Raychaudhuri equation in quantum gravitational optics

The equation of Raychaudhuri is one of the key concepts in the formulation of the singularity theorems introduced by Penrose and Hawking. In the present article, taking into account QED vacuum polarization, we study the propagation of a bundle of rays in a background gravitational field through the perturbative deformation of Raychaudhuri’s equation. In a sense, this could be seen as another semiclassical study in which geometry is treated classically but matter (which means the photon here) is allowed to exhibit quantum characteristics that are encoded in its coupling to the background curvature.      

On the stability of systems of coupled partial differential equations with random excitation

The stability of the null solution of a class of a system of coupled partial differential equations with stationary random coefficients is studied. Criteria for the almost sure asymptotic stability of the equilibrium state are established. Some examples of the application of the results to engineering problems are presented. A variational scheme for improvement of the stability criteria is also discussed.     

Exact Solutions of Dirac Equation on (1+1)-Dimensional Spacetime Coupled to a Static Scalar Field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.     

Analysis and optimization of optical bistability in one-dimensional nonlinear photonic crystal with (HL)(D)(LH) and (LH)(D)(HL) structures

Although one-dimensional nonlinear photonic crystal (1D-NPC) has been widely studied, there is no comprehensive analysis on decreasing the bistability threshold power.In this paper, conditions required to create bistability have been specified for two types of structures of alternative high and low refractive index layers and defect layers with Kerr nonlinearity effect, in the order of (HL)^p(D)^q(LH)^p and (LH)^p(D)^q(HL)^p, where L and H denote low and high refractive index layers, respectively, D stands for the defect layers, p is the number of LH or HL layers and q is the number of defect layers.One of the essentials for the bistability is appropriate shifts of frequency of the defect mode, so the effect of the order of layer's arrangement in (1D-NPC) structures have been studied. Different structures have been introduced and the best structure for the lowest bistability threshold power has been proposed. Nonlinear finite-difference time-domain (NFDTD) in C++ has been employed for simulation.     

Models for concurrent product and process design

We propose procedures to address product design and manufacturing process configurations concurrently in environments characterized by large degrees of product proliferation. Exploiting the intrinsic flexibility of product and process design, we present two approaches that synchronize production flows through the manufacturing system. These approaches integrate product and manufacturing system design decisions with operational concerns and provide powerful means for managing production in environments characterized by a proliferation of products. Experimental results show that the proposed methods can substantially reduce manufacturing lead times, work in process (WIP), and overall system complexity.     

Theoretical investigation of imidazolium based ionic liquid/alcohol mixture: a molecular dynamic simulation

In this work, molecular dynamic simulation of the mixture of imidazolium based ionic liquids with alcohols is implemented in order to investigate mixing excess properties and some structural and physical properties of the mixture. Excess volumes and enthalpies are evaluated for 11 different mole fractions of ionic liquids at each 0.1, in the range of 0 to 1. Radial distribution function, cohesive energy density, potential of mean force, solvation energy, and diffusion coefficient are reported and analysed. The effects of the cationic alkyl chain length, in comparison with changes of the anions, on these properties are reported. Results reveal that the methanol molecule participates with its hydrophilic characteristics in the mixing process and tends to aggregate around anion part of the ionic liquids, especially in the case of Cl.     

A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation

An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is presented such that it can be used for adaptive strategies based on dual weighted residual methods. A posteriori error estimates based on weighted global projections and local projections are also proved.     

Reductivity of the Lie Algebra of a Bilinear Form

Let f: V × V → F be a totally arbitrary bilinear form defined on a finite dimensional vector space V over a field F, and let L(f) be the subalgebra of 𝔤𝔩(V) of all skew-adjoint endomorphisms relative to f. Provided F is algebraically closed of characteristic not 2, we determine all f, up to equivalence, such that L(f) is reductive. As a consequence, we find, over an arbitrary field, necessary and sufficient conditions for L(f) to be simple, semisimple or isomorphic to 𝔰𝔩(n) for some n.