Related papers: Mean Field Approximation to a Spatial Host-Pathoge…
We study layered systems and heterostructures of s-wave superconductors by means of a suitable generalization of Dynamical Mean-Field Theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively…
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of all constituting ions. One feature of active…
We consider the mean field analog of the p-star model for homogeneous random networks, and compare its behaviour with that of the p-star model and its classical mean field approximation in the thermodynamic regime. We show that the…
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger (J. Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field fluid'' over a…
The $t-J$ Hamiltonian is studied in a mean-field approximation by taking into account antiferromagnetic and d-wave pairing correlations. Considering the presence of antiferromagnetic fluctuations, the weaknesses of a mean-field…
In this paper we consider different models for soft modes in jammed hard spheres. We show how one can construct mean field models that can be solved analytically. The analytic solution of these models displays an excess of low energy soft…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…
Near-field multi-antenna wireless communication has attracted growing research interest in recent years. Despite this development, most of the current literature on antennas and reflecting structures relies on simplified models, whose…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
We propose a new approach to deriving quantitative mean field approximations for any probability measure $P$ on $\mathbb{R}^n$ with density proportional to $e^{f(x)}$, for $f$ strongly concave. We bound the mean field approximation for the…
We present a simple one-dimensional model with molecular interactions favouring the formation of clusters with a defined optimal size. Increasing the density, at low temperature, the system goes from a nearly-ideal gas of independent…
We present a mean field model for coagulation ($A+A\to A$) and annihilation ($A+A\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is…
We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
The matrix model of random surfaces with c = inf. has recently been solved and found to be identical to a random surface coupled to a q-states Potts model with q = inf. The mean field-like solution exhibits a novel type of tree structure.…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
We study the many body Schr\"odinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles.…
A new approach is developed to derive an analytical form for mobility corrections in phase-field models for pure material solidification. Similar to the thin interface limit approach (Karma and Rappel, 1996) it seeks to remove systematic…