Electromagnetic wormholes via handlebody constructions

Cloaking devices are prescriptions of electrostatic, optical or electromagnetic parameter fields (conductivity $\sigma(x)$, index of refraction $n(x)$, or electric permittivity $\epsilon(x)$ and magnetic permeability $\mu(x)$) which are piecewise smooth on $\mathbb R^3$ and singular on a hypersurface $\Sigma$, and such that objects in the region enclosed by $\Sigma$ are not detectable to external observation by waves. Here, we give related constructions of invisible tunnels, which allow electromagnetic waves to pass between possibly distant points, but with only the ends of the tunnels visible to electromagnetic imaging. Effectively, these change the topology of space with respect to solutions of Maxwell's equations, corresponding to attaching a handlebody to $\mathbb R^3$. The resulting devices thus function as electromagnetic wormholes.Comment: 25 pages, 6 figures (some color

Electromagnetic wormholes and virtual magnetic monopoles

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $\epsilon$ and magnetic permeability $\mu$, that allow one to construct from metamaterials objects that function as invisible tunnels. These allow EM wave propagation between two points, but the tunnels and the regions they enclose are not detectable to EM observations. Such devices function as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-a-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles.Comment: 4 pages, 3 figure

Enhancement of near-cloaking. Part II: the Helmholtz equation

The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.Comment: 16pages, 12 fugure

Spatial Distribution and Insect Associations of Frangula alnus in the Allegheny National Forest, Pennsylvania: Implications for Management

Glossy buckthorn (Frangula alnus) (Rosales: Rhamnaceae) is an invasive European shrub that threatens to displace native vegetation in roadsides and disturbed forests in North America due to its lack of natural enemies, long leaf-out periods, and its ability to survive in a multitude of soil conditions. While well understood in its native range, information regarding F. alnus in North America is lacking. Currently, the management of this invasive shrub relies on an understanding of where it can be found and thus where treatments should be applied. This research investigated the spatial distribution patterns of F. alnus and profiled the insects associated with F. alnus in the Allegheny National Forest (ANF) in Pennsylvania to explore solutions for the improved management of F. alnus. To determine the spatial distribution patterns of F. alnus, the density and presence of F. alnus were recorded in 1,412 transect sample points located on four sites. Buffer analyses were conducted to measure the relationships between proximity to unpaved forest roads (UFR) and both F. alnus density and presence. Geostatistical analyses were used to determine spatial autocorrelation between individual F. alnus samples via the creation of variograms; spatial dependency was measured via degrees of dependency. Spatial patterns were determined using spatial analyses by distance indices (SADIE). The density and abundance of F. alnus were found to be negatively associated with proximity to UFR. The maximum distance of spatial dependency between F. alnus individuals ranged from 30.9-340.8 m based on the density and 3.5-203.8 m based on the presence. We also found F. alnus to be significantly aggregated; this was expected as F. alnus is also capable of spreading by suckering. Identifying the insects associated with F. alnus could help control F. alnus. To determine the insects associated with F. alnus, arthropod samples were collected from 16 plots of F. alnus on five collection dates using an insect net and from fruit collections from F. alnus on three collection dates. The orders and morphospecies with the highest abundances were identified. The proportion of immature hemipterans relative to adults was measured as an indication of use and preference as immature stages are often less mobile and more likely to be present on plants that they prefer, particularly if the eggs were laid on that plant. Order abundance, species richness, and species diversity were measured for dependence over time. The number and identity of insects that emerged from the fruits of F. alnus and their sex ratio were recorded. The most predominant insect species found on F. alnus in the ANF was Psylla carpinicola (Hemiptera: Psyllidae) followed by Drosophila suzukii (Diptera: Drosophilidae). The collection was dominated by the orders Hemiptera (39.8%) and Diptera (22.3%). Of the hemipterans collected, 16.2 % of individuals and 36.3% of morphospecies were juveniles. Order abundance, richness, and diversity are all dependent on time. Spotted-wing drosophila D. suzukii was found to be utilizing the fruits of F. alnus for egg and larval stages. The results of this research provide recommendations for how far from the road treatments of F. alnus should be applied. Since F. alnus was found to be aggregated, we recommend precision management for increased cost efficiency and to reduce unnecessary negative effects on surrounding wildlife. This research also concludes that many insects and arachnids are associated with F. alnus. We found D. suzukii to be utilizing the fruits of F. alnus; these flies could be decreasing the germination and recruitment of F. alnus where they are found together. In the future, this research can be furthered by examining the fruit production and recruitment of F. alnus existing further into the forest to determine whether they pose a threat and require treatment. We also suggest a more in-depth investigation regarding the nature of the relationships between the insects found to be most prevalent on F. alnus. Lastly, the effects of D. suzukii on F. alnus may be further investigated to determine the degree to which D. suzukii mitigates F. alnus

Human acclimation and acclimatization to heat: A compendium of research, 1968-1978

Abstracts and annotations of the majority of scientific works that elucidate the mechanisms of short-term acclimation to heat in men and women are presented. The compendium includes material from 1968 through 1977. Subject and author indexes are provided and additional references of preliminary research findings or work of a peripheral nature are included in a bibliography

Superantenna made of transformation media

We show how transformation media can make a superantenna that is either completely invisible or focuses incoming light into a needle-sharp beam. Our idea is based on representating three-dimensional space as a foliage of sheets and performing two-dimensional conformal maps on each shee

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped. We thus analyse the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

Full-wave invisibility of active devices at all frequencies

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic

Effects of Hypohydration on Work Performance and Tolerance to plus Gz Acceleration in Man

Hypohydration effects on work performance and tolerance to acceleration stress in ma