Related papers: Periodic homogenization in the context of structur…
We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor…
A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of the process of condensation in such a system is constructed. The free energy of formation of the…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
A system of a metastable phase with several sorts of the heterogeneous centers is considered. An analytical theory for the process of condensation in such a system is constructed in dynamic conditions. The free energy of formation of the…
We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…
These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…
A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and…
Nowadays, nonhomogeneous and periodic ferromagnetic materials are the subject of a growing interest. Actually such periodic configurations often combine the attributes of the constituent materials, while sometimes, their properties can be…
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
Pseudopotential theory has greatly driven first-principles calculations in materials, replacing the explicit treatment of the chemically inert core electrons with an effective potential acting only on the valence states. This is inherently…
The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation.…
Most elemental metals under ambient conditions adopt simple structures such as BCC, FCC and HCP in specific groupings across the Periodic Table, and on compression, many of these elements undergo transitions to surprisingly complex…
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a…
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…