Related papers: A Multiscale Model of Partial Melts 1: Effective E…
In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…
A two-component interaction model is introduced herein, which allows to describe macroscopic miscibility with various modes of tunable micro-segregation, ranging from phase separation to micro-segregation, and in excellent agreement for…
Quantitative and realistic computer simulations of mass transfer associated with CO2 disposal in subsurface aquifers is a challenging endeavor. This article has proposed a novel and efficient multiscale modeling framework, and has examined…
It is shown that the one- and two-dimensional solids may exist and melt
Temperature stabilization of oil and gas wells is used to ensure stability and prevent deformation of a subgrade estuary zone. In this work, we consider the numerical simulation of thermal stabilization using vertical seasonal freezing…
In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or…
We present a simple unifying model for crystallization and melting temperatures by showing that homogeneous nucleation and phase transformations driven by thickening of pre-existing surface layers are limiting conditions of the more general…
A multiscale model for real-time simulation of terrain dynamics is explored. To represent the dynamics on different scales the model combines the description of soil as a continuous solid, as distinct particles and as rigid multibodies. The…
A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat…
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of…
We use the notion of stochastic two-scale convergence to solve the problem of stochastic homogenization of the elastic plate in the bending regime.
Our previous molecular dynamic simulation studies of simple two-dimensional (2D) systems \cite{matt_big} suggested that both geometrical defects (localized, large-amplitude deviations from hexagonal ordering) and topological defects…
This review is devoted to the large-scale rheology of suspensions of rigid particles in Stokes fluid. After describing recent results on the definition of the effective viscosity of such systems in the framework of homogenization theory, we…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…
Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the…