Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of the errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.Comment: 33 pages, 14 figure

An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (10pJ/word on-die to 10,000pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use more and more cores on each compute nodes ("fat nodes") that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignement constraints and avoids gather/scatter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of $\times 2$ to $\times 2.5$ speed-up in double precision for particle shape factor of order $1$ to $3$. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles).Comment: 36 pages, 5 figure

Novel Josephson effects between multi-gap and single-gap superconductors

Multi-gap superconductors can exhibit qualitatively new phenomena due to existence of multiple order parameters. Repulsive electronic interactions may give rise to a phase difference of $\pi$ between the phases of the order parameters. Collective modes due to the oscillation of the relative phases of these order parameters are also possible. Here we show that both these phenomena are observable in Josephson junctions between a single-gap and a multi-gap superconductor. In particular, a non-monotonic temperature dependence of the Josephson current through the junction reveals the existence of the $\pi$ phase differences in the multi-gap superconductor. This mechanism may be relevant for understanding several experiments on the Josephson junctions with unconventional superconductors. We also discuss how the presence of the collective mode resonantly enhances the DC Josephson current when the voltage across the junction matches the mode frequency. We suggest that our results may apply to MgB$_2$, 2H-NbSe$_2$, spin ladder and bilayer cuprates.Comment: 4 pages, 2 figure

Correlated defects, metal-insulator transition, and magnetic order in ferromagnetic semiconductors

The effect of disorder on transport and magnetization in ferromagnetic III-V semiconductors, in particular (Ga,Mn)As, is studied theoretically. We show that Coulomb-induced correlations of the defect positions are crucial for the transport and magnetic properties of these highly compensated materials. We employ Monte Carlo simulations to obtain the correlated defect distributions. Exact diagonalization gives reasonable results for the spectrum of valence-band holes and the metal-insulator transition only for correlated disorder. Finally, we show that the mean-field magnetization also depends crucially on defect correlations.Comment: 4 pages RevTeX4, 5 figures include

Investigation of Wing Characteristics at a Mach Number of 1.53 II : Swept Wings of Taper Ratio 0.5

Measured values of lift, drag, and pitching moment at M(sub o) = 1.53 are presented for seven wings varying in sweep angle from 60 degrees sweepforward to 60 degrees sweepback. All wings had a cambered, double-wedge section 5-percent thick and a common taper ratio of 0.5. The experimental results are compared with the predictions of the linear theory