Related papers: An Objective Definition of Damage Spreading - Appl…

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with…

We study the connection between damage spreading, a phenomenon long discussed in the physics literature, and the coupling of Markov chains, a technique used to bound the mixing time. We discuss in parallel the Edwards-Anderson spin glass…

The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…

We consider numerically the crossover scaling behavior from the directed percolation universality class to the compact directed percolation universality class within the one-dimensional Domany-Kinzel cellular automaton. Our results are…

We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…

In this paper, we propose that a tree-like network with damage can be modeled as the product of a fractional-order nominal plant and a fractional-order multiplicative disturbance, which is well structured and completely characterized by the…

The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…

We propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanical stress, or both. The…

In this paper, we relate the coupling of Markov chains, at the basis of perfect sampling methods, with damage spreading, which captures the chaotic nature of stochastic dynamics. For two-dimensional spin glasses and hard spheres we point…

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

The technique of damage spreading is used to study the phase diagram of the easy axis anisotropic Heisenberg antiferromagnet on two geometrically frustrated lattices. The triangular and kagome systems are built up from triangular units that…

We investigate dynamic crack propagation and fragmentation with the phase-field fracture approach. The method was chosen for its ability to yield crack paths that are independent of the underlying mesh, thanks to the damage regularization…

In this paper we develop mathematical models for collective cell motility. Initially we develop a model using a linear diffusion-advection type equation and fit the parameters to data from cell motility assays. This approach is helpful in…

A cellular automaton (CA)-based modeling approach to simulate wildfire spread, emphasizing its strengths in capturing complex fire dynamics and its integration with geographic information systems (GIS). The model introduces an enhanced…

This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…

In the context of epidemic spreading, many intricate dynamical patterns can emerge due to the cooperation of different types of pathogens or the interaction between the disease spread and other failure propagation mechanism. To unravel such…

Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a…

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable,…

Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…