Related papers: Self-energy of dislocations and dislocation pileup…
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
This paper studies the economic role of persistent dispersion in allocations across agents. We develop a tractable model in which firms allocate resources under imperfect information and behavioral updating, generating sustained…
The essential role of long range elastic interactions in recrystallization is demonstrated using a simple analytical model: pileup rearrangements following absorption of leading dislocations by a dislocation-free embryo provides an…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
The dynamics of defect excitations in crystalline solids is necessary to understand the macroscopic low-energy properties of elastic media. We use fracton-elasticity duality to systematically study the defect dynamics and interactions in…
This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that…
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…
A large family of diffusive models of transport that has been considered in the past years admits a transformation into the same model in contact with an equilibrium bath. This mapping holds at the full dynamical level, and is independent…
In this paper, we study the global in time existence problem for the Groma-Balogh model describing the dynamics of dislocation densities. This model is a two-dimensional model where the dislocation densities satisfy a system of transport…
Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is…
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
We study a 2D quasi-static discrete {\it crack} anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transfered to all elements through elastic forces.…
The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress…
We investigate a one-dimensional rice-pile model. We show that the distribution of dissipated potential energy decays as a power law with an exponent $\alpha=1.53$. The system thus provides a one-dimensional example of self-organized…
The energy-momentum localization for a new four-dimensional and spherically symmetric, charged black hole solution that through a coupling of general relativity with non-linear electrodynamics is everywhere non-singular while it satisfies…
A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and…
In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide due…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
We reexamine two essential issues within the Peierls-Nabarro model which are critical in obtaining accurate values for the Peierls stress. The first issue is related to the sampling scheme of the misfit energy across the glide plane and the…