相关论文: Non-singular dislocation loops in gradient elastic…

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…

We extend the generalized gradient-flow framework of Peletier, Rossi, Savar\'e, and Tse to singular jump processes on abstract metric spaces, moving beyond the translation-invariant kernels considered in $\mathbb{R}^d$ and $\mathbb{T}^d$ in…

We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model consists of a Peierls-Nabarro type energy penalizing non-integer slip and…

We derive asymptotic expansions for the displacement at the boundary of a smooth, elastic body in the presence of small inhomogeneities. Both the body and the inclusions are allowed to be anisotropic. This work extends prior work of…

A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization.…

In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for…

We introduce a phenomenological theory of dislocation motion appropriate for two dimensional lattices. A coarse grained description is proposed that involves as primitive variables local lattice rotation and Burgers vector densities along…

Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory…

We investigate nonlinear aggregation dynamics of phase elements distributed on the unit circle under parametrically modulated external fields. Our model, inspired by flaky particle rotation in fluids, employs the equation ${d\alpha/dt} =…

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes…

The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…

The utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects like defected grain and phase boundaries, dislocations and disclinations. The…

Grain boundaries (GBs) merge and grains disappear during microstructure evolution. However, the Peach-Koehler model predicts that particular stress states may reverse such a process by exerting differential Peach-Koehler forces on different…

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily-oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary…

Slender structures are ubiquitous in biological and physical systems, from bacterial flagella to soft robotic arms. The Cosserat rod provides a mathematical framework for slender bodies that can stretch, shear, twist and bend. In viscous…

We investigate the realization of non-singular bouncing cosmologies driven by causal bulk-viscous fluids within General Relativity, $f(R)$ gravity, and Loop Quantum Cosmology. Building on the no-go result of Eckart theory in spatially flat…

The elastodynamic Peach-Koehler force is computed for a fully-regularized straight dislocation with isotropic core in continuum isotropic elastic elasticity, in compact forms involving partial mass or impulsion functions relative to shear…

In this work we investigate lump-like solutions in models described by a single real scalar field. We start considering non-topological solutions with the usual lump-like form, and then we study other models, where the bell-shape profile…

We study the sharp interface limit and well-posedness of a phase field model for self-climb of prismatic dislocation loops in periodic settings. The model is set up in a Cahn-Hilliard/Allen-Cahn framework featured with degenerate…

We introduce a model for nonlinear viscoelastic solids where traveling shear waves with compact support are possible. We obtain an exact compact solution. We also derive a new Burger's type evolution equation associated with the introduced…