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At least 523 records · Page 29Linked to original sources
arXiv1996

Transport in Sand Piles, Interface Depinning, and Earthquake Models

Recent numerical results for a model describing dispersive transport in rice piles are explained by mapping the model to the depinning transition of an interface that is dragged at one end through a random medium. The average velocity of transport vanishes with system size $L$ as $ \sim L^{2-D}\sim L^{-0.23}$, and the avalanche size distribution exponent $τ= 2 - 1/D \simeq 1.55$, where $D\simeq 2.23$ from interface depinning. We conjecture that the purely deterministic Burridge-Knopoff ``train'' model for earthquakes is in the same universality class.

cond-mat↗
arXiv1996

Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model

We derive an infinite hierarchy of exact equations for the Bak-Sneppen model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model are the same above and below the critical point and express the universal amplitude ratio of the avalanche spatial size in terms of the critical exponents. The equations uniquely determine the shape of the scaling function of the avalanche distribution. It is suggested that in the BS model there is only one independent critical exponent.

adap-org↗
arXiv1995

Onsager reciprocity relations without microscopic reversibility

In this paper we show that Onsager--Machlup time reversal properties of thermodynamic fluctuations and Onsager reciprocity relations for transport coefficients can hold also if the microscopic dynamics is not reversible. This result is based on the explicit construction of a class of conservative models which can be analysed rigorously.

adap-org↗
arXiv1996

Field Theories for Learning Probability Distributions

Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to expect. From a Bayesian point of view we need an {\it a priori} distribution on the space of possible probability distributions, which defines a scalar field theory. In one dimension, free field theory with a constraint provides a tractable formulation of the problem, and we also discus generalizations to higher dimensions.

cond-mat↗
arXiv1996

Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics

We show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the KPZ equation. Numerical simulations in 1d confirm this prediction, and yield other exponents of the multiplicative noise problem. The numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values, and show that the exponent governing the divergence in this range varies continuously with control parameter.

adap-org↗
arXiv1997

Stochastic Multiresonance

We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic signals may be enhanced at multiple values of the noise level, instead of at a single value which has occurred in systems considered up to now in the framework of stochastic resonance.

cond-mat↗
arXiv1997

Spatiotemporal Stochastic Resonance in the Swift-Hohenberg Equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

cond-mat↗
arXiv1997

Self-Organized Short-Term Memories

We report short-term memory formation in a nonlinear dynamical system with many degrees of freedom. The system ``remembers'' a sequence of impulses for a transient period, but it coarsens and eventually ``forgets'' nearly all of them. The memory duration increases as the number of degrees of freedom in the system increases. We demonstrate the existence of these transient memories in a laboratory experiment.

cond-mat↗
arXiv1997

Dissipative Dynamics of Collisionless Nonlinear Alfven Wave Trains

The nonlinear dynamics of collisionless Alfven trains, including resonant particle effects is studied using the kinetic nonlinear Schroedinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven waves to be sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. The combined effects of both wave nonlinearity and Landau damping result in the evolutionary formation of stationaryOA S- and arc-polarized directional and rotational discontinuities. These waveforms are freqently observed in the interplanetary plasma.

physics.space-ph↗
arXiv1996

Finite size scaling in neural networks

We demonstrate that the fraction of pattern sets that can be stored in single- and hidden-layer perceptrons exhibits finite size scaling. This feature allows to estimate the critical storage capacity α_c from simulations of relatively small systems. We illustrate this approach by determining α_c, together with the finite size scaling exponent ν, for storing Gaussian patterns in committee and parity machines with binary couplings and up to K=5 hidden units.

cond-mat.dis-nn↗
arXiv1997

Evolution on a Rugged Landscape:Pinning and Aging

Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank equation which allows us to describe the dynamics of the population in terms of thermo-activated Langevin diffusion of a single particle in a specific random potential. We found that the randomness in the mutation rate leads to pinning of the population and on average to a logarithmic slowdown of the evolution, resembling aging phenomenon in spin glass systems. In contrast, the randomness in the replication rate turns out to be irrelevant for evolution in the long-time limit as it is smoothed out by increasing ``evolution temperature''. The analytic results are in a good agreement with numerical simulations.

adap-org↗
arXiv1997

Speciation as Pattern Formation by Competition in a Smooth Fitness Landscape

We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasi-species. By suggesting an analogy between the competition among strains and the diffusion of a chemical inhibitor in a reaction-diffusion system, the speciation phenomenon is considered the analogous of chemical pattern formation in genetic space. In the limit of vanishing mutation rate we obtain analytically the conditions for speciation. Using different forms of the competition interaction we show that the speciation is absent for the genetic equivalent of a normal diffusing inhibitor, and is present for shorter-range interactions. The comparison with numerical simulations is very good.

cond-mat.stat-mech↗
arXiv1997

Aging in a Model of Self-Organized Criticality

Temporal autocorrelation functions for avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical simulations show that they decay as power laws with two distinct regimes separated by a time scale which is the waiting time, or age, of the avalanche. Thus, time-translational invariance is dynamically broken. The critical exponent of the initial decay is that of the familiar stationary dynamics while a new critical exponent for the late-time behavior appears. This new exponent characterizes a non-stationary regime that has not been previously considered in the context of self-organized criticality.

cond-mat↗
arXiv1997

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.

cond-mat.stat-mech↗
arXiv1997

Multiresolution wavelet analysis of heartbeat intervals discriminates healthy patients from those with cardiac pathology

We applied multiresolution wavelet analysis to the sequence of times between human heartbeats (R-R intervals) and have found a scale window, between 16 and 32 heartbeats, over which the widths of the R-R wavelet coefficients fall into disjoint sets for normal and heart-failure patients. This has enabled us to correctly classify every patient in a standard data set as either belonging to the heart-failure or normal group with 100% accuracy, thereby providing a clinically significant measure of the presence of heart-failure from the R-R intervals alone. Comparison is made with previous approaches, which have provided only statistically significant measures.

adap-org↗
arXiv1998

Interacting Individuals Leading to Zipf's Law

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics

cond-mat.stat-mech↗