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.     

A semi-empirical approach to determine gamma activities in environmental cylindrical samples

A semi-empirical method to determine radionuclide concentrations in large environmental samples without the use of reference material and avoiding the typical complexity of Monte-Carlo codes is proposed. The calculation of full-energy peak efficiencies was carried out from a relative efficiency curve (obtained from the gamma spectra data), and the geometric (simulated by Monte-Carlo), absorption, sample and intrinsic efficiencies for energies between 130 and 3000 keV. The absorption and sample efficiencies were determined from the mass absorption coefficients, whereas the intrinsic efficiency was approximated by an empirical function. The deviations between calculated and experimental efficiencies for a reference material in most cases are less than 10%. Radionuclide activities in marine sediment samples calculated by the proposed method and by the experimental comparative method were not significantly different. This new method can be used for routine environmental monitoring when uncertainties up to 10% are acceptable.     

Transcendence of Certain Reciprocal Sums of Linear Recurrences

 Suppose that {R _n } _n ⩾ 0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers

The Rank of a Direct Power of a Small-Cancellation Group

We construct an example of a finitely generated group G such that rank((G )ⁿ)=2 for all n1. For each n, we construct a finitely presented group G _n such that rank((G _n )ⁿ)=2. We conjecture that if G is a word-hyperbolic group then rank(G ⁿ ) as $ n. For each m we give an example of a residually finite group K _m such that K _m has exactly two relators, but K _m has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D.     

Every closed convex set is the set of minimizers of some -smooth convex function

We show that for every closed convex set in a separable Banach space there is a -smooth convex function so that . We also deduce some interesting consequences concerning smooth approximation of closed convex sets and continuous convex functions.

     

Representation type of Hecke algebras of type

In this paper we provide a complete classification of the representation type for the blocks for the Hecke algebra of type , stated in terms of combinatorical data. The computation of the complexity of Young modules is a key component in the proof of this classification result.     

Extensions for finite Chevalley groups II

Let be a semisimple simply connected algebraic group defined and split over the field with elements, let be the finite Chevalley group consisting of the -rational points of where , and let be the th Frobenius kernel. The purpose of this paper is to relate extensions between modules in and with extensions between modules in . Among the results obtained are the following: for 2$"> and , the -extensions between two simple -modules are isomorphic to the -extensions between two simple -restricted -modules with suitably ``twisted" highest weights. For , we provide a complete characterization of where and is -restricted. Furthermore, for , necessary and sufficient bounds on the size of the highest weight of a -module are given to insure that the restriction map is an isomorphism. Finally, it is shown that the extensions between two simple -restricted -modules coincide in all three categories provided the highest weights are ``close" together.

     

An EMA study of VCV coarticulatory direction

This study addresses three issues that are relevant to coarticulation theory in speech production: whether the degree of articulatory constraint model (DAC model) accounts for patterns of the directionality of tongue dorsum coarticulatory influences; the extent to which those patterns in tongue dorsum coarticulatory direction are similar to those for the tongue tip; and whether speech motor control and phonemic planning use a fixed or a context-dependent temporal window. Tongue dorsum and tongue tip movement data on vowel-to-vowel coarticulation are reported for Catalan VCV sequences with vowels /i/, /a/, and /u/, and consonants /p/, /n/, dark /l/, /s/, /S/, alveolopalatal /n/ and /k/. Electromidsagittal articulometry recordings were carried out for three speakers using the Carstens articulograph. Trajectory data are presented for the vertical dimension for the tongue dorsum, and for the horizontal dimension for tongue dorsum and tip. In agreement with predictions of the DAC model, results show that directionality patterns of tongue dorsum coarticulation can be accounted for to a large extent based on the articulatory requirements on consonantal production. While dorsals exhibit analogous trends in coarticulatory direction for all articulators and articulatory dimensions, this is mostly so for the tongue dorsum and tip along the horizontal dimension in the case of lingual fricatives and apicolaminal consonants. This finding results from different articulatory strategies: while dorsal consonants are implemented through homogeneous tongue body activation, the tongue tip and tongue dorsum act more independently for more anterior consonantal productions. Discontinuous coarticulatory effects reported in the present investigation suggest that phonemic planning is adaptative rather than context independent.     

Gluing and Wormholes for the Einstein Constraint Equations

 We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions can be made either when the initial manifold is compact or asymptotically Euclidean or asymptotically hyperbolic, with suitable corresponding conditions on the extrinsic curvature. In the compact setting a mild nondegeneracy condition is required. In the final section of the paper, we list a number ways this construction may be used to produce new types of vacuum spacetimes. Received: 4 October 2001 / Accepted: 26 July 2002 Published online: 29 October 2002 RID="*" ID="*" Supported by the NSF under Grant PHY-0099373 RID="**" ID="**" Supported by the NSF under Grant DMS-9971975 and at MSRI by NSF grant DMS-9701755 RID="***" ID="***" Supported by the NSF under Grant DMS-9704515