Related papers: Inertial and retardation effects for dislocation i…
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…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are…
Dislocations are one-dimensional (1D) topological line defects where the lattice deviates from the perfect crystal structure. The presence of dislocations transcends condensed matter research and gives rise to a diverse range of emergent…
We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian whose solution represents the atom dislocation in a crystal. The equation comprises the evolutive version of the classical…
We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems like ion traps, semicondutor quantum dots…
In this paper, a new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem is introduced, and the discontinuous Galerkin technique of this work is different from the general discontinuous…
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…
In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to…
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…
Particle-particle interactions in sedimenting systems have been investigated in the present study considering the many-body hydrodynamic and electrodynamic interactions. These interactions primarily occur in two modes: near-field and…
A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schr\"odinger equation shows that the…
We introduce a method for determining the functional form of the stochastic and dissipative interactions in a dissipative particle dynamics (DPD) model from projected phase space trajectories. The DPD model is viewed as a coarse graining of…
These lectures provide an introduction to the theory of disordered interacting electron systems. In particular, we concentrate on those aspects which are fundamental for the problem of the metal-insulator transition due to the interplay of…
We report results from a computer simulation study on the rotational ratchet effect in systems of magnetic particles interacting via dipolar interactions. The ratchet effect consists of directed rotations of the particles in an oscillating…
We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…
Recently, a static gravitational field, such as that of the Earth, was proposed as a new source of decoherence [1]. We study the conditions under which it becomes the dominant decoherence effect in typical interferometric experiments. The…
Elastodynamic cohesive-zone models for defects such as cracks or dislocations (such as the Geubelle-Rice model for cracks, or the Dynamic Peierls Equation for flat-core dislocations), feature the same stress-response convolution kernel in…
We derive a continuum-level plasticity model for polycrystalline materials in the high energy density regime, based on a single dislocation density and single mobility mechanism, with an evolution model for the dislocation density. The…