Bouncing universe models in an extended gravity theory

Some bouncing models are investigated in the framework of an extended theory of gravity. The extended gravity model is a simple extension of the General Relativity where an additional matter geometry coupling is introduced to account for the late time cosmic speed up phenomena. The dynamics of the models are discussed in the background of a flat FRW universe. Some viable models are reconstructed for specifically assumed bouncing scale factors. The behavior of the models are found to be decided mostly by the parameters of the respective models. The extended gravity based minimal matter-geometry coupling parameter has a role to remove the omega singularity occurring at the bouncing epoch. It is noted that the constructed models violate the energy conditions, however, in some cases this violation leads to the evolution of the models in phantom phase. The stability of the models are analyzed under linear homogeneous perturbations and it is found that, near the bounce, the models show instability but the perturbations decay out smoothly to provide stable models at late times.     

Localized Plastic Deformation of Metal-Intermetallic Laminated Composites after Equal Channel Angular Pressing

Russian Physics Journal - The paper presents mathematical simulation of localized plastic deformation of metal-intermetallic laminated composites after equal channel angular pressing. Deformation...     

Stability Issues in Two-Dimensional Mathematical Models of Plasma Equilibrium in Magnetic Galathea Traps

Differential Equations - Galathea traps for confining plasma in a magnetic field created by current-carrying conductors immersed in the plasma volume constitute a promising class of objects for...     

Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.     

On Transformations of Three-Valued Random Variables by Bivariate Functions

Journal of Applied and Industrial Mathematics - We consider transformations of three-valued random variables by functions of the three-valued logic. For arbitrary systems of bivariate functions...     

Nonlinear Evolutionary Schrödinger Equation in the Supercritical Case

Theoretical and Mathematical Physics - We prove that for some initial data, solutions of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case are destroyed after...