Electromagnetic Non-contact Gears: Prelude

We calculate the lateral Lifshitz force between corrugated dielectric slabs of finite thickness. Taking the thickness of the plates to infinity leads us to the lateral Lifshitz force between corrugated dielectric surfaces of infinite extent. Taking the dielectric constant to infinity leads us to the conductor limit which has been evaluated earlier in the literature.Comment: 7 pages, 2 figures, Contribution to Proceedings of 9th Conference on Quantum Field Theory Under the Influence of External Conditions (QFEXT09), Norman, OK, September 21-25, 200

Casimir energy of Sierpinski triangles

Using scaling arguments and the property of self-similarity we derive the Casimir energies of Sierpinski triangles and Sierpinski rectangles. The Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is introduced and the Berry-Weyl conjecture is discussed for these geometries. We propose that for a class of fractals, comprising of compartmentalized cavities, it is possible to establish a finite value to the Casimir energy even while the Casimir energy of the individual cavities consists of divergent terms.Comment: 7 pages, 5 figures, minor typos correcte

Quantum vacuum energy of self-similar configurations

We offer in this review a description of the vacuum energy of self-similar systems. We describe two views of setting self-similar structures and point out the main differences. A review of the authors’ work on the subject is presented, where they treat the self-similar system as a many-object problem embedded in a regular smooth manifold. Focused on Dirichlet boundary conditions, we report a systematic way of calculating the Casimir energy of self-similar bodies where the knowledge of the quantum vacuum energy of the single building block element is assumed and in fact already known. A fundamental property that allows us to proceed with our method is the dependence of the energy on a geometrical parameter that makes it possible to establish the scaling property of self-similar systems. Several examples are given. We also describe the situation, shown by other authors, where the embedded space is a fractal space itself, having fractal dimension. A fractal space does not hold properties that are rather common in regular spaces like the tangent space. We refer to other authors who explain how some self-similar configurations “do not have any smooth structures and one cannot define differential operators on them directly”. This gives rise to important differences in the behavior of the vacuum

ESTRUCTURA DE MANDO DE UNIDADES AISLADAS TIPO COMPAÑÍA

En el Trabajo de Fin de Grado del Grado de Ingeniería de Organización Industrial, se ha elegido el proyecto “Estructura de Mando de Unidades Aisladas Tipo Compañía” con el fin de crear un equipo auxiliar o plana que asesore y ayude a coordinar las actividades a realizar por el jefe de un Subgrupo Táctico cuando actúa de manera aislada. Para ello es necesario realizar un estudio de la estructura de mando vigente a día de hoy, así como sobre las necesidades de una base semipermanente. Para la realización de este proyecto se tendrá en cuenta la opinión de personal de la Tercera Bandera Paracaidista que tenga experiencia en misiones internacionales desarrolladas dentro de bases semipermanentes, que actuarán como expertos en la materia con el fin de crear dicho equipo de apoyo o auxiliar partiendo de la experiencia personal de cada encuestado.<br /

Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates

We calculate the lateral Casimir force between corrugated parallel plates, described by $\delta$-function potentials, interacting through a scalar field, using the multiple scattering formalism. The contributions to the Casimir energy due to uncorrugated parallel plates is treated as a background from the outset. We derive the leading- and next-to-leading-order contribution to the lateral Casimir force for the case when the corrugation amplitudes are small in comparison to corrugation wavelengths. We present explicit results in terms of finite integrals for the case of the Dirichlet limit, and exact results for the weak-coupling limit, for the leading- and next-to-leading-orders. The correction due to the next-to-leading contribution is significant. In the weak coupling limit we calculate the lateral Casimir force exactly in terms of a single integral which we evaluate numerically. Exact results for the case of the weak limit allows us to estimate the error in the perturbative results. We show that the error in the lateral Casimir force, in the weak coupling limit, when the next-to-leading order contribution is included is remarkably low when the corrugation amplitudes are small in comparison to corrugation wavelengths. We expect similar conclusions to hold for the Dirichlet case. The analogous calculation for the electromagnetic case should reduce the theoretical error sufficiently for comparison with the experiments.Comment: 25 pages, 10 figures, appendix added, references corrected, typos correcte

