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We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we…
The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the…
We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes…
A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the…
An exact analysis is performed for the two-point correlation function C(r,t) in dissipative Burgers turbulence with bounded initial data, in arbitrary spatial dimension d. Contrary to the usual scaling hypothesis of a single dynamic length…
We examine the role of boundaries and the structure of nontrivial duality functions for three non conservative interacting particle systems in one dimension that model epidemic spreading: (i) the diffusive contact process (DCP), (ii) a…
We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…
We consider a one-dimensional system with particles having either positive or negative velocity, which annihilate on contact. To the ballistic motion of the particle, a diffusion is superimposed. The annihilation may represent a reaction in…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
Using numerical simulations, we examine the structure and diffusion of a two-dimensional dusty plasma (2DDP) in the presence of a one-dimensional periodic substrate (1DPS) as a function of increasing substrate strength. Both the pair…
We propose a diffusion model designed to generate point-based shape representations with correspondences. Traditional statistical shape models have considered point correspondences extensively, but current deep learning methods do not take…
The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional periodic substrate with varied widths is investigated using Langevin dynamical simulations. When the substrate is narrow and the dust particles form a single row,…
Interplay between kinetic roughening and phase ordering is studied in a growth SOS model with two kinds of particles and Ising-like interaction by Monte Carlo simulations. We found that, for a sufficiently large coupling, growth is strongly…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
We present a model to describe the concentration-dependent growth of protein filaments. Our model contains two states, a low entropy/high affinity ordered state and a high entropy/low affinity disordered state. Consistent with experiments,…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with…