相关论文: Models of fragmentation with power law log-normal …
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…
We investigate universal features of the off-equilibrium sequential and conservative fragmentation processes with the dissipative effects which are simulated by the Gaussian random inactivation process. The relation between the fragment…
Many phenomena, both natural and human-influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a…
We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…
We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the…
There is a gap between single-species model predictions, and empirical studies, regarding the effect of habitat fragmentation per se, i.e., a process involving the breaking apart of habitat without loss of habitat. Empirical works indicate…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size…
We simulate binary soft disk systems in two dimensions, and investigate how the dynamics slow as the area fraction is increased toward the glass transition. The "fragility" quantifies how sensitively the relaxation time scale depends on the…
We use simulations to investigate collision time distributions as one approaches the static limit of steady-state flow of dry granular matter. The collision times fall in a power-law distribution with an exponent dictated by whether the…
Decay law of a complicated unstable state formed in a high energy collision is described by the Fourier transform of the two-point correlation function of the scattering matrix. Although each constituent resonance state decays exponentially…
We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse…
A simple model of ballistic aggregation and fragmentation is proposed. The model is characterized by two energy thresholds, Eagg and Efrag, which demarcate different types of impacts: If the kinetic energy of the relative motion of a…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
We review limiting models for fracture in bundles of fibers, with statistically distributed thresholds for breakdown of individual fibers. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur,…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
We analyze systems of clusters and interacting upon colliding---a collision between two clusters may lead to merging or fragmentation---and we also investigate the influence of additional spontaneous fragmentation events. We consider both…