Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell's Equations

The technique of applying form-invariant, spatial coordinate transformations of Maxwell's equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.Comment: submitted to "Photonics and Nanostructures", Special Issue "PECS VII", Elsevie

The Dirichlet Casimir effect for ϕ4\phi^4 theory in (3+1) dimensions: A new renormalization approach

We calculate the next to the leading order Casimir effect for a real scalar field, within $\phi^4$ theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.Comment: JHEP3 format,20 pages, 2 figures, to appear in JHE

The Intersections of Biological Diversity and Cultural Diversity: Towards Integration

There is an emerging recognition that the diversity of life comprises both biological and cultural diversity. In the past, however, it has been common to make divisions between nature and culture, arising partly out of a desire to control nature. The range of interconnections between biological and cultural diversity are reflected in the growing variety of environmental sub-disciplines that have emerged. In this article, we present ideas from a number of these sub-disciplines. We investigate four bridges linking both types of diversity (beliefs and worldviews, livelihoods and practices, knowledge bases and languages, and norms and institutions), seek to determine the common drivers of loss that exist, and suggest a novel and integrative path forwards. We recommend that future policy responses should target both biological and cultural diversity in a combined approach to conservation. The degree to which biological diversity is linked to cultural diversity is only beginning to be understood. But it is precisely as our knowledge is advancing that these complex systems are under threat. While conserving nature alongside human cultures presents unique challenges, we suggest that any hope for saving biological diversity is predicated on a concomitant effort to appreciate and protect cultural diversity

Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients

Casimir energy is a nonlocal effect; its magnitude cannot be deduced from heat kernel expansions, even those including the integrated boundary terms. On the other hand, it is known that the divergent terms in the regularized (but not yet renormalized) total vacuum energy are associated with the heat kernel coefficients. Here a recent study of the relations among the eigenvalue density, the heat kernel, and the integral kernel of the operator $e^{-t\sqrt{H}}$ is exploited to characterize this association completely. Various previously isolated observations about the structure of the regularized energy emerge naturally. For over 20 years controversies have persisted stemming from the fact that certain (presumably physically meaningful) terms in the renormalized vacuum energy density in the interior of a cavity become singular at the boundary and correlate to certain divergent terms in the regularized total energy. The point of view of the present paper promises to help resolve these issues.Comment: 19 pages, RevTeX; Discussion section rewritten in response to referees' comments, references added, minor typos correcte

Focus, Vol. 1 No. 1

A literary magazine of student writing published by the Department of English of Stephen F. Austin State College.https://scholarworks.sfasu.edu/focus/1000/thumbnail.jp

To the Editor:

No abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35187/1/5_ftp.pd

Concocting a divisive theory

No abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38589/1/1_ftp.pd

Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section

The heat-kernel expansion and $\zeta$-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with constant curvature are discussed in detail. Several mathematical results, relevant to physical applications are presented, including exact solutions of the heat-kernel equation, a simple exposition of hyperbolic geometry and an elementary derivation of the Selberg trace formula. With regards to the physical applications, the vacuum energy for scalar fields, the one-loop renormalization of a self-interacting scalar field theory on a hyperbolic space-time, with a discussion on the topological symmetry breaking, the finite temperature effects and the Bose-Einstein condensation, are considered. Some attempts to generalize the results to extended objects are also presented, including some remarks on path integral quantization, asymptotic properties of extended objects and a novel representation for the one-loop (super)string free energy.Comment: Latex file, 122 page

A Comment on: The Recognition and Evaluation of Homoplasy in Primate and Human Evolution. (Lockwood, C.A., and J.G. Fleagle, 1999, Yrbk Phys Anthropol 42:189–232.)

No abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34271/1/9_ftp.pd