Related papers: Dispersion Relations for Dislocation Modes and the…

If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution that could in principle be…

This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…

Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal…

We have calculated the general dispersion relationship for surface waves on a ferrofluid layer of any thickness and viscosity, under the influence of a uniform vertical magnetic field. The amplification of these waves can induce an…

Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave vector…

The Lie-group approach was applied to determine symmetries of the third-order non-linear equation formulated for description of shear elastic disturbances in soft solids. Invariant solutions to this equation are derived and it turned out…

The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very…

Existence of localized modes supported by the PT-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems it possesses families (branches) of solutions, which can…

We overview recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which…

The technique of distributed dislocations proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work is intended to extend this technique in studying crack problems within…

The modulational instability and discrete matter wave solitons in dipolar BEC, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instability of nonlinear plane matter waves in a…

We investigate the effects of anisotropy on dispersion relations and convergence in relativistic hydrodynamics. In particular, we show that for dispersion relations with a branch point at the origin (such as sound modes), there exists a…

We study collective modes in anisotropic double layer systems. To this end, we derive a zero-$T$ dynamic polarization function for a conductor with a paraboloidal dispersion. Following this, we demonstrate the dependence of the plasmonic…

A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…

A recent study demonstrated that granular crystals containing a single dislocation exhibit dislocation glide analogous to that observed in atomic-scale crystals, resulting in plastic deformation at yield stresses several orders of magnitude…

We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We…

High entropy alloys gained significant scientific interest in recent years due to their enhanced mechanical properties including high yield strength combined with outstanding ductility. The strength of these materials originates from their…

The paper addresses the bistability caused by spontaneous symmetry breaking bifurcation in a one-dimensional periodically corrugated nonlinear waveguide pumped by coherent light at normal incidence. The formation and the stability of the…

We study collective dynamics of interacting centers of exciton-polariton condensation in presence of spatial inhomogeneity, as modeled by diatomic active oscillator lattices. The mode formalism is developed and employed to derive existence…