Related papers: Multinomial Diffusion Equation
We present a macroscopic model of the decay of a coherent classical scalar field into statistical fluctuations through the process of parametric amplification. We solve the field theory (henceforth,"microscopic") model to leading order in a…
We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…
The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving…
We study the large-scale behaviour of a class of driven diffusive systems modelled by a Stochastic Partial Differential Equation, the Stochastic Burgers Equation (SBE) with general nonlinearity, at the critical dimension and in infinite…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low light…
We present a three-dimensional model, based on cohesive spherical particles, of rain-induced landslides. The rainwater infiltration into the soil follow the either the fractional or the fractal diffusion equations. We solve analytically the…
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…
Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…
A simple manner to describe the diffusive relaxation of a colloidal fluid adsorbed in a porous medium is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in…
For large systems of Brownian particles interacting through their ranks introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative distribution function satisfies a porous medium PDE. However, when we introduce a common…