相关论文: Drift-diffusion processes from elimination of fast…

Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…

The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…

A modified version of the Ginzburg-Landau equation is introduced which accounts for asymmetric couplings between neighbors sites on a one-dimensional lattice, with periodic boundary conditions. The drift term which reflects the imposed…

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…

Drift theory is an intuitive tool for reasoning about random processes: It allows turning expected stepwise changes into expected first-hitting times. While drift theory is used extensively by the community studying randomized search…

The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number $\epsilon$, evolution equations are…

We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion type. The model is set over a one dimensional bounded interval,…

In this paper we will study homogenization of for stable-like process with divergence-free drift in ergodic environments. In particular, neither the drift nor the stream function are required to be bounded.

Irreversible drift-diffusion processes are very common in biochemical reactions. They have a non-equilibrium stationary state (invariant measure) which does not satisfy detailed balance. For the corresponding Fokker-Planck equation on a…

A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…

In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…

We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of…

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…

The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor…

Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…

Denoising diffusion models trained at web-scale have revolutionized image generation. The application of these tools to engineering design is an intriguing possibility, but is currently limited by their inability to parse and enforce…

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations…