Computing the Casimir energy using the point-matching method

We use a point-matching approach to numerically compute the Casimir interaction energy for a two perfect-conductor waveguide of arbitrary section. We present the method and describe the procedure used to obtain the numerical results. At first, our technique is tested for geometries with known solutions, such as concentric and eccentric cylinders. Then, we apply the point-matching technique to compute the Casimir interaction energy for new geometries such as concentric corrugated cylinders and cylinders inside conductors with focal lines.Comment: 11 pages, 18 figure

Superconductive proximity effect in interacting disordered conductors

We present a general theory of the superconductive proximity effect in disordered normal--superconducting (N-S) structures, based on the recently developed Keldysh action approach. In the case of the absence of interaction in the normal conductor we reproduce known results for the Andreev conductance G_A at arbitrary relation between the interface resistance R_T and the diffusive resistance R_D. In two-dimensional N-S systems, electron-electron interaction in the Cooper channel of normal conductor is shown to strongly affect the value of G_A as well as its dependence on temperature, voltage and magnetic field. In particular, an unusual maximum of G_A as a function of temperature and/or magnetic field is predicted for some range of parameters R_D and R_T. The Keldysh action approach makes it possible to calculate the full statistics of charge transfer in such structures. As an application of this method, we calculate the noise power of an N-S contact as a function of voltage, temperature, magnetic field and frequency for arbitrary Cooper repulsion in the normal metal and arbitrary values of the ratio R_D/R_T.Comment: RevTeX, 28 pages, 18 PostScript figures; added and updated reference

Accurate 2.5-D boundary element method for conductive media

The solution of the time-harmonic Maxwell equations using a boundary element method, for 2-D geometries illuminated by arbitrary 3-D excitations, gives rise to numerical difficulties if highly conductive media are present. In particular, the interaction integrals arising in the method of moments involve kernels that strongly oscillate in space and, at the same time, decay exponentially. We present an accurate method to tackle these issues over a very broad conductivity range (from lossy dielectric to conductor skin-effect regime), for both magnetic and nonmagnetic conductors. Important applications are the modal analysis of waveguides with nonperfect conductors, scattering problems, and shielding problems with enclosures with arbitrary permeability and conductivity and 3-D noise sources

Electron-electron interaction corrections to the thermal conductivity in disordered conductors

We evaluate the electron-electron interaction corrections to the electronic thermal conductivity in a disordered conductor in the diffusive regime. We use a diagrammatic many-body method analogous to that of Altshuler and Aronov for the electrical conductivity. We derive results in one, two and three dimensions for both the singlet and triplet channels, and in all cases find that the Wiedemann-Franz law is violated.Comment: 8 pages, 2 figures Typos corrected in formulas (15) and (A.4) and Table 1; discussion of previous work in introduction extended; reference clarifying different definitions of parameter F adde

Spin polarization in a T-shape conductor induced by strong Rashba spin-orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spin-orbit interaction in a T-shaped conductor proposed by A.A. Kiselev and K.W. Kim (Appl. Phys. Lett. {\bf 78} 775 (2001)). The recursive Green function method is used to calculate the three terminal spin dependent transmission probabilities. We focus on single-channel transport and show that the spin polarization becomes nearly 100 % with a conductance close to $e^{2}/h$ for sufficiently strong spin-orbit coupling. This is interpreted by the fact that electrons with opposite spin states are deflected into an opposite terminal by the spin dependent Lorentz force. The influence of the disorder on the predicted effect is also discussed. Cases for multi-channel transport are studied in connection with experiments

Numerical Simulation of Vortex-Induced Vibrations of Riser-Conductor Systems Including Soil-Structure Interactions

A fully three-dimensional numerical approach for analyzing deepwater drilling riser-conductor system vortex-induced vibrations (VIV) including soil-structure interactions (SSI) is presented. The drilling riser-conductor system is modeled as a tensioned beam with linearly distributed tension and is solved by a fully implicit discretization scheme. The fluid field around the riser-conductor system is obtained by Finite-Analytic Navier-Stokes (FANS) code, which numerically solves the unsteady Navier-Stokes equations. The SSI is taken into account by modeling the lateral soil resistance force according to p-y curves. Overset grid method is adopted to mesh the fluid domain with approximately 0.86 million computational points in total. Meshes are much finer in regions close to the pipe outer boundary and coarser in the far-field regions. A partitioned Fluid-Structure Interaction (FSI) method is achieved by communication between the fluid solver and pipe motion solver. A pipe VIV simulation without SSI is firstly presented and served as a benchmark case for following simulations. Two SSI models based on a popular p-y curve are then applied to the VIV simulations. Results from those simulations are compared and analyzed. The effects of two key soil properties on the VIV simulations of riser-conductor systems are then studied. Conclusions are made and suggestions are given for VIV analysis of riser-conductor systems and future researc

Superconducting proximity effects in metals with a repulsive pairing interaction

Studies of the superconducting proximity effect in normal conductor/superconductor $(N/S)$ junctions almost universally assume no effective electron-electron coupling in the $N$ region. While such an approximation leads to a simple description of the proximity effect, it is unclear how it could be rigorously justified. We reveal a much more complex picture of the proximity effect in $N/S$ bilayers, where $S$ is a clean s-wave BCS superconductor and $N$ is a simple metal with a repulsive effective electron coupling. We elucidate the proximity effect behavior using a highly accurate method to self-consistently solve the Bogoliubov-deGennes equations. We present our results for a wide range of values of the interface scattering, the Fermi wave vector mismatch, the temperature, and the ratio $g$ of the effective interaction strengths in the $N$ and $S$ region. We find that the repulsive interaction, represented by a negative $g$, strongly alters the signatures of the proximity effect as can be seen in the spatial dependence of the Cooper pair amplitude and the pair potential, as well as in the local density of states near the interface.Comment: 12 pages, including 10 figures. To appear in Phys. Rev.

Computer aided design of printed wiring boards

A method is described for the computer-aided layout of printed wiring boards. The type of board considered is a single sided board containing discrete components. The required input for the layout algorithm is coded from the relevant circuit diagram, together with a description of the component dimensions. This information is then stored within the computer in a data structure. The circuit components and their interconnections are represented by a set of nodes and branches. The principles of graph theory are used to construct an abstract model of the layout. A number of the nodes and branches of the circuit are first used in the construction of a planar graph. A method is then described for inserting the remaining branches into the graph to form a "pseudo planar graph". This represents a set of components and conductor paths which can be laid out on a single sided board without intersections. The number of conductor crossings is thus minimised before the actual layout commences. An algorithm is then described for automatically constructing a board layout from the pseudo planar graph. The relative interconnections are already known so the placement of components and routing of conductor paths can proceed simultaneously. The layout is therefore constructed in a series of logical steps working across from one edge of the board to the other. This approach contrasts with the more usual methods of layout in which components are placed first, followed by a search for conductor routes. The layout algorithm is also provided with facilities for man-machine interaction by means of a graphical display and light pen. Interaction allows the user to alter the positions of components during the construction of the layout. Thus the skill and experience of the user can be combined with the speed and accuracy of the automatic algorithm. Interaction also enables special conditions to be incorporated into the layout which would otherwise entail considerable programming effort. Three different circuits are used to test the layout algorithm. The results are shown for layouts constructed both automatically and by the use of interaction. One layout is also compared with a manually-produced layout of the same circuit. The results show that a feasible method has been developed for the layout of printed wiring boards by computer. Comparable results are produced in considerably less time than normal layout methods