding values of the Taylor Reynolds number at the start of the isotropic region are 290 and 400, and the variance decay exponent and virtual origin are found to be respectively -1.707 and -1.298 and -27.95 and -5.757. The exponents in the decay law for the other parameters are found to be within +/- 3% of the expected values. University of California Irvine Research Funds.
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) .
On the power law of passive scalars in turbulence
NASA Astrophysics Data System (ADS)
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-11-01
It has long been considered that the moments of the scalar increment with separation distance r obey power law with scaling exponents in the inertial convective range and the exponents are insensitive to variation of pumping of scalar fluctuations at large scales, thus the scaling exponents are universal. We examine the scaling behavior of the moments of increments of passive scalars 1 and 2 by using DNS up to the grid points of 40963. They are simultaneously convected by the same isotropic steady turbulence atRλ = 805 , but excited by two different methods. Scalar 1 is excited by the random scalar injection which is isotropic, Gaussian and white in time at law wavenumber band, while Scalar 2 is excited by the uniform mean scalar gradient. It is found that the local scaling exponents of the scalar 1 has a logarithmic correction, meaning that the moments of the scalar 1 do not obey simple power law. On the other hand, the moments of the scalar 2 is found to obey the well developed power law with exponents consistent with those in the literature. Physical reasons for the difference are explored. Grants-in-Aid for Scientific Research 15H02218 and 26420106, NIFS14KNSS050, HPCI project hp150088 and hp140024, JHPCN project jh150012.