Related papers: Dislocations in a layered elastic medium with appl…
The seismically active regions often correlate with fault lines, and the movement of these faults plays a crucial role in defining how stress is stored or released in these areas. To investigate the deformation and accumulation/release of…
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the…
An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By…
We introduce in this study an algorithm for the imaging of faults and of slip fields on those faults. The physics of this problem are modeled using the equations of linear elasticity. We define a regularized functional to be minimized for…
During the life of animals, epithelial tissues undergo extensive deformations--first to form organs during embryogensis and later to preserve integrity and function in adulthood. To what extent these deformations resemble that of non-living…
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…
We consider the problem of a rigid surface moving over a flat plane. The surfaces are separated by a small gap filled by a lubricant fluid. The relative position of the surfaces is unknown except for the initial time $t=0$. The total load…
A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface…
Within the lattice dynamics formulation, we present an exact solution for anti-plane surface waves in a square lattice strip with a surface row of material particles of two types separated by a linear interface. The considered problem is a…
We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The…
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing…
We prove uniqueness and stability for an inverse boundary problem associated to an anisotropic elliptic equation arising in the modeling of prestressed elastic membranes.
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
This paper is concerned with the problem of scattering of a time-harmonic electromagnetic field by a three-dimensional elastic body. General transmission conditions are considered to model the interaction between the electromagnetic field…
We study the surface fluctuations of a tissue with a dynamics dictated by cell-rearrangement, cell-division, and cell-death processes. Surface fluctuations are calculated in the homeostatic state, where cell division and cell death…
Metallic materials under high stress often exhibit deformation localization, manifesting as slip banding. Over seven decades ago, Frank and Read introduced the well-known model of dislocation multiplication at a source, explaining slip band…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the…