Related papers: A density-constrained model for Chemotaxis
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
We study theoretically vesicle locomotion due to haptotaxis. Haptotaxis is referred to motion induced by an adhesion gradient on a substrate. The problem is solved within a local approximation where a Rayleigh-type dissipation is adopted.…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
We study a kinetically constrained lattice glass model in which continuous local densities are randomly redistributed on neighbouring sites with a kinetic constraint that inhibits the process at high densities, and a random bias accounting…
We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we…
In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive…
We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased random walk. In order to take into account…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
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 analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…
Mathematical models that describe the tumor growth process have been formulated by several authors in order to understand how cancer develops and to develop new treatment approaches. In this study, it is aimed to investigate the long-time…
Motivated by the reported peculiar dynamics of a red blood cell in shear flow, we develop an analytical theory for the motion of a nearly--spherical fluid particle enclosed by a visco--elastic incompressible interface in linear flows. The…
Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive…
In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible…
A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…