147 research outputs found
Influence of a magnetic fluxon on the vacuum energy of quantum fields confined by a bag
We study the simultaneous influence of boundary conditions and external
fields on quantum fluctuations by considering vacuum zero-point energies for
quantum fields in the presence of a magnetic fluxon confined by a bag, circular
and spherical for bosons and circular for fermions. The Casimir effect is
calculated in a generalized cut-off regularization after applying zeta-function
techniques to eigenmode sums and using recent techniques about Bessel zeta
functions at negative arguments
Complete zeta-function approach to the electromagnetic Casimir effect for spheres and circles
A technique for evaluating the electromagnetic Casimir energy in situations
involving spherical or circular boundaries is presented. Zeta function
regularization is unambiguously used from the start and the properties of
Bessel and related zeta functions are central. Nontrivial results concerning
these functions are given. While part of their application agrees with previous
knowledge, new results like the zeta-regularized electromagnetic Casimir energy
for a circular wire are included.Comment: accepted in Ann. Phy
On the asymptotic spatial behaviour of the solutions of the nerve system
In this paper we investigate the asymptotic spatial behavior of the solutions for several models for the nerve fibers.
First, our analysis deals with the coupling of two parabolic equations. We prove that, under suitable assumptions on the coefficients
and the nonlinear function, the decay is similar to the one corresponding to the heat equation. A limit case of this system
corresponds to the coupling of a parabolic equation with an ordinary differential equation. In this situation, we see that for suitable
boundary conditions the solution ceases to exist for a finite value of the spatial variable. Next two sections correspond to
the coupling of a hyperbolic/parabolic and hyperbolic/ordinary differential problems. For the first one we obtain that the decay
is like an exponential of a second degree polynomial in the spatial variable. In the second one, we prove a similar behaviour to
the one corresponding to the wave equation. In these two sections we use in a relevant way an exponentially weighted Poincaré
inequality which has been revealed very useful in several thermal and mechanical problems. This kind of results have relevance
to understand the propagation of perturbations for nerve models.Peer ReviewedPostprint (author’s final draft
On (non-)exponential decay in generalized thermoelasticity with two temperatures
Konstanzer Schriften in Mathematik ; 355We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential
stability for the Lord-Shulman modelPreprin
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