Related papers: Modeling of a diffusion with aggregation: rigorous…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
Diffusion limited aggregation is studied from the perspective of computational complexity. A parallel algorithm is exhibited that requires a number of steps that scales as the depth of the tree defined by the cluster. The existence of this…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…
The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex-energy solutions of the Schr\"odinger equation, typically when calculating their inner products. In quantum scattering theory the…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
Dissipative particle dynamics (DPD) is a relatively new technique which has proved successful in the simulation of complex fluids. We caution that for the equilibrium achieved by the DPD simulation of a simple fluid the temperature depends…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
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,…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
We introduce a novel particle-based algorithm for end-to-end training of latent diffusion models. We reformulate the training task as minimizing a free energy functional and obtain a gradient flow that does so. By approximating the latter…
Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…