相关论文: Diffusion and Mixing in Fluid Flow

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

We provide sufficient conditions on a positive function so that its associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow.

In dense flowing bidisperse particle mixtures varying in size or density alone, smaller particles sink (driven by percolation) and lighter particles rise (driven by buoyancy). But when the particle species differ from each other in both…

Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy…

The transport of single-phase fluid mixtures in porous media is described by cross-diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy's law, and the van der…

Three-dimensional laminar flow structures with mixing, chemical reaction, normal strain, and shear strain qualitatively representative of turbulent combustion at the small scales are analyzed. A mixing layer is subjected to counterflow in…

We investigate the spectral distribution of the damped wave equation on a compact Riemannian manifold, especially in the case of a metric of negative curvature, for which the geodesic flow is Anosov. The main application is to obtain…

In this paper we prove the existence and uniqueness of very weak solutions to linear diffusion equations involving a singular absorption potential and/or an unbounded convective flow on a bounded open set of $\mathbb R^N$. In most of the…

Fundamental properties of the multicomponent diffuse-interface model (DIM), such as the maximum entropy principle and conservation laws, are used to explore the basic interfacial dynamics and phase transitions in fluids. Flat interfaces…

We illustrate the flow or wave character of the metrics and curvatures of evolving manifolds, introducing the Riemann flow and the Riemann wave via the bialternate product Riemannian metric. This kind of evolutions are new and very natural…

Flow matching (FM) has gained significant attention as a simulation-free generative model. Unlike diffusion models, which are based on stochastic differential equations, FM employs a simpler approach by solving an ordinary differential…

The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically.…

We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…

Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…

Majority of theoretical results regarding turbulent mixing are based on the model of ideal flows with zero correlation time. We discuss the reasons why such results may fail for real flows and develop a scheme which makes it possible to…

Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a…

Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…

We prove the existence of weak solutions to a system of two diffusion equations that are coupled by a pointwise volume constraint. The time evolution is given by gradient dynamics for a free energy functional. Our primary example is a model…

A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the nonlinear stage of the…