Related papers: A Diffusion-Based Embedding of the Stochastic Simu…
Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. \rev{At the level of particle-resolved descriptions, where chemical reactions are coupled…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
In large-eddy simulations of atmospheric boundary layer turbulence, the lumped coefficient in the eddy-diffusion subgrid-scale (SGS) model is known to depend on scale for the case of inert scalars. This scale dependence is predominant near…
The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded)…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply…
Smoluchowski-type models for diffusion-influenced reactions (A+B -> C) can be formulated within two frameworks: the probabilistic-based approach for a pair A, B of reacting particles and the concentration-based approach for systems in…
Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary…
Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…
The stochastic simulation of large-scale biochemical reaction networks is of great importance for systems biology since it enables the study of inherently stochastic biological mechanisms at the whole cell scale. Stochastic Simulation…
The coarse-grained molecular dynamics (MD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the…
Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…
Diffusion models (DMs) have shown promising results on single-image super-resolution and other image-to-image translation tasks. Benefiting from more computational resources and longer inference times, they are able to yield more realistic…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…