Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions

Finite temperature Casimir theory of the Dirichlet scalar field is developed, assuming that there is a conventional Casimir setup in physical space with two infinitely large plates separated by a gap R and in addition an arbitrary number q of extra compacified dimensions. As a generalization of earlier theory, we assume in the first part of the paper that there is a scalar 'refractive index' N filling the whole of the physical space region. After presenting general expressions for free energy and Casimir forces we focus on the low temperature case, as this is of main physical interest both for force measurements and also for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity q=1, by taking into account dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to appear in Physica Script

Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities

Eigenmodes of electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE modes and one polarization for TM modes, giving rise to a total of (D-1) polarizations. In case of a D-dimensional ball, the eigenfrequencies of electromagnetic field with perfectly conducting boundary condition coincides with the eigenfrequencies of gauge one-forms with relative boundary condition; whereas the eigenfrequencies of electromagnetic field with infinitely permeable boundary condition coincides with the eigenfrequencies of gauge one-forms with absolute boundary condition. Casimir energy for a D-dimensional spherical shell configuration is computed using both cut-off regularization and zeta regularization. For a double spherical shell configuration, it is shown that the Casimir energy can be written as a sum of the single spherical shell contributions and an interacting term, and the latter is free of divergence. The interacting term always gives rise to an attractive force between the two spherical shells. Its leading term is the Casimir force acting between two parallel plates of the same area, as expected by proximity force approximation.Comment: 28 page

Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming

This paper considers an optimum nonuniform FIR transmultiplexer design problem subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then a solution exists. Since the problem is formulated as a convex problem, if a solution exists, then the solution obtained is unique and the local solution is a global minimum

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.Comment: 20 pages, 4 figure

Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit

In this paper, the finite temperature Casimir force acting on a two-dimensional Casimir piston due to electromagnetic field is computed. It was found that if mixed boundary conditions are assumed on the piston and its opposite wall, then the Casimir force always tends to restore the piston towards the equilibrium position, regardless of the boundary conditions assumed on the walls transverse to the piston. In contrary, if pure boundary conditions are assumed on the piston and the opposite wall, then the Casimir force always tend to pull the piston towards the closer wall and away from the equilibrium position. The nature of the force is not affected by temperature. However, in the high temperature regime, the magnitude of the Casimir force grows linearly with respect to temperature. This shows that the Casimir effect has a classical limit as has been observed in other literatures.Comment: 14 pages, 3 figures, accepted by Journal of Physics

Relationship between macroscopic physical properties and local distortions of low doping La{1-x}Ca{x}MnO3: an EXAFS study

A temperature-dependent EXAFS investigation of La{1-x}Ca{x}MnO3 is presented for the concentration range that spans the ferromagnetic-insulator (FMI) to ferromagnetic-metal (FMM) transition region, x = 0.16-0.22. The samples are insulating for x = 0.16-0.2 and show a metal/insulator transition for x = 0.22. All samples are ferromagnetic although the saturation magnetization for the 16% Ca sample is only ~ 70% of the expected value at 0.4T. We find that the FMI samples have similar correlations between changes in the local Mn-O distortions and the magnetization as observed previously for the colossal magnetoresistance (CMR) samples (0.2 < x < 0.5) - except that the FMI samples never become fully magnetized. The data show that there are at least two distinct types of distortions. The initial distortions removed as the insulating sample becomes magnetized are small and provides direct evidence that roughly 50% of the Mn sites have a small distortion/site and are magnetized first. The large remaining Mn-O distortions at low T are attributed to a small fraction of Jahn-Teller-distorted Mn sites that are either antiferromagnetically ordered or unmagnetized. Thus the insulating samples are very similar to the behavior of the CMR samples up to the point at which the M/I transition occurs for the CMR materials. The lack of metallic conductivity for x <= 0.2, when 50% or more of the sample is magnetic, implies that there must be preferred magnetized Mn sites and that such sites do not percolate at these concentrations.Comment: 27 pages, 8 figures, to be submitted to Phys. Rev.

Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions

We compute the finite temperature Casimir energy for massive scalar field with general curvature coupling subject to Dirichlet or Neumann boundary conditions on the walls of a closed cylinder with arbitrary cross section, located in a background spacetime of the form $M^{d_1+1}\times \mathcal{N}^n$, where $M^{d_1+1}$ is the $(d_1+1)$-dimensional Minkowski spacetime and $\mathcal{N}^n$ is an $n$-dimensional internal manifold. The Casimir energy is regularized using the criteria that it should vanish in the infinite mass limit. The Casimir force acting on a piston moving freely inside the closed cylinder is derived and it is shown that it is independent of the regularization procedure. By letting one of the chambers of the cylinder divided by the piston to be infinitely long, we obtain the Casimir force acting on two parallel plates embedded in the cylinder. It is shown that if both the plates assume Dirichlet or Neumann boundary conditions, the strength of the Casimir force is reduced by the increase in mass. Under certain conditions, the passage from massless to massive will change the nature of the force from long range to short range. Other properties of the Casimir force such as its sign, its behavior at low and high temperature, and its behavior at small and large plate separations, are found to be similar to the massless case. Explicit exact formulas and asymptotic behaviors of the Casimir force at different limits are derived. The Casimir force when one plate assumes Dirichlet boundary condition and one plate assumes Neumann boundary condition is also derived and shown to be repulsive.Comment: 28 pages, 4 figure

Optimal control strategies for tuberculosis treatment: a case study in Angola

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Axially symmetric rotating traversable wormholes

This paper generalizes the static and spherically symmetric traversable wormhole geometry to a rotating axially symmetric one with a time-dependent angular velocity by means of an exact solution. It was found that the violation of the weak energy condition, although unavoidable, is considerably less severe than in the static spherically symmetric case. The radial tidal constraint is more easily met due to the rotation. Similar improvements are seen in one of the lateral tidal constraints. The magnitude of the angular velocity may have little effect on the weak energy condition violation for an axially symmetric wormhole. For a spherically symmetric one, however, the violation becomes less severe with increasing angular velocity. The time rate of change of the angular velocity, on the other hand, was found to have no effect at all. Finally, the angular velocity must depend only on the radial coordinate, confirming an earlier result.Comment: 17 pages, AMSTe

A hybrid approach to constrained global optimization

In this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to