Computing the Similarity Between Moving Curves

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fr\'echet distance between surfaces. While the Fr\'echet distance between surfaces is not even known to be computable, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on max-flow min-cut duality

Radiation and scattering from loaded microstrip antennas over a wide bandwidth

The integral equation and moment method solution is developed for two different antennas in the presence of an infinite grounded dielectric substrate. The first antenna is a rectangular microstrip patch antenna. This antenna is analyzed for excitation by an incident plane wave in free space and a vertical filament of uniform current in the dielectric. This antenna can be loaded by a lumped impedance in a vertical filament of uniform current extending from the patch through the dielectric to the ground plane. The radar cross section of the microstrip antenna is found from the plane wave excitation and shows good agreement to measurement for both an unloaded and loaded antenna. The input impedance is found from the current filament excitation. This is compared to the measured input impedance of a coaxially fed microstrip antenna and shows good agreement for both unloaded and loaded antennas when the dielectric substrate is much less than a wavelength. The second antenna is a vertical thin wire extending from the ground plane into or through the dielectric substrate. The mutual impedance between two imbedded monopoles is compared to a previous calculation

Bi2Te3Bi_2Te_3: Implications of the rhombohedral k-space texture on the evaluation of the in-plane/out-of-plane conductivity anisotropy

Different computational scheme for calculating surface integrals in anisotropic Brillouin zones are compared. The example of the transport distribution function (plasma frequency) of the thermoelectric Material \BiTe near the band edges will be discussed. The layered structure of the material together with the rhombohedral symmetry causes a strong anisotropy of the transport distribution function for the directions in the basal (in-plane) and perpendicular to the basal plane (out-of-plane). It is shown that a thorough reciprocal space integration is necessary to reproduce the in-plane/out-of-plane anisotropy. A quantitative comparison can be made at the band edges, where the transport anisotropy is given in terms of the anisotropic mass tensor.Comment: 7 pages, 6 figs., subm. to J. Phys. Cond. Ma

Constrained-Transport Magnetohydrodynamics with Adaptive-Mesh-Refinement in CHARM

We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full 12-solve spatially unsplit Corner-Transport-Upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the Piecewise-Parabolic-Method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a Constrained-Transport (CT) method. The multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a {\it reflux-curl} operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.Comment: 53 pages, 17 figs, under review by ApJ

Singular Higher Order Divergence-Conforming Bases of Additive Kind and Moments Method Applications to 3D Sharp-Wedge Structures

We present new subsectional, singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges. The bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighborhood. Singular bases of this kind, complete to arbitrarily high order, are described in a unified and consistent manner for curved quadrilateral and triangular elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. Our singular bases guarantee normal continuity along the edges of the elements allowing for the discontinuity of tangential components, adequate modelling of the divergence, and removal of spurious solutions. These singular high-order bases provide more accurate and efficient numerical solutions of surface integral problems. Several test-case problems are considered in the paper, thereby obtaining highly accurate numerical results for the current and charge density induced on 3D sharp-wedge structures. The results are compared with other solutions when available and confirm the faster convergence of these bases on wedge problem