A Posteriori Error Estimation for the p-curl Problem

We derive a posteriori error estimates for a semi-discrete finite element approximation of a nonlinear eddy current problem arising from applied superconductivity, known as the $p$-curl problem. In particular, we show the reliability for non-conforming N\'{e}d\'{e}lec elements based on a residual type argument and a Helmholtz-Weyl decomposition of $W^p_0(\text{curl};\Omega)$. As a consequence, we are also able to derive an a posteriori error estimate for a quantity of interest called the AC loss. The nonlinearity for this form of Maxwell's equation is an analogue of the one found in the $p$-Laplacian. It is handled without linearizing around the approximate solution. The non-conformity is dealt by adapting error decomposition techniques of Carstensen, Hu and Orlando. Geometric non-conformities also appear because the continuous problem is defined over a bounded $C^{1,1}$ domain while the discrete problem is formulated over a weaker polyhedral domain. The semi-discrete formulation studied in this paper is often encountered in commercial codes and is shown to be well-posed. The paper concludes with numerical results confirming the reliability of the a posteriori error estimate.Comment: 32 page

Nonlinear ER effects in an ac applied field

The electric field used in most electrorheological (ER) experiments is usually quite high, and nonlinear ER effects have been theoretically predicted and experimentally measured recently. A direct method of measuring the nonlinear ER effects is to examine the frequency dependence of the same effects. For a sinusoidal applied field, we calculate the ac response which generally includes higher harmonics. In is work, we develop a multiple image formula, and calculate the total dipole moments of a pair of dielectric spheres, embedded in a nonlinear host. The higher harmonics due to the nonlinearity are calculated systematically.Comment: Presented at Conference on Computational Physics (CCP2000), held at Gold Coast, Australia from 3-8, December 200

Quasiscarred modes and their branching behavior at an exceptional point

We study quasiscarring phenomenon and mode branching at an exceptional point (EP) in typically deformed microcavities. It is shown that quasiscarred (QS) modes are dominant in some mode group and their pattern can be understood by short-time ray dynamics near the critical line. As cavity deformation increases, high-Q and low-Q QS modes are branching in an opposite way, at an EP, into two robust mode types showing QS and diamond patterns, respectively. Similar branching behavior can be also found at another EP appearing at a higher deformation. This branching behavior of QS modes has its origin on the fact that an EP is a square-root branch point.Comment: 5 pages, 5 figure

SSW Library: An SIMD Smith-Waterman C/C++ Library for Use in Genomic Applications

Summary: The Smith Waterman (SW) algorithm, which produces the optimal pairwise alignment between two sequences, is frequently used as a key component of fast heuristic read mapping and variation detection tools, but current implementations are either designed as monolithic protein database searching tools or are embedded into other tools. To facilitate easy integration of the fast Single Instruction Multiple Data (SIMD) SW algorithm into third party software, we wrote a C/C++ library, which extends Farrars Striped SW (SSW) to return alignment information in addition to the optimal SW score. Availability: SSW is available both as a C/C++ software library, as well as a stand alone alignment tool wrapping the librarys functionality at https://github.com/mengyao/Complete- Striped-Smith-Waterman-Library Contact: [email protected]: 3 pages, 2 figure