相关论文: Effective interface conditions for a porous medium…

We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…

We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is…

We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The…

In this study, we analyze the behavior of monotone traveling waves of a one-dimensional porous medium equation modeling mechanical properties of living tissues. We are interested in the asymptotics where the pressure, which governs the…

We consider a mathematical model of cancer cell invasion of the extracellular matrix (ECM), comprising a strongly degenerate parabolic partial differential equation for the cell volume fraction, coupled with an ordinary differential…

The recent development of the massive multiple-input multiple-output (MIMO) paradigm, has been extensively based on the pursuit of favorable propagation: in the asymptotic limit, the channel vectors become nearly orthogonal and inter-user…

We present a detailed solution of the active interface equations in the inviscid limit. The active interface equations were previously introduced as a toy model of membrane-protein systems: they describe a stochastic interface where growth…

Tuning cell rearrangements is essential in collective cell movement that underlies cancer progression, wound repair, and embryonic development. A key question is how tissue material properties and morphology emerge from cellular factors…

We consider a symmetric, finite-range contact process with two types of infection; both have the same (supercritical) infection rate and heal at rate 1, but sites infected by Infection 1 are immune to Infection 2. We take the initial…

We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of $\Gamma$-convergence for two singular phenomena. First, for densities constrained near a hyperplane we recover the…

The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…

We study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density. We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according with the behavior…

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…

The nonlinear Forchheimer equations are used to describe the dynamics of fluid flows in porous media when Darcy's law is not applicable. In this article, we consider the generalized Forchheimer flows for slightly compressible fluids and…

The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…

Recent X-ray imaging experiments have revealed that multiphase flow through porous media involves transient fluctuations in local occupancy, even under fixed macroscopic steady-state conditions where capillary forces dominate at the pore…

We use a diffuse interface method for solving Poisson's equation with a Dirichlet condition on an embedded curved interface. The resulting diffuse interface problem is identified as a standard Dirichlet problem on approximating regular…

The phase field theory of crystal nucleation described in [L. Granasy, T. Borzsonyi, T. Pusztai, Phys. Rev. Lett. 88, 206105 (2002)] is applied for nucleation in hard--sphere liquids. The exact thermodynamics from molecular dynamics is…

Interstitial fluid flow is a feature of many solid tumours. In vitro Experiments have shown that such fluid flow can direct tumour cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis…

We show that the short-scale elastic distortions that are excited in the vicinity of the joint between different lipidic membrane domains (at a scale of \~10 nm) may produce a "crease" from the point of view of the standard elastic…