Related papers: A spatially-dependent fragmentation process
We consider the evolution of a connected set on the plane carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order sqrt{t} away…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domain with a sharp boundary which evolves under a change in the…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
The self-similar growth-fragmentation equation describes the evolution of a medium in which particles grow and divide as time proceeds, with the growth and splitting of each particle depending only upon its size. The critical case of the…
In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause…
Spatial networks of land cover are well-described by power law rank-size distributions. Continuous field proxies for human settlements, agriculture and forest cover have similar spatial scaling properties spanning 4 to 5 orders of…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Fragmentation of the planetesimals is found to play a role whose importance is greater than previously believed and depends on the average characteristic size of the primordial planetesimals but not on their mass distribution. In the small…
We give a proof of a result on the growth of the number of particles along chosen paths in a branching Brownian motion. The work follows the approach of classical large deviations results, in which paths in $C[0,1]$ are rescaled onto…
We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot exceed $1$. The dispersion kernel is taken to have density…
We consider the impact fragmentation of two spherical solid bodies sensitive to strain rate in a three-dimensional (3D) setting. We use both dimensional analysis and numerical simulations by smoothed-particle hydrodynamics (SPH) method to…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the long range coulomb repulsion between protons, the system has structural inhomogeneities. These structural inhomogeneities arise…