相关论文: Discrete variance decay analysis of spurious mixin…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…

We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with finitely many critical points, recently proven in [1]. Our…

A sequence of two and three-dimensional simulations is conducted for the double diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. The flow is confined between two horizontal plates which are maintained…

We introduce Discrete Voxel Diffusion (DVD), a discrete diffusion framework to generate, assess, and edit sparse voxels for SLat (Structured LATent) based 3D generative pipelines. Although discrete diffusion has not generally displaced…

In assumed probability density function (pdf) methods of turbulent combustion, the shape of the scalar pdf is assumed a priori and the pdf is parametrized by its moments for which model equations are solved. In non-premixed flows the beta…

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The…

We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…

Recent diffusion distillation methods have achieved remarkable progress, enabling high-quality ${\sim}4$-step sampling for large-scale text-conditional image and video diffusion models. However, further reducing the number of sampling steps…

We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…

With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…

Spatially-explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density Surface Models (DSMs) are a two-stage approach for estimating spatially-varying…

The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…

The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…

Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…

The analysis of the vertical velocity dispersion of disc stars is the most direct astronomical means of estimating the local dark matter density, $\rho_{DM}$. Current estimates based on the mid-plane dynamic density use a local baryonic…

The local field correction to the spontanous dacay rate of an impurity source atom imbedded in a disordered dielectric is calculated to second order in the dielectric density. The result is found to differ from predictions associated with…

Score Distillation Sampling (SDS) has emerged as a prevalent technique for text-to-3D generation, enabling 3D content creation by distilling view-dependent information from text-to-2D guidance. However, they frequently exhibit shortcomings…

We study the mixing dynamics of a solute that is transported by advection and dispersion in a heterogeneous Darcy scale porous medium. We quantify mixing and dynamic uncertainty in terms of the mean squared solute concentration and the…