Sandpile model on a quenched substrate generated by kinetic self-avoiding trails

Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net outflow of grains from a toppling site and the total inflow of grains to the same site when all its neighbors topple once is maintained at all sites. Within numerical accuracy this model behaves in the same way as the multiscaling BTW model.Comment: Four pages, five figure

Precise toppling balance, quenched disorder, and universality for sandpiles

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class.Comment: 5 Revtex pages, 4 figure

Statistical Physics of Elasto-Plastic Steady States in Amorphous Solids: Finite Temperatures and Strain Rates

The effect of finite temperature $T$ and finite strain rate $\dot\gamma$ on the statistical physics of plastic deformations in amorphous solids made of $N$ particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, $T<T_{\rm cross}(N)$, and the strain is quasi-static. In this regime the elasto-plastic steady state exhibits highly correlated plastic events whose statistics are characterized by anomalous exponents. In the second regime $T_{\rm cross}(N)<T<T_{\rm max}(\dot\gamma)$ the system-size dependence of the stress fluctuations becomes normal, but the variance depends on the strain rate. The physical mechanism of the cross-over is different for increasing temperature and increasing strain rate, since the plastic events are still dominated by the mechanical instabilities (seen as an eigenvalue of the Hessian matrix going to zero), and the effect of temperature is only to facilitate the transition. A third regime occurs above the second cross-over temperature $T_{\rm max}(\dot\gamma)$ where stress fluctuations become dominated by thermal noise. Throughout the paper we demonstrate that scaling concepts are highly relevant for the problem at hand, and finally we present a scaling theory that is able to collapse the data for all the values of temperatures and strain rates, providing us with a high degree of predictability.Comment: 12 pages, 13 figure

NEW SELF-GRAVITATIONAL OSCILLATORY EIGENMODE PATTERNS OF SOLAR PLASMA WITH BOLTZMANN-DISTRIBUTED ELECTRONS

We attempt to propose a simplified theoretical model to study new stationary states of the nonlinear self-gravitational fluctuation dynamics of the solar plasma with the zero-inertia electrons against weakly nonlinear perturbation within the framework of the Jeans homogenization assumption. This is based on a bi-fluidic approach with the thermal electrons treated as the Boltzmann-distributed species. The joint effects of space-charge polarization, sheath-formation, and bi-layer plasma-boundary interaction through gravito-electrostatic interplay in a spherically symmetric geometry are considered. Applying a standard multiscale technique, a unique form of extended Korteweg-de Vries-Burger (e-KdVB) equation with a new selfconsistent linear sink is methodologically developed. The origin of the unique sink lies in the spherically symmetric self-gravity contributed by the massive ions. A numerical shape-analysis with multi-parameter variation depicts the co-existence of two distinct classes of new eigenmode excitations. The fluctuation patterns evolve as oscillatory soliton-like and oscillatory shock-like patterns in judicious plasma conditions under the adiabatic electronic response. Their oscillations, arising due to resonant and non-resonant coupling phenomena with the background spectral components, get gradually damped out due to the sink. This scientific study allows us to conjecture that the model supports self-gravitational solitary (shock) waves having tails (fronts) composed of a sequence of slightly overlapping solitons with smoothly varying characteristic parameters. Our results are compared with the earlier theoretical model predictions, on-board multispace satellite data and spacecraft observations highlighting tentative future scopes

Flood Frequency Analysis Using Copula with Mixed Marginal Distributions

In flood frequency analysis, a flood event is mainly characterized by peak flow, volume and duration. These three variables or characteristics of flood are random in nature and mutually correlated. In this article, a methodology is developed to derive bivariate joint distributions of the flood characteristics using the concept of copula considering a set of parametric and nonparametric marginal distributions for peak flow, volume and duration to mathematically model the correlated nature among them. A set of parametric distribution functions, and nonparametric methods based on kernel density estimation and orthonormal series are used to determine the marginal distribution functions for peak flow, volume and duration. In conventional method of flood frequency analysis, the marginal distribution functions of peak flow, volume and duration are assumed to follow some specific parametric distribution function. The concept of copula relaxes the restriction of traditional flood frequency analysis by selecting marginals from different families of probability distribution functions for flood characteristics. The present work performs a better selection of marginal distribution functions for flood characteristics by parametric and nonparametric estimation procedures, and demonstrates how the concept of copula may be used for establishing joint distribution function with mixed marginal distributions. The methodology is demonstrated with seventy years streamflow data of Red River at Grand Forks of North Dakota, US. The research work reported here is already submitted by the authors as a manuscript for review to Water Resources Research, AGU.https://ir.lib.uwo.ca/wrrr/1017/thumbnail.jp