相关论文: Homogenization of linear transport equations in a …

The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…

We study the homogenization of a stationary conductivity problem in a random heterogeneous medium with highly oscillating conductivity coefficients and an ensemble of simply closed conductivity resistant membranes. This medium is randomly…

It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…

On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is…

Inflationary spatially homogeneous cosmological models within an Einstein-Aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the aether field expansion and shear scalars…

We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such…

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…

A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…

We establish homogenization for nondegenerate viscous Hamilton-Jacobi equations in one space dimension when the diffusion coefficient $a(x,\omega) > 0$ and the Hamiltonian $H(p,x,\omega)$ are general stationary ergodic processes in $x$. Our…

This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp $O(\varepsilon)$ convergence rate and characterize the effective constant. In the multi-scale setting, our results…

We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is…

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular…

We consider the kinetic transport equation that arise in the Boltzmann-Grad limit of the two-dimensional periodic Lorentz Gas. This equation has been obtained by extending the phase space of positions and velocities through the introduction…

We study the geodesic deviation equation for a quantum particle in a linearized quantum gravitational field. Particle's Heisenberg equations of motion are treated as stochastic equations with a quantum noise. We explore the stochastic…

We study the absorbing state transition in particulate systems under spatially inhomogeneous driving using a modified random organization model. For smoothly varying driving the steady state results map onto the homogeneous absorbing state…

We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: {\em micro-macro}). The geometry we have in mind includes regions of…

We examine the phenomenon of dynamical heterogeneity in computer simulations of an equilibrium, glass-forming liquid. We describe several approaches to quantify the spatial correlation of single-particle motion, and show that spatial…

We prove homogenization for degenerate viscous Hamilton-Jacobi equations in dimension one in stationary ergodic environments with a quasiconvex and superlinear Hamiltonian of fairly general type. We furthermore show that the effective…

This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We…

We derive equations of motion for dissipative spin hydrodynamics from kinetic theory up to first order in a gradient expansion. Choosing a specific form of the matching conditions, relating the change in the spin potential to the spin…