相关论文: Dimension-splitting for simplifying diffusion in l…

The goal of this work is to analyze the long-term behavior of reaction-diffusion systems arising in two-species chemical models and to identify the minimal set of modes that determine their dynamics. The models considered include, as…

A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth-death lattice gas model taking into account the influence of an economic…

We analyze the tagged particle diffusion for kinetically constrained models for glassy systems. We present a method, focusing on the Kob-Andersen model as an example, which allows to prove lower and upper bounds for the self diffusion…

The dynamics of interacting particles in orbital magnetic fields are notoriously difficult to study, as this physics is inherently connected to electronic correlations in two-dimensional systems, for which no straightforward theoretical…

Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…

We show that reaction-diffusion processes in three dimensions can be efficiently handled by event-driven numerical simulations, based on statistical waiting times (Gillespie's Monte-Carlo method). The algorithm is efficient for dilute…

A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic…

Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…

Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are…

We present a simple mechanical model for dynamic wetting phenomena. Metallic balls spread along a periodically corrugated surface simulating molecules of liquid advancing along a solid substrate. A vertical stack of balls mimics a liquid…

We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction or size. The scheme employs a periodically shaken two dimensional dissipative lattice and hinges on a simultaneous transport…

In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…

This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical…

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

We discuss stationary aspects of a set of driven lattice gases in which hard-core particles with spatial extent, covering more than one lattice site, diffuse and reconstruct in one dimension under nearest-neighbor interactions. As in the…