Local Casimir Energies for a Thin Spherical Shell

The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness $\delta$, where it has height $h$, with the constraint $h\delta=1$. In the limit of zero thickness, an ideal $\delta$-function shell is recovered. The behavior of the energy density as the surface of the shell is approached is studied in both the strong and weak coupling regimes. The former case corresponds to the well-known Dirichlet shell limit. New results, which shed light on the nature of surface divergences and on the energy contained within the shell, are obtained in the weak coupling limit, and for a shell of finite thickness. In the case of zero thickness, the energy has a contribution not only from the local energy density, but from an energy term residing entirely on the surface. It is shown that the latter coincides with the integrated local energy density within the shell. We also study the dependence of local and global quantities on the conformal parameter. In particular new insight is provided on the reason for the divergence in the global Casimir energy in third order in the coupling.Comment: 16 pages, revtex 4, no figures. Major additions, clarifications, and corections, references adde

Non-contact gears: II. Casimir torque between concentric corrugated cylinders for the scalar case

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for non-contact gears. To this end, we calculate the Casimir torque between two such cylinders, described by $\delta$-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed.Comment: 9 pages, 3 figures, references correcte

Mejoras en el diseño actual de la Sección de Nodos de Referencia de los CIS desplagables del Regimiento de Transmisiones Nº 21, para el apoyo a los nodos SIMACET del Ejército de Tierra.

El objetivo de este trabajo es mejorar la estructura y el funcionamiento de la Sección de Nodos de Referencia de los CIS (Sistemas de Telecomunicaciones y Sistemas de Información) Desplegables del Regimiento de Transmisiones 21. Ante la necesidad de establecer un nodo, el cual cumpla con todas las certificaciones para trabajar en el ámbito OTAN y esté listo para poder dar servicio a cualquier Unidad del Ejército de Tierra, es esencial abordar algunos aspectos que necesitan un avance o perfeccionamiento. La mejora de ellos supondrá un mejor apoyo en el Mando y Control de las operaciones o ejercicios del Ejército de Tierra. Los principales aspectos a mejorar son, en primer lugar, el establecimiento de un personal de dedicación exclusiva. El personal necesita estar lo suficientemente cualificado para poder establecer la configuración del Nodo de Referencia. El alto nivel de preparación e instrucción técnica de estos profesionales se hace imprescindible para que puedan realizar su trabajo de una manera eficiente. Por otro lado, se han de disminuir los tiempos de transmisión de configuraciones del Nodo de Referencia al resto de Unidades del Ejercito de Tierra para ser capaces de afrontar la preparación de los ejercicios o de las operaciones en el menor tiempo posible. Por último, surge la necesidad de la creación de una base de datos de conocimiento para poder dejar constancia de cómo solventar los fallos que ya han sido detectados y resueltos anteriormente por personal del Nodo de Referencia. Esta base de datos es realmente útil debido a la complejidad en la creación de cero de un nodo que sea capaz de dar servicio, cumpliendo además con las continuas actualizaciones de las acreditaciones que el CCN (Centro Criptológico Nacional) impone al Ejercito de Tierra. Estas acreditaciones son necesarias para poder trabajar en el ámbito OTAN. <br /

Local and Global Casimir Energies for a Semitransparent Cylindrical Shell

The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a $\lambda\delta$-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined for both weak and strong coupling, the latter being the well-studied Dirichlet cylinder case. For weak-coupling,through $\mathcal{O}(\lambda^2)$, the total energy is shown to vanish by both analytic and numerical arguments, based both on Green's-function and zeta-function techniques. Divergences occurring in the calculation are shown to be absorbable by renormalization of physical parameters of the model. The global energy may be obtained by integrating the local energy density only when the latter is supplemented by an energy term residing precisely on the surface of the cylinder. The latter is identified as the integrated local energy density of the cylindrical shell when the latter is physically expanded to have finite thickness. Inside and outside the delta-function shell, the local energy density diverges as the surface of the shell is approached; the divergence is weakest when the conformal stress tensor is used to define the energy density. A real global divergence first occurs in $\mathcal{O}(\lambda^3)$, as anticipated, but the proof is supplied here for the first time; this divergence is entirely associated with the surface energy, and does {\em not} reflect divergences in the local energy density as the surface is approached.Comment: 28 pages, REVTeX, no figures. Appendix added on perturbative divergence

PT-Symmetry Quantum Electrodynamics--PTQED

The construction of $\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are discussed.Comment: 11 pages, 1 figure, contributed to Proceedings of 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physic