Dynamics and instability of false vacuum bubbles

This paper examines the classical dynamics of false vacuum regions embedded in surrounding regions of true vacuum, in the thin-wall limit. The dynamics of all generally relativistically allowed solutions -- most but not all of which have been previously studied -- are derived, enumerated, and interpreted. We comment on the relation of these solutions to possible mechanisms whereby inflating regions may be spawned from non-inflating ones. We then calculate the dynamics of first order deviations from spherical symmetry, finding that many solutions are unstable to such aspherical perturbations. The parameter space in which the perturbations on bound solutions inevitably become nonlinear is mapped. This instability has consequences for the Farhi-Guth-Guven mechanism for baby universe production via quantum tunneling.Comment: 16 PRD-style pages including 11 embedded figures; accepted by PRD. Revised version includes new solution, discussion of 'thermal activation', added reference, fixed typo

Linear orderings of random geometric graphs (extended abstract)

In random geometric graphs, vertices are randomly distributed on [0,1]^2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain \NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.Postprint (published version

Convergence theorems for some layout measures on random lattice and random geometric graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. For full square lattices, we give optimal layouts for the problems still open. Our convergence theorems can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidian TSP on random points in the $d$-dimensional cube. As the considered layout measures are non-subadditive, we use percolation theory to obtain our results on random lattices and random geometric graphs. In particular, we deal with the subcritical regimes on these class of graphs.Postprint (published version

Antenna Design and Interface Dynamics for Cellular Handsets

This project involves the design and computational analysis of a Planar Inverted-F Antenna at a resonant frequency of 850 MHz in an effort to investigate and optimize its performance in the LG Nexus 5 D820 smartphone. A three-dimensional, full-wave computational model of the antenna was created with HFSS and variations of different physical parameters were conducted. The data from HFSS was exported into ADS for analog circuit modeling. The modeling predictions were successfully tested with a designed and constructed antenna

Puerto Rico Light Pollution

In Puerto Rico, light pollution is a serious problem for people living in urban environments as well as organisms in the wild. The goal of this project is to develop a procedure for measuring ground level light pollution, and to carry out initial light measurements to lay the groundwork for future studies. Surveys of Puerto Rican citizens were done to get an idea of public awareness of light pollution. The outcomes of the project are a manual for collecting data, initial measurements using the procedure at key locations, as well as a better understanding of public opinion. Our results will be presented to Para la Naturaleza and la Junta de Calidad Ambiental so they can use it to create a plan for future regulation and control of light pollution in Puerto Rico

Black Holes at the IceCube Neutrino Telescope

If the fundamental Planck scale is about a TeV and the cosmic neutrino flux is at the Waxman-Bahcall level, quantum black holes are created daily in the Antarctic ice-cap. We re-examine the prospects for observing such black holes with the IceCube neutrino-detection experiment. To this end, we first revise the black hole production rate by incorporating the effects of inelasticty, i.e., the energy radiated in gravitational waves by the multipole moments of the incoming shock waves. After that we study in detail the process of Hawking evaporation accounting for the black hole's large momentum in the lab system. We derive the energy spectrum of the Planckian cloud which is swept forward with a large, O (10^6), Lorentz factor. (It is noteworthy that the boosted thermal spectrum is also relevant for the study of near-extremal supersymmetric black holes, which could be copiously produced at the LHC.) In the semiclassical regime, we estimate the average energy of the boosted particles to be less than 20% the energy of the neutrino-progenitor. Armed with such a constraint, we determine the discovery reach of IceCube by tagging on "soft" (relative to what one would expect from charged current standard model processes) muons escaping the electromagnetic shower bubble produced by the black hole's light descendants. The statistically significant 5-sigma excess extends up to a quantum gravity scale ~ 1.3 TeV.Comment: Matching version to be published in Phys. Rev.

Patterns of Duality in N=1 SUSY Gauge Theories

We study the patterns in the duality of a wide class of N=1 supersymmetric gauge theories in four dimensions. We present many new generalizations of the classic duality models of Kutasov and Schwimmer, which have themselves been generalized numerous times in works of Intriligator, Leigh and the present authors. All of these models contain one or two fields in a two-index tensor representation, along with fields in the defining representation. The superpotential for the two-index tensor(s) resembles A_k or D_k singularity forms, generalized from numbers to matrices. Looking at the ensemble of these models, classifying them by superpotential, gauge group, and ``level'' -- for terminology we appeal to the architecture of a typical European-style theatre -- we identify emerging patterns and note numerous interesting puzzles.Comment: 34 pages, 4 figures, uses harvmac and table

Regulating Eternal Inflation II: The Great Divide

In a previous paper, two of the authors presented a "regulated" picture of eternal inflation. This picture both suggested and drew support from a conjectured discontinuity in the amplitude for tunneling from positive to negative vacuum energy, as the positive vacuum energy was sent to zero; analytic and numerical arguments supporting this conjecture were given. Here we show that this conjecture is false, but in an interesting way. There are no cases where tunneling amplitudes are discontinuous at vanishing cosmological constant; rather, the space of potentials separates into two regions. In one region decay is strongly suppressed, and the proposed picture of eternal inflation remains viable; sending the (false) vacuum energy to zero in this region results in an absolutely stable asymptotically flat space. In the other region, we argue that the space-time at vanishing cosmological constant is unstable, but not asymptotically Minkowski. The consequences of our results for theories of supersymmetry breaking are unchanged.Comment: JHEP3, 19 Pages, 7 Figure

Reproductive Failure in UK Harbour Porpoises Phocoena phocoena : Legacy of Pollutant Exposure?

This research was supported by a Marie Curie International Outgoing Fellowship within the Seventh European Community Framework Programme (Project Cetacean-stressors, PIOF-GA-2010-276145 to PDJ and SM). Additional funding was provided through the Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas (ASCOBANS) (Grants SSFA/2008 and SSFA / ASCOBANS / 2010 / 5 to SM). Analysis of Scottish reproductive and teeth samples was funded by the EC-funded BIOCET project (BIOaccumulation of persistent organic pollutants in small CETaceans in European waters: transport pathways and impact on reproduction, grant EVK3-2000-00027 to GJP), and Marine Scotland (GJP). Samples examined in this research were collected under the collaborative Cetacean Strandings Investigation Programme (http://ukstrandings.org/), which is funded by the Department for Environment, Food and Rural Affairs (Defra) and the UK’s Devolved Administrations in Scotland and Wales (http://sciencesearch.defra.gov.uk/Defaul​t.aspx?Menu=Menu&Module=More&Location=No​ne&Completed=0&ProjectID=15331) (grants to PDJ, RD). UK Defra also funded the chemical analysis under a service-level agreement with the Centre for Environment, Fisheries and Aquaculture Science (grants to RJL, JB). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Geometric Algebra Techniques for General Relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.Comment: 34 pages, 0 figures; submitted to Annals of Physic