Related papers: The discrete generalized exchange-driven system
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
The paper studies a PDE model for the growth of a tree stem or a vine, having the form of a differential inclusion with state constraints. The equations describe the elongation due to cell growth, and the response to gravity and to external…
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate…
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of…
We study the global existence of solutions of a discrete (ODE based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We propose an adaptation of this model so that a macroscopic…
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to…
In this paper we introduce 1-$D$ and 2-$D$ discrete models for the dynamic granular matter formation process in the form of a system of difference equations. This approach allows us to differentiate between the influx of the rolling layer…
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…
We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. Isolated…
We consider the coagulation-decoagulation model on an one-dimensional lattice of length $L$ with open boundary conditions. Based on the empty interval approach the time evolution is described by a system of $\frac{L(L+1)}{2}$ differential…
It is well known that in the gradient expansion approximation to density functional theory (DFT) the gradient and Laplacian of the density make interchangeable contributions to the exchange correlation (XC) energy. This is an arbitrary…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional…
We introduce a multivariate multidimensional mixed-effects regression model in a finite mixture framework. We relax the usual unidimensionality assumption on the random effects multivariate distribution. Thus, we introduce a…
Starting from configurations having homogeneous spatial density, we study kinetics in a two-dimensional system of inelastically colliding hard particles, a popular model for cooling granular matter. Following an initial time period, the…
We study damped wave propagation problems phrased as abstract evolution equations in Hilbert spaces. Under some general assumptions, including a natural compatibility condition for initial values, we establish exponential decay estimates…
We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$.…
We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of…
A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and…