相关论文: Kinetic decomposition for periodic homogenization …
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
In this paper, we study the kinetic Vicsek model, which serves as a starting point for describing the polarization phenomena observed in the experiments of fibroblasts moving on liquid crystalline substrates. The long-time behavior of the…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…
Via hydrodynamics preserving molecular dynamics simulations we study growth phenomena in a phase separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap,…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…
This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by…
We investigate expansive solutions of the $N$-body problem in $\mathbb{R}^d$ ($d\ge2$) driven by homogeneous Newtonian potentials of degree $-\alpha$. We establish the existence of half-entire expansive motions with prescribed initial…
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions on the sphere. In particular, we address a problem of…
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
This article studies the homogenization of hyperbolic-parabolic equations in porous media with tiny holes. We assume that the holes are periodically distributed and that the coefficients of the equations are periodic. Using the multi-scale…