The scattering of a cylindrical invisibility cloak: reduced parameters and optimization

We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary conditions but also from the spatial variation of the component of permittivity/permeability. According to our formulation, we propose some restrictions to the invisibility cloak in order to minimize its scattering after the simplification has taken place. With our theoretical analysis, it is possible to design a simplified cloak by using some peculiar composites like photonic crystals (PCs) which mimic an effective refractive index landscape rather than offering effective constitutives, meanwhile canceling the scattering from the inner and outer boundaries.Comment: Accepted for J. Phys.

Grating-coupled excitation of multiple surface plasmon-polariton waves

The excitation of multiple surface-plasmon-polariton (SPP) waves of different linear polarization states and phase speeds by a surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied theoretically, using rigorous coupled-wave-analysis. The incident plane wave can be either p or s polarized. The excitation of SPP waves is indicated by the presence of those peaks in the plots of absorbance vs. the incidence angle that are independent of the thickness of the rugate filter. The absorbance peaks representing the excitation of s-polarized SPP waves are narrower than those representing p-polarized SPP waves. Two incident plane waves propagating in different directions may excite the same SPP wave. A line source could excite several SPP waves simultaneously

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

The Magnetorotational Instability in a Collisionless Plasma

We consider the linear axisymmetric stability of a differentially rotating collisionless plasma in the presence of a weak magnetic field; we restrict our analysis to wavelengths much larger than the proton Larmor radius. This is the kinetic version of the magnetorotational instability explored extensively as mechanism for magnetic field amplification and angular momentum transport in accretion disks. The kinetic calculation is appropriate for hot accretion flows onto compact objects and for the growth of very weak magnetic fields, where the collisional mean free path is larger than the wavelength of the unstable modes. We show that the kinetic instability criterion is the same as in MHD, namely that the angular velocity decrease outwards. However, nearly every mode has a linear kinetic growth rate that differs from its MHD counterpart. The kinetic growth rates also depend explicitly on beta, i.e., on the ratio of the gas pressure to the pressure of the seed magnetic field. For beta ~ 1 the kinetic growth rates are similar to the MHD growth rates while for beta >> 1 they differ significantly. For beta >> 1, the fastest growing mode has a growth rate of sqrt{3} Omega for a Keplerian disk, larger than its MHD counterpart; there are also many modes whose growth rates are negligible, < beta^{-1/2} Omega << Omega. We provide a detailed physical interpretation of these results and show that gas pressure forces, rather than just magnetic forces, are central to the behavior of the magnetorotational instability in a collisionless plasma. We also discuss the astrophysical implications of our analysis.Comment: Accepted by ApJ; 24 pages (4 figures

Stability of the Zagreb Carnegie-Mellon-Berkeley model

In ref. [1] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions, and that it can reliably predict the pole positions of the fitted partial wave amplitudes.Comment: 25 pages, 12 figures, 19 table

Interleukin-13 Genetic Variants, Household Carpet Use and Childhood Asthma

10.1371/journal.pone.0051970PLoS ONE81

Casimir-Polder interaction between an atom and a small magnetodielectric sphere

On the basis of macroscopic quantum electrodynamics and point-scattering techniques, we derive a closed expression for the Casimir-Polder force between a ground-state atom and a small magnetodielectric sphere in an arbitrary environment. In order to allow for the presence of both bodies and media, local-field corrections are taken into account. Our results are compared with the known van der Waals force between two ground-state atoms. To continuously interpolate between the two extreme cases of a single atom and a macroscopic sphere, we also derive the force between an atom and a sphere of variable radius that is embedded in an Onsager local-field cavity. Numerical examples illustrate the theory.Comment: 9 pages, 4 figures, minor addition

Balancing Minimum Spanning and Shortest Path Trees

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the two trees and epsilon > 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1+epsilon times the shortest-path distance, and yet the total weight of the tree is at most 1+2/epsilon times the weight of a minimum spanning tree. This is the best tradeoff possible. The paper also describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993

The HBI in a quasi-global model of the intracluster medium

In this paper we investigate how convective instabilities influence heat conduction in the intracluster medium (ICM) of cool-core galaxy clusters. The ICM is a high-beta, weakly collisional plasma in which the transport of momentum and heat is aligned with the magnetic field. The anisotropy of heat conduction, in particular, gives rise to instabilities that can access energy stored in a temperature gradient of either sign. We focus on the heat-flux buoyancy-driven instability (HBI), which feeds on the outwardly increasing temperature profile of cluster cool cores. Our aim is to elucidate how the global structure of a cluster impacts on the growth and morphology of the linear HBI modes when in the presence of Braginskii viscosity, and ultimately on the ability of the HBI to thermally insulate cores. We employ an idealised quasi-global model, the plane-parallel atmosphere, which captures the essential physics -- e.g. the global radial profile of the cluster -- while letting the problem remain analytically tractable. Our main result is that the dominant HBI modes are localised to the the innermost (~<20%) regions of cool cores. It is then probable that, in the nonlinear regime, appreciable field-line insulation will be similarly localised. Thus, while radio-mode feedback appears necessary in the central few tens of kpc, heat conduction may be capable of offsetting radiative losses throughout most of a cool core over a significant fraction of the Hubble time. Finally, our linear solutions provide a convenient numerical test for the nonlinear codes that tackle the saturation of such convective instabilities in the presence of anisotropic transport.Comment: MNRAS, in press; minor modifications from v