Related papers: The Porous Medium Equation: Large Deviations and G…
Based on non-equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two-phase flow in porous media. These equations…
We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered…
The gradient flow equation in the 2D $O(N)$ nonlinear sigma model with lattice regularization is solved in the leading order of the $1/N$ expansion. By using this solution, we analytically compute the thermal expectation value of a lattice…
The energy--momentum tensor and the tensor continuity equation serve as the conservation laws of energy, linear momentum, and angular momentum for a continuous flow. Previously, we derived equations of motion for macroscopic electromagnetic…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
We study incompressible fluid flow through a thin poroelastic layer and rigorously derive a macroscopic model when the thickness of the layer tends to zero. Within the layer we assume a periodic structure and both, the periodicity and the…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…
A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing from fluid content…
In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living tissues development including chemotaxis. We extend the…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the…
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…
The classical Prats' problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This…
The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple,…
We study a model problem on the filtration of a conducting fluid through a porous layer. A porous medium is presented as an assemblage of identical spherical cells. Each cell consists of a porous core and liquid shell. We show the…