Related papers: Homogenization for advection-diffusion in a perfor…
We deal with the rigorous homogenization and dimension reduction of flow and transport problems posed in thin $\varepsilon$-periodic perforated layers with thickness of order $\varepsilon^{\alpha}$ with $\alpha \in (0,1)$ and therefore the…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
The aim of this paper is to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field with the systematic use of the two-timing method. Our…
Let $(\xi(s))_{s\geq 0}$ be a standard Brownian motion in $d\geq 1$ dimensions and let $(D_s)_{s \geq 0}$ be a collection of open sets in $\R^d$. For each $s$, let $B_s$ be a ball centered at 0 with $\vol(B_s) = \vol(D_s)$. We show that…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
In this paper, we consider the homogenization of evolutionary incompressible purely viscous non-Newtonian flows of Carreau-Yasuda type in porous media with small perforation parameter $0< \varepsilon \ll 1$, where the small holes are…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
For every $\alpha < \frac13$, we construct an explicit divergence-free vector field $\mathbf{b}(t,x)$ which is periodic in space and time and belongs to $C^0_t C^{\alpha}_x \cap C^{\alpha}_t C^0_x$ such that the corresponding scalar…
We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh-B\'enard convection for the Rayleigh number range $10^5 \le Ra \le 10^{11}$ and $Pr=0.7$. Using a Cartesian slab…
We investigate the asymptotic behavior of the solutions to the Neumann sieve problem for the Poisson equation in a thin, randomly perforated domain. The perforations (sieve-holes) are generated by a stationary marked point process.…
We explore a connection of the forced Burgers equation with the Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to…
We consider the homogenisation of a diffusion equation in a porous medium. The microstructure is time-dependent and oscillating on a small time scale. This oscillation causes a novel advection in the homogenised equations. Allowing for a…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…
We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…
We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…
We consider the growth of a polymer layer on a flat surface in a good solvent by in-situ polymerization. This is viewed as a modified form of diffusion-limited aggregation without branching. We predict theoretically the formation of a…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
We consider coupled diffusions in $n$-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a…