Related papers: A Statistical Model of Aggregates Fragmentation

A variational discrete element method is applied to simulate quasi-static crack propagation. Cracks are considered to propagate between the mesh cells through the mesh facets. The elastic behaviour is parametrized by the continuous…

Large-mass condensates, which coexist with a power-law-decaying distribution in the one-dimensional Takayasu model of mass aggregation with input, were recently found in numerical simulations. Here, we establish the occurrence of…

Impact-induced fragmentation is a fundamental dissipative process in geosciences, yet its stochastic nature makes predicting debris evolution a persistent challenge. Here, we introduce a discrete element framework to resolve fragmentation…

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are…

We study a scalar lattice model for inter-grain forces in static, non-cohesive, granular materials, obtaining two primary results. (i) The applied stress as a function of overall strain shows a power law dependence with a nontrivial…

We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability $p$ an incoming agent…

We study the splitting of regular square lattices subject to stochastic intermittent flows. Various flow patterns are produced by different groupings of the nodes, based on their random alternation between two possible states. The resulting…

We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…

Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used…

As a consequence of shearing, wing cracks can emerge from pre-existing fractures. The process involves the interaction of sliding of the existing fracture surfaces and the tensile material failure that creates wing cracks. This work devises…

The propagation of a 3D crack in an heterogeneous material is studied using a phase field model. It is shown that in the case of randomly distributed inclusions of soft material in a matrix, the nature of the distribution has little effect…

Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to…

A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact-line in a starburst pattern. In this paper,…

A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

We investigate through extensive molecular dynamics simulations the fragmentation process of two-dimensional Lennard-Jones systems. After thermalization, the fragmentation is initiated by a sudden increment to the radial component of the…

We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between…

We show that the intermittent and self-similar fluctuations displayed by a slow crack during the propagation in a heterogeneous medium can be quantitatively described by an extension of a classical statistical model for fracture. The model…

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

We study the genesis and the selective propagation of complex crack networks induced by thermal shock or drying of brittle materials. We use a quasi-static gradient damage model to perform large scale numerical simulations showing that the…