BCS Instability and Finite Temperature Corrections to Tachyon Mass in Intersecting D1-Branes

A holographic description of BCS superconductivity is given in arxiv:1104.2843. This model was constructed by insertion of a pair of D8-branes on a D4-background. The spectrum of intersecting D8-branes has tachyonic modes indicating an instability which is identified with the BCS instability in superconductors. Our aim is to study the stability of the intersecting branes under finite temperature effects. Many of the technical aspects of this problem are captured by a simpler problem of two intersecting D1-branes on flat background. In the simplified set-up we compute the one-loop finite temperature corrections to the tree-level tachyon mass using the frame-work of SU(2) Yang-Mills theory in (1 + 1)-dimensions. We show that the one-loop two-point functions are ultraviolet finite due to cancellation of ultraviolet divergence between the amplitudes containing bosons and fermions in the loop. The amplitudes are found to be infrared divergent due to the presence of massless fields in the loops. We compute the finite temperature mass correction to all the massless fields and use these temperature dependent masses to compute the tachyonic mass correction. We show numerically the existence of a transition temperature at which the effective mass of the tree-level tachyons becomes zero, thereby stabilizing the brane configuration.Comment: Article, 95 pages, 59 figures, improved numerics, added reference

Neotenic Representations in Gerald Durrell’s Works

Neoteny refers to a set of infant-like characteristics which, if present in even adult non-human animals, are found endearing by humans and activates nurturing responses in them. These features are large eyes, short limbs, a  large head compared to the body, upright posture and a generally rounded configuration etc. Konrad Lorenz calls these features collectively as ‘child schema.’ In culture industries, toy and doll-makers, as well as cartoon film-makers, exploit this tendency of their consumers to increase their sales by representing animals neotenically. It is a process of deliberate juvenilization.  Though a form of anthropocentric representation, Gerald  Durrell has shown in his works how neoteny can be used ecocentrically to change human attitudes towards neglected and so-called  ‘ugly’  creatures.  Combined often with anthropomorphism, neoteny becomes a  potent tool in  Durrell’s hands to fight anthropocentrism and promote ecocentrism

Finite Temperature Corrections to Tachyon Mass in Intersecting D-Branes

We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in arxiv:1403.0389. In this paper we extend the computation to the case of intersecting D3-branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8-branes in D4-brane background was proposed in arxiv:1104.2843. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and show that the result is finite. Analyzing the amplitudes further we numerically compute the transition temperature at which the Tachyon becomes massless. The analytic expressions for the one-loop amplitudes obtained here reduce to those for intersecting D1-branes obtained in arxiv:1403.0389 as well as those for intersecting D2-branes.Comment: 73 pages, 24 figures, articl

A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C0C^0 IP methods

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers reliable and efficient a posteriori error estimators. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posed ness of the problem. Subsequently, applications of $C^0$ interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings. Finally, we also discuss the variational discontinuous discretization method (without discretizing the control) and its corresponding error estimates.Comment: 23 pages, 5 figures, 1 tabl

Theoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters

The dependence of the dimensionless Brans-Dicke (BD) coupling parameter upon time and the scalar field has been determined, for an isotropic and homogeneous space of zero curvature, by solving BD field equations and the wave equation for the scalar field. For this purpose, very simple expressions of empirical scale factors, that generate constant deceleration parameters, have been used here in two theoretical models. The characteristics of time dependence of the BD parameter, obtained from these two models, are in qualitative agreement with each other. The mathematical expressions representing the rate of change of the BD parameter with time, based on these two models, are found to have identical forms. Combining the expressions of the BD parameter obtained from these two models, a method for the determination of the present value of the equation-of-state (EoS) parameter of the cosmic fluid has been discussed. Its value is found to be consistent with the ranges of values obtained from other studies based on recent observations

Non-Conforming Finite Element Method For Constrained Dirichlet Boundary Control Problem

This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It employs an ultra weak formulation and utilizes Crouzeix-Raviart finite elements to discretize the state variable, while employing piecewise constants for the control variable discretization. The study demonstrates that the energy norm of an enriched discrete optimal control is uniformly bounded with respect to the discretization parameter. Furthermore, it establishes an optimal order a priori error estimate for the control variable.Comment: 21 page

Theoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters

The dependence of the dimensionless Brans-Dicke (BD) coupling parameter upon time and the scalar field has been determined, for an isotropic and homogeneous space of zero curvature, by solving BD field equations and the wave equation for the scalar field. For this purpose, very simple expressions of empirical scale factors, that generate constant deceleration parameters, have been used here in two theoretical models. The characteristics of time dependence of the BD parameter, obtained from these two models, are in qualitative agreement with each other. The mathematical expressions representing the rate of change of the BD parameter with time, based on these two models, are found to have identical forms. Combining the expressions of the BD parameter obtained from these two models, a method for the determination of the present value of the equation-of-state (EoS) parameter of the cosmic fluid has been discussed. Its value is found to be consistent with the ranges of values obtained from other studies based on recent observations