相关论文: A Cellular Automaton Model of Damage

Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the…

The theory, the design and the experimental validation of a catastrophe machine based on a flexible element are addressed for the first time. A general theoretical framework is developed by extending that of the classical catastrophe…

A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This…

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we…

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose…

We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing…

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…

The steady-state and nonequilibrium properties of the model of environmental-economic interactions are studied. The interacting heterogeneous agents are simulated on the platform of the emission dynamics of cellular automaton. The model…

We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…

The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently, a new fully discrete scheme for this model was proposed in [46], mass conservation, positivity and energy decay were proved for the proposed scheme,…

Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process…

We discuss elastic tensegrity frameworks made from rigid bars and elastic cables, depending on many parameters. For any fixed parameter values, the stable equilibrium position of the framework is determined by minimizing an energy function…

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The…

The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that…

The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…

Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the…

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical…

Zero-range processes, in which particles hop between sites on a lattice, are closely related to equilibrium networks, in which rewiring of links take place. Both systems exhibit a condensation transition for appropriate choices of the…

The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi- infinite…

This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…