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In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells,…
Extensions to kinetic theory and hydrodynamic models are proposed that account for the existence of multi-particle contacts. In the presence of multi-particle contacts (involving elastic, reversible, potential contact energy), dissipation…
Machine learning models for the global atmosphere that are capable of producing stable, multi-year simulations of Earth's climate have recently been developed. However, the ability of these ML models to generalize beyond the training…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
We determine the asymptotic behavior of the solutions to the linear elastodynamic equations in a stratified medium comprising an alternation of possibly very stiff layers with much softer ones, when the thickness of the layers tends to…
Many-body perturbation theory within the G$_0$W$_0$ approximation is used to determine molecular orbital level alignment at a liquid water/Pt(111) interface generated through $ab~ initio$ molecular dynamics. Molecular orbital energy levels…
A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…
Working at the Lifshitz level, we investigate the van der Waals interactions across a series of layers with a periodic motif. We derive the complete form of the van der Waals interaction as an explicit function of the number of periodic…
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear…
This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel…
We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of…
Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up…
Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for…
This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction.…
For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of…
Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed,…
The paper presents results of investigations of small bodies dynamics in a vicinity of giant planets. We used the most simple body model: gravitationally bounded, rotating contact binary affected by the tidal force acting from a planet.…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…