6,352 research outputs found
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 ,
where is the -dimensional Minkowski spacetime and
is an -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
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
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
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
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