Gap Symmetry and Thermal Conductivity in Nodal Superconductors

Here we consider the universal heat conduction and the angular dependent thermal conductivity in the vortex state for a few nodal superconductors. We present the thermal conductivity as a function of impurity concentration and the angular dependent thermal conductivity in a few nodal superconductors. This provides further insight in the gap symmetry of superconductivity in Sr$_2$RuO$_4$ and UPd$_2$Al$_3$.Comment: 2 pages, proceedings of SCES '0

Gap Symmetry an Thermal Conductivity in Nodal Superconductors

There are now many nodal superconductors in heavy fermion (HF) systems, charge conjugated organic metals, high Tc cuprates and ruthenates. On the other hand only few of them have a well established gap function. We present here a study of the angular dependent thermal conductivity in the vortex state of some of the nodal superconductors. We hope it will help to identify the nodal directions in the gap function of UPd_2Al_3, UNi_2Al_3, UBe_13 and URu_2Si_2.Comment: 4 pages, 5 figure

Multi-frequency topological derivative for approximate shape acquisition of curve-like thin electromagnetic inhomogeneities

In this paper, we investigate a non-iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and/or magnetic permeability differ from those in the embedding (homogeneous) space. The main objective is the imaging of crack-like thin inclusions, but the algorithm can be applied to arbitrarily shaped inclusions. For this purpose, we apply multiple time-harmonic frequencies and normalize the topological derivative imaging function by its maximum value. In order to verify its validity, we apply it for the imaging of two-dimensional crack-like thin electromagnetic inhomogeneities completely hidden in a homogeneous material. Corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm.Comment: 25 pages, 28 figure

The noncommutative schemes of generalized Weyl algebras

The first Weyl algebra over $k$, $A_1 = k \langle x, y\rangle/(xy-yx - 1)$ admits a natural $\mathbb{Z}$-grading by letting $\operatorname{deg} x = 1$ and $\operatorname{deg} y = -1$. Paul Smith showed that $\operatorname{gr}- A_1$ is equivalent to the category of quasicoherent sheaves on a certain quotient stack. Using autoequivalences of $\operatorname{gr}- A_1$, Smith constructed a commutative ring $C$, graded by finite subsets of the integers. He then showed $\operatorname{gr}- A_1 \equiv \operatorname{gr}- (C, \mathbb{Z}_{\mathrm{fin}})$. In this paper, we generalize results of Smith by using autoequivalences of a graded module category to construct rings with equivalent graded module categories. For certain generalized Weyl algebras, we use autoequivalences defined in a companion paper so that these constructions yield commutative rings.Comment: Revised versio

Topological derivative-based technique for imaging thin inhomogeneities with few incident directions

Many non-iterative imaging algorithms require a large number of incident directions. Topological derivative-based imaging techniques can alleviate this problem, but lacks a theoretical background and a definite means of selecting the optimal incident directions. In this paper, we rigorously analyze the mathematical structure of a topological derivative imaging function, confirm why a small number of incident directions is sufficient, and explore the optimal configuration of these directions. To this end, we represent the topological derivative based imaging function as an infinite series of Bessel functions of integer order of the first kind. Our analysis is supported by the results of numerical simulations.Comment: 14 pages, 29 figure

Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions

Recently, a non-iterative multi-frequency subspace migration imaging algorithm was developed based on an asymptotic expansion formula for thin, curve-like electromagnetic inclusions and the structure of singular vectors in the Multi-Static Response (MSR) matrix. The present study examines the structure of subspace migration imaging functional and proposes an improved imaging functional weighted by the frequency. We identify the relationship between the imaging functional and Bessel functions of integer order of the first kind. Numerical examples for single and multiple inclusions show that the presented algorithm not only retains the advantages of the traditional imaging functional but also improves the imaging performance.Comment: 15 pages, 20 figure