Related papers: A Retarded Mean-Field Approach for Interacting Fib…
Accurately rendering the appearance of fabrics is challenging, due to their complex 3D microstructures and specialized optical properties. If we model the geometry and optics of fabrics down to the fiber level, we can achieve unprecedented…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived,…
In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur…
We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geometric regions of different dynamical regimes, and thus…
We propose a microscopic stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. It is shown that, for small amplitude fluctuations, the proposed model gives a result for the…
We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering…
Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion…
We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…
The mean-field framework has been used to find approximate solutions to problems involving very large populations of symmetric, anonymous agents, which may be intractable by other methods. The cooperative mean-field control (MFC) problem…
This article formalizes the problem of modeling social networks into an interacting particle system on random geometric graphs. Each vertex of the graph is associated with a geometric position in a latent space describing the unobserved…
The mean-field theory (MFT) of simple glasses, which is exact in the limit of infinite spatial dimensions, $d\rightarrow\infty$, offers theoretical insight as well as quantitative predictions about certain features of $d=3$ systems. In…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
Suppose sender-receiver transmission links in a downlink network at given data rate are subject to fading, path-loss and inter-cell interference, and that transmissions either pass, suffer loss, or incur retransmission delay. We introduce a…
One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the…
We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…