Related papers: Stability Analysis for Magnetic Resonance Elastogr…
We investigate the inverse problem of determining nonlinear elastic material parameters from boundary stress measurements corresponding to prescribed boundary displacements. The material law is described by a nonlinear, space-independent…
The shear viscosity in the dilute regime of a model for confined granular matter is studied by simulations and kinetic theory. The model consists on projecting into two dimensions the motion of vibrofluidized granular matter in shallow…
Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…
A theory of mechanical behaviour of the magneto-sensitive elastomers is developed in the framework of a linear elasticity approach. Using a regular rectangular lattice model, different spatial distributions of magnetic particles within a…
In amorphous materials, plasticity is localized and occurs as shear transformations. It was recently shown by Wu et al. that these shear transformations can be predicted by applying topological defect concepts developed for liquid crystals…
Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging.…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and $L^\infty$ estimates for the pressure as…
We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…
Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
The essential feature of the method is the employment of Elasto-Magnetic Resonance Spectroscopy (EMRS) for precise local measurements of the attenuation of shear elastic waves introduced into a biological sample. Such a measurement can be…
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity…