Related papers: Homogenization of hydrodynamic transport in Dirac …
We study heat transport in two systems without momentum conservation: a hydrodynamic system, and a holographic system with spatially dependent, massless scalar fields. When momentum dissipates slowly, there is a well-defined, coherent…
This paper concerns the diffusion-homogenization of transport equations when both the adimensionalized scale of the heterogeneities $\alpha$ and the adimensionalized mean-free path $\eps$ converge to 0. When $\alpha=\eps$, it is well known…
We predict hydrodynamic Turing instability of current-carrying Dirac electron fluids that drives spontaneous self-oscillatory transport. The instability arises near charge neutrality, where carrier kinetics make current dissipation strongly…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…
Thermomigration is the driving force for hydrogen transport due to a temperature gradient. It can compete with hydrogen transport induced by stress gradients. While stress-driven hydrogen migration is well established, thermomigration…
The rising interest in Dirac materials, condensed matter systems where low-energy electronic excitations are described by the relativistic Dirac Hamiltonian, entails a need for microscopic effective models to analytically describe their…
A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…
Segregation induced by a thermal gradient of an impurity in a driven low-density granular gas is studied. The system is enclosed between two parallel walls from which we input thermal energy to the gas. We study here steady states occurring…
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…
This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its…
In recent years, research and development in nanoscale science and technology have grown significantly, with electrical transport playing a key role. A natural challenge for its description is to shed light on anomalous behaviours observed…
This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to…
Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively.…
We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the…
In this work we develop a homogenisation methodology to upscale mathematical descriptions of microcirculatory blood flow from the microscale (where individual vessels are resolved) to the macroscopic (or tissue) scale. Due to the assumed…