Related papers: Homogenization of Stokes System using Bloch Waves
Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem…
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…
The single- and multi- particle inclusive spectra for strongly inhomogeneous thermal boson systems are studied using the method of statistical operator. The thermal Wick's theorem is generalized and the analytical solution of the problem…
This paper is concerned with the asymptotic description of high-frequency waves in locally periodic media. A key issue is that the Bloch-dispersion curves vary with the local microstructure, giving rise to hidden singularities associated…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
We prove the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. The fluid satisfies a no-slip boundary condition at the…
This paper is devoted to the study of the stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media. It is shown by the stochastic two-scale convergence method extended to periodic surfaces that results in a…
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq-Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on…
In this article, we consider a stochastic ferrohydrodynamic system which describes the Bloch-Torrey regularization of the motion of an electrically conducting ferrofluids driven by transport noise filling a 3D bounded domain with a smooth…
We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Well-posedness of the…
This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear…
Under the action of a weak constant force a wavepacket in periodic potential undergoes periodic oscillations in space, returning to the initial position after one oscillation cycle. This wave phenomenon, known as Bloch oscillations (BOs),…
Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leading order like a Stokes fluid with some explicit effective…
We consider an elastic/viscoelastic transmission problem for the Bresse system with fully Dirichlet or Dirichlet-Neumann-Neumann boundary conditions. The physical model consists of three wave equations coupled in certain pattern. The system…
In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…
The steady motion of a viscous incompressible fluid in a multiply-connected, planar, bounded domain (perforated with a large number of small holes) is modeled through the Navier-Stokes equations with non-homogeneous Dirichlet boundary data…
We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain.…
This work is devoted to the long-standing open problem of homogenization of 2D perfect incompressible fluid flows, such as the 2D Euler equations with impermeable inclusions modeling a porous medium, and such as the lake equations. The main…