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Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…

Computer Vision and Pattern Recognition · Computer Science 2023-10-05 Zike Wu , Pan Zhou , Kenji Kawaguchi , Hanwang Zhang

We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial…

Soft Condensed Matter · Physics 2023-10-24 David Rower , Misha Padidar , Paul J. Atzberger

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…

Soft Condensed Matter · Physics 2023-02-28 P. J. Atzberger , P. R. Kramer , C. S. Peskin

Including the effect of thermal fluctuations in traditional computational fluid dynamics requires developing numerical techniques for solving the stochastic partial differential equations of fluctuating hydrodynamics. These Langevin…

Computational Physics · Physics 2015-06-12 S. Delong , B. E. Griffith , E. Vanden-Eijnden , A. Donev

The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in…

Quantum Physics · Physics 2010-12-06 Adrian A. Budini

Continuing on our previous work [ArXiv:1212.2644], we develop semi-implicit numerical methods for solving low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with…

Numerical Analysis · Mathematics 2016-01-20 A. J. Nonaka , Y. Sun , J. B. Bell , A. Donev

Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…

Machine Learning · Computer Science 2026-01-30 Kaiyuan Tan , Kendra Givens , Peilun Li , Thomas Beckers

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…

Numerical Analysis · Mathematics 2022-07-13 Wenyuan Li , Anatoly Alikhanov , Yalchin Efendiev , Wing Tat Leung

The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…

Statistics Theory · Mathematics 2007-06-13 Sergey Plyasunov

In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…

Soft Condensed Matter · Physics 2023-02-28 Paul J. Atzberger

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)…

Computational Physics · Physics 2007-05-23 H. Rafii-Tabar , H. R. Sepangi

A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…

Probability · Mathematics 2019-02-11 Jennifer Krüger , Wilhelm Stannat

The Rayleigh-Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to surface energy densities. Consequently, at these scales,…

Fluid Dynamics · Physics 2023-06-21 Bryn Barker , John B. Bell , Alejandro L. Garcia

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Analysis of PDEs · Mathematics 2024-10-31 Rômulo Damasclin Chaves dos Santos , Jorge Henrique de Oliveira Sales

The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit…

Statistical Mechanics · Physics 2022-01-11 Alberto Montefusco , Christof Schütte , Stefanie Winkelmann

The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

Numerical Analysis · Mathematics 2023-11-14 Mohammad Partohaghighi , Emmanuel Asante-Asamani , Olaniyi S. Iyiola

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

We present the spatial regime conversion method (SRCM), a novel hybrid modelling framework for simulating reaction-diffusion systems that adaptively combines stochastic discrete and deterministic continuum representations. Extending the…

Quantitative Methods · Quantitative Biology 2025-07-08 Charles G. Cameron , Cameron A. Smith , Christian A. Yates

We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…

Numerical Analysis · Mathematics 2024-04-30 Yu Zhao , Zhennan Zhou

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…

Statistical Mechanics · Physics 2015-05-14 Sven Dorosz , Michel Pleimling