Related papers: Numerical analysis on mixing processes for transcr…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
Coupling between chemical fuel consumption and phase separation can lead to condensation at a nonequilibrium steady state, resulting in phase behaviors that are not described by equilibrium thermodynamics. Theoretical models of such…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
Recently Whitaker et al. (2017) considered Bayesian estimation of diffusion driven mixed effects models using data-augmentation. The missing data, diffusion bridges connecting discrete time observations, are drawn using a "residual bridge…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
The dispersion and dissipation properties of a scheme are important to realize high-fidelity simulations of the compressible flow, especially the cases with broadband length scales. It has been recognized that the minimization of dispersion…
Binary droplet collisions are of importance in a variety of practical applications comprising dispersed two-phase flows. The background of our research is the prediction of properties of particulate products formed in spray processes. To…
Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating…
This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still…
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…