Related papers: An Analysis of the Evolution Equations for a Gener…
We derive the pressure tensor and the heat flux to accompany the new macroscopic conservation equations that we developed previously in a volume-based kinetic framework for gas flows. This kinetic description allows for expansion or…
The behaviour of solutions to the Einstein equations with a causal viscous fluid source is investigated. In this model we consider a spatially flat Robertson-Walker metric, the bulk viscosity coefficient is related to the energy density as…
We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…
A 2D numerical hydrodynamics approach is considered for modelling recent experimental results on the oscillation and collective behavior of convective flows. Our simulations consider the rising dynamics of heated fluid columns in a…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell models allow one to define well motions…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of the convective rolls via a…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
We study the phenomenon of evolution by horizontal mean curvature flow in sub-Riemannian geometries. We use a stochastic approach to prove the existence of a generalized evolution in these spaces. In particular we show that the value…
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is…
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions , and such that…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
Gravitational and hydrodynamical perturbations are analysed in a relativistic plasma containing a mixture of interacting fluids characterized by a non-negligible bulk viscosity coefficient. The energy-momentum transfer between the…
We develop a rigorous formalism for the description of the kinetic evolution of interacting entities modeling systems in mathematical biology within the framework of the evolution of marginal observables. For this purpose we construct the…
We find that waves develop in a time-decaying mixing layer of viscoelastic fluid, leading the mean-flow to yo-yo. This is in sharp contrast with Newtonian fluids, where laminar mixing layers evolve monotonically. We combine direct numerical…