The proximity force approximation for the Casimir energy as a derivative expansion

The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next to leading order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function $\psi$ in front of a plane. By regarding the Casimir energy as a functional of $\psi$, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of corresponding NTLO correction, which involves two derivatives of $\psi$. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy.Comment: Minor changes. Version to appear in Phys. Rev.

Urban Water Pricing: The Metro Manila and Metro Cebu Cases

Water is a critical commodity for human survival and a scarce resource that must be appropriately priced to ensure that it is not wastefully and unsuitably consumed. This Notes offers an optimal pricing scheme, together with suggestions on the improvement of the overall water resource management that could provide the proper environment by which such pricing scheme can succeed.urban management, water sector, water demand

Chaos in black holes surrounded by gravitational waves

The occurrence of chaos for test particles moving around Schwarzschild black holes perturbed by a special class of gravitational waves is studied in the context of the Melnikov method. The explicit integration of the equations of motion for the homoclinic orbit is used to reduce the application of this method to the study of simple graphics.Comment: 15 pages, LaTex

Long-range interactions and non-extensivity in ferromagnetic spin models

The Ising model with ferromagnetic interactions that decay as $1/r^\alpha$ is analyzed in the non-extensive regime $0\leq\alpha\leq d$, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model in the $N\rightarrow\infty$ limit ($N$ being the number of spins) we propose a generalization of the Curie-Weiss model, for which the $N\rightarrow\infty$ limit is well defined for all $\alpha\geq 0$. We conjecture that mean field theory is {\it exact} in the last model for all $0\leq\alpha\leq d$. This conjecture is supported by Monte Carlo heat bath simulations in the $d=1$ case. Moreover, we confirm a recently conjectured scaling (Tsallis\cite{Tsallis}) which allows for a unification of extensive ($\alpha>d$) and non-extensive ($0\leq\alpha\leq d$) regimes.Comment: RevTex, 12 pages, 1 eps figur

Noncommutative field gas driven inflation

We investigate early time inflationary scenarios in an Universe filled with a dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic gas is a gas composed of bosonic scalar field with noncommutative field space on a commutative spacetime. Such noncommutative field theories was recently introduced as a generalization of quantum mechanics on a noncommutative spacetime. As key features of these theories are Lorentz invariance violation and CPT violation. In the present study we use a noncommutative bosonic field theory that besides the noncommutative parameter $\theta$ shows up a further parameter $\sigma$. This parameter $\sigma$ controls the range of the noncommutativity and acts as a regulator for the theory. Both parameters play a key role in the modified dispersion relations of the noncommutative bosonic field, leading to possible striking consequences for phenomenology. In this work we obtain an equation of state $p=\omega(\sigma,\theta;\beta)\rho$ for the noncommutative bosonic gas relating pressure $p$ and energy density $\rho$, in the limit of high temperature. We analyse possible behaviours for this gas parameters $\sigma$, $\theta$ and $\beta$, so that $-1\leq\omega<-1/3$, which is the region where the Universe enters an accelerated phase.Comment: Reference added. Version to appear in Journal of Cosmology and Astroparticle Physics - JCA

Art+Politics

For the exhibition Art + Politics, students worked closely with the holdings of Gettysburg College\u27s Special Collections and College Archives to curate an exhibition in Schmucker Art Gallery that engages with issues of public policy, activism, war, propaganda, and other critical socio-political themes. Each of the students worked diligently to contextualize the objects historically, politically, and art-historically. The art and artifacts presented in this exhibition reveal how various political events and social issues have been interpreted through various visual and printed materials, including posters, pins, illustrations, song sheets, as well as a Chinese shoe for bound feet. The students\u27 essays that follow demonstrate careful research and thoughtful reflection on the American Civil War, nineteenth-century politics, the First and Second World Wars, World\u27s Fairs, Dwight D. Eisenhower\u27s campaign, Vietnam-War era protests, and the Cultural Revolution in China. [excerpt]https://cupola.gettysburg.edu/artcatalogs/1009/thumbnail.jp

Fundamental limitations on "warp drive" spacetimes

"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously been remarked upon, if it could be built, the warp drive would be an example of a "reaction-less drive". For both the Alcubierre and Natario warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds. An interesting feature of this construction is that it is now meaningful to place a finite mass spaceship at the center of the warp bubble, and compare the warp field energy with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the center of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natario formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natario warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.Comment: 18 pages, Revtex4. V2: one reference added, some clarifying comments and discussion, no physics changes, accepted for publication in Classical and Quantum Gravit

Random-mass Dirac fermions in an imaginary vector potential: Delocalization transition and localization length

One dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. Especially we numerically calculate both the "typical" and "mean" localization lengths as a function of energy and the correlation length of the random mass. To this end we introduce an imaginary vector potential as suggested by Hatano and Nelson and solve the eigenvalue problem. Numerical calculations are in good agreement with the results of the analytical calculations.Comment: 4 page

Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes

This paper presents a simple analytical circuit-like model to study the transmission of electromagnetic waves through stacked twodimensional (2-D) conducting meshes. When possible the application of this methodology is very convenient since it provides a straightforward rationale to understand the physical mechanisms behind measured and computed transmission spectra of complex geometries. Also, the disposal of closed-form expressions for the circuit parameters makes the computation effort required by this approach almost negligible. The model is tested by proper comparison with previously obtained numerical and experimental results. The experimental results are explained in terms of the behavior of a finite number of strongly coupled Fabry-Pérot resonators. The number of transmission peaks within a transmission band is equal to the number of resonators. The approximate resonance frequencies of the first and last transmission peaks are obtained from the analysis of an infinite structure of periodically stacked resonators, along with the analytical expressions for the lower and upper limits of the pass-band based on the circuit model.Ministerio de Ciencia e Innovación TEC2007-65376, CSD2008- 00066Junta de Andalucía TIC-459

Numerical Approaches to Spacetime Singularities

This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev. Relativity 2002-1 at www.livingreviews.or