The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

Protecting Against the Harms of the Mistaken Utility Undercharge

First, Part I introduces the basic law concerning estoppel. Then, Part II discusses the application of estoppel doctrine to the collection of undercharges by public utilities. Next, Part III examines whether, even in situations where the utility may collect the undercharge, it may be prohibited from using service disconnection as a collection device. Part IV analyzes the right of a consumer to bring a counter-claim for damages resulting from a utility\u27s mistaken undercharge. Finally, Part V recommends the adoption of a new approach to the problem of the utility undercharge as it relates to low-income households

Discrimination As a Sword for the Poor: Use of an “Effects Test” in Public Utility Litigation

This Article looks at how the effects test might be applied in the utility area. Part I discusses the definition and application of the prohibition against discrimination in utility cases. Part II examines the use of an effects test in the non-utility context. Part III describes how such an analysis can be used in seeking to prove utility discrimination. Part IV provides illustrative uses of an effects test in customer service situations and reviews one particular case to determine if application of this test might have given rise to different results

"Oxide-free" tip for scanning tunneling microscopy

We report a new tip for scanning tunneling microscopy and a tip repair procedure that allows one to reproducibly obtain atomic images of highly oriented pyrolytic graphite with previously inoperable tips. The tips are shown to be relatively oxide-free and highly resistant to oxidation. The tips are fabricated with graphite by two distinct methods

GPU LSM: A Dynamic Dictionary Data Structure for the GPU

We develop a dynamic dictionary data structure for the GPU, supporting fast insertions and deletions, based on the Log Structured Merge tree (LSM). Our implementation on an NVIDIA K40c GPU has an average update (insertion or deletion) rate of 225 M elements/s, 13.5x faster than merging items into a sorted array. The GPU LSM supports the retrieval operations of lookup, count, and range query operations with an average rate of 75 M, 32 M and 23 M queries/s respectively. The trade-off for the dynamic updates is that the sorted array is almost twice as fast on retrievals. We believe that our GPU LSM is the first dynamic general-purpose dictionary data structure for the GPU.Comment: 11 pages, accepted to appear on the Proceedings of IEEE International Parallel and Distributed Processing Symposium (IPDPS'18

Active Exterior Cloaking

A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the two-dimensional Helmholtz equation, it is numerically shown that three active exterior devices placed around the object suffice to produce very good cloaking.Comment: 4 pages, 3 figures, submitted to Physical Review Letter