
Pedro Morales-AlmazanUniversity of California, Santa Cruz | UCSC · Department of Mathematics
Pedro Morales-Almazan
PhD Mathematics
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13
Publications
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Introduction
My work has been directed towards the application of spectral zeta functions in calculations of the Casimir Effect. I have studied spectral zeta functions arising from Laplace type differential operators defined on different types of Riemannian manifolds, their relation with heat kernel coefficients and zero point energy.
Additional affiliations
July 2018 - present
January 2013 - June 2018
January 2013 - present
Education
January 2008 - December 2011
January 2008 - August 2012
January 2003 - May 2008
Publications
Publications (13)
This article explores the parallels between improvisational theater, commonly known as improv, and active teaching. Specifically, it focuses in the impact of improv techniques on instructor and teaching assistant professional development. The implementation of an active teaching seminar is analyzed, where improv techniques were used in developing t...
This article explores the parallels between improvisational theater (Improv) and teaching in an Active Learning environment. It presents the notions of Active Teaching as a natural complement to Active Learning, and discusses how unexpected situations give rise to valuable Teaching Moments. These Teaching Moments can be strategically utilized follo...
In this article, we consider the functional determinant on an annulus and elliptic regions with a variety of boundary conditions. Known results for the annulus are rederived and extended using contour integration techniques. Conformal transformations are then used to relate these results to ellipsoidal annuli, providing very explicit answers. Simil...
In this paper, we explore the zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and on the change of the Casimir energy associated with the surface.
In this article we consider a spherical piston modeled by a spherically symmetric potential. The piston is positioned between two spherical shells and the corresponding Casimir energy and force are computed. Zeta function regularization based upon suitable contour integral representations is utilized. A numerical analysis of the Casimir force is pr...
We present a geometric way of describing the irrationality of a number using
the area of a circular sector $A(r)$. We establish a connection between this
and the continued fraction expansion of the number, and prove bounds for $A(r)$
as $r\to\infty$ by describing the asymptotic behavior of the ratios of the
denominators of the convergents.
In this paper we explore the Zeta function arising from a small perturbation
on a surface of revolution and the effect of this on the functional determinant
and in the change of the Casimir energy associated with this configuration.
In this work the Casimir effect is studied for scalar fields in the presence
of boundaries and under the influence of arbitrary smooth potentials of compact
support. In this setting, piston configurations are analyzed in which the
piston is modeled by a potential. For these configurations, analytic results
for the Casimir energy and force are obtai...
We de?ne a special type of hypersurface varieties inside $\mathbb{P}_k^{n-1}$
arising from connected planar graphs and then find their equivalence classes
inside the Gr\"othendieck ring of projective varieties. Then we find a
characterization for graphs in order to de?ne irreducible hypersurfaces in
general.
We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extra dimensions and of the cross section of the piston. Furthermore, we evaluate the zeta regularized determinant for this configuration.
In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function ass...
We consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration. In order to compute the determinant and Casimir force, we employ the zeta function scheme. Essentially, the computation reduces to the analysis of the zeta function associated with a...
We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extradimensions and of the cross section of the piston. Furthermore, we evaluate the zeta regularized determinant for this configuration.