Related papers: Three Scale Unfolding Homogenization Method Applie…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
In this work, we apply phase field simulations to examine the coarsening behavior of morphologically complex two-phase microstructures in which the phases have highly dissimilar mobilities, a condition approaching that found in experimental…
In cardiac cells, structural organization is an important indicator of cell maturity and healthy function. Healthy cardiomyocytes exhibit well-aligned morphology with densely packed and organized sarcomeres. Immature or diseased…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
We perform one and two-parameter numerical bifurcation analysis of a mechanotransduction model approximating the dynamics of mesenchymal stem cell differentiation into neurons, adipocytes, myocytes and osteoblasts. For our analysis, we use…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
Background and Objective: This proof of concept study investigates mathematical modelling of blood flow and oxygen transport in cerebral microcirculation, focusing on understanding hemodynamic responses. By coupling oxygen transport models…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also…
This paper presents methodology for the computation of whole sets of heteroclinic connections between iso-energetic slices of center manifolds of center x center x saddle fixed points of autonomous Hamiltonian systems. It involves: (a)…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…
In this work we present the homogenization of a reaction-diffusion model that includes an evolving microstructure. Such type of problems model, for example, mineral dissolution and precipitation in a porous medium. Hence, we are dealing…
This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal…
We investigate, both experimentally and theoretically, the bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled either as a smooth or as border-collision period-doubling bifurcation. Using a new…
Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be…
Mathematical modeling of cardiac function can provide augmented simulation-based diagnosis tool for complementing and extending human understanding of cardiac diseases which represent the most common cause of worldwide death. As the…
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…
The technique of periodic homogenization with two-scale convergence is applied to the analysis of a two-phase Stefan-type problem that arises in the study of a periodic array of melting ice bars. For this "reduced model" we prove results on…