Related papers: An Analysis of the Evolution Equations for a Gener…
The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom. It makes use of a continuous reconstruction and does not require a Riemann solver. An evolution operator is used for the additional degrees of freedom on…
We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are…
We prove existence and uniqueness of weak solutions to anisotropic and crystalline mean curvature flows, obtained as limit of the viscosity solutions to flows with smooth anisotropies.
Metabolism and evolution are closely connected: if a mutation incurs extra energetic costs for an organism, there is a baseline selective disadvantage that may or may not be compensated for by other adaptive effects. A long-standing, but to…
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally…
We investigate the stochastic evolution equations describing the motion of a Non-Newtonian fluids excited by multiplicative noise of L\'evy type. By making use of Galerkin approximation we can prove that the system has a global…
The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such…
Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of…
We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble…
Turbulence has been recognized as a factor of paramount importance for the survival or extinction of sinking phytoplankton species. However, dealing with its multiscale nature in models of coupled fluid and biological dynamics is a…
In most fluid dynamics problems, the governing equations are nonlinear because of the presence of convective terms. Nevertheless, existence of solutions can be shown by direct sum provided one identifies, in the relevant Banach space of…
Many bacteria live in natural and clinical environments with abundant macromolecular polymers. Macromolecular fluids commonly display viscoelasticity and non-Newtonian rheological behavior; it is unclear how these complex-fluid properties…
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…
Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the…
We study the flow generated by an incompressible viscoelastic fluid in a fractured porous medium. The model consists of a fluid flow governed by Stokes-Volterra equations evolving in a periodic double-porosity medium. Using the multiscale…
It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological…
Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at…
The large-scale collective behavior of biological systems can be characterized by macroscopic transport, which arises from the non-equilibrium microscopic interactions among individual constituents. A prominent example is the formation of…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution…