Related papers: Fractal homogenization of multiscale interface pro…
The analysis and homogenization of a moving boundary problem for a highly heterogeneous, periodic two-phase medium is considered. In this context, the normal velocity governing the motion of the interface separating the two competing phases…
This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagrangian finite element space on polytopial meshes. We introduce…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
The self-similarity of complex systems has been studied intensely across different domains due to its potential applications in system modeling, complexity analysis, etc., as well as for deep theoretical interest. Existing studies rely on…
In this paper, we are interested in the reiterated homogenization of linear elliptic equations of the form $-\frac{\partial}{\partial x_{i}} \left(a_{i j} \left(\frac{x}{\varepsilon}, \frac{x}{\varepsilon^{2}}\right) \frac{\partial…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
We present a complete numerical analysis for a general discretization of a coupled flow-mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix-fracture interfaces, as well as…
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…
This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartesian mesh. The local IFE space on each interface element…
We investigate the asymptotic behavior of solutions for quasilinear parabolic equations in bounded intervals. In particular, we are concerned with a special class of solutions, called interface solutions, which exhibit e metastable…
We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
We study homogenization of a locally periodic two-scale dual-continuum system where each continuum interacts with the other. Equations for each continuum are written separately with interaction terms (exchange terms) added. The…
We formally derive interface conditions for modeling fractures in Darcy flow problems and, more generally, thin inclusions in heterogeneous diffusion problems expressed as the divergence of a flux. Through a formal integration of the…
Zonal jets manifest themselves as bands with sharp interfaces in the vorticity configuration. We develop an algorithm to track these fluctuating vorticity interfaces and systematically investigate their characteristic spatio-temporal…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…