Related papers: Stochastic homogenization of multicontinuum hetero…
Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear…
In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in…
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise…
Multiphase flow in porous media underpins subsurface energy and environmental technologies, including geological CO$_2$ storage and underground hydrogen storage, yet pore-scale dynamics in realistic three-dimensional materials remain…
We study the effect of spatially-correlated heterogeneity on isothermal drying of porous media. We combine a minimal pore-scale model with microfluidic experiments with the same pore geometry. Our simulated drying behavior compare favorably…
Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem…
Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…
Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a…
We show by means of experiments, theory and simulations, that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multi-point…
By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham…
This work concerns about forward-backward multivalued stochastic systems. First of all, we prove one average principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a convergence rate…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We study the generalized Forchheimer flows of slightly compressible fluids in heterogeneous porous media. The media's porosity and coefficients of the Forchheimer equation are functions of the spatial variables. The partial differential…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
This paper establishes a quantitative, uniform-in-time diffusion approximation for the joint law of a broad class of fully coupled multiscale stochastic systems. We derive a precise characterization of the limiting joint distribution as a…
This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…
In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many applications, coarse-grid macroscopic models are developed.…
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion…