Regularity Theory and Superalgebraic Solvers for Wire Antenna Problems

We consider the problem of evaluating the current distribution $J(z)$ that is induced on a straight wire antenna by a time-harmonic incident electromagnetic field. The scope of this paper is twofold. One of its main contributions is a regularity proof for a straight wire occupying the interval $[-1,1]$. In particular, for a smooth time-harmonic incident field this theorem implies that $J(z) = I(z)/\sqrt{1-z^2}$, where $I(z)$ is an infinitely differentiable function—the previous state of the art in this regard placed $I$ in the Sobolev space $W^{1,p}$, $p>1$. The second focus of this work is on numerics: we present three superalgebraically convergent algorithms for the solution of wire problems, two based on Hallén's integral equation and one based on the Pocklington integrodifferential equation. Both our proof and our algorithms are based on two main elements: (1) a new decomposition of the kernel of the form $G(z) = F_1(z) \ln\! |z| + F_2(z)$, where $F_1(z)$ and $F_2(z)$ are analytic functions on the real line; and (2) removal of the end-point square root singularities by means of a coordinate transformation. The Hallén- and Pocklington-based algorithms we propose converge superalgebraically: faster than $\mathcal{O}(N^{-m})$ and $\mathcal{O}(M^{-m})$ for any positive integer $m$, where $N$ and $M$ are the numbers of unknowns and the number of integration points required for construction of the discretized operator, respectively. In previous studies, at most the leading-order contribution to the logarithmic singular term was extracted from the kernel and treated analytically, the higher-order singular derivatives were left untreated, and the resulting integration methods for the kernel exhibit $\mathcal{O}(M^{-3})$ convergence at best. A rather comprehensive set of tests we consider shows that, in many cases, to achieve a given accuracy, the numbers $N$ of unknowns required by our codes are up to a factor of five times smaller than those required by the best solvers previously available; the required number $M$ of integration points, in turn, can be several orders of magnitude smaller than those required in previous methods. In particular, four-digit solutions were found in computational times of the order of four seconds and, in most cases, of the order of a fraction of a second on a contemporary personal computer; much higher accuracies result in very small additional computing times

The Microstructure of the Bond Market in the 20th Century

Bonds are traded in OTC markets, where opacity and fragmentation imply large transaction costs for retail investors. Is there something special about bonds, in contrast to stocks, that precludes trading in transparent, limit-order markets? Historical experience suggests this is not the case. Before WWII, there was an active market in corporate and municipal bonds on the NYSE. Activity dropped dramatically, in the late 1920s for municipals and in the mid 1940s for corporate, as trading migrated to the OTC market. This migration occurred simultaneously with an increase in the role of institutional investors, which fare better than retail investors in OTC market. Based on current and historical high frequency data, we find that, for retail investors, trading costs in municipal bonds were half as large in 1926-1927 as they are now. The difference in transactions costs is likely to reflect the difference in market structures.

Communications system evolutionary scenarios for Martian SEI support

In the Space Exploration Initiative (SEI) mission scenarios, expanding human presence is the primary driver for high data rate Mars-Earth communications. To support an expanding human presence, the data rate requirement will be gradual, following the phased implementation over time of the evolving SEI mission. Similarly, the growth and evolution of the space communications infrastructure to serve this requirement will also be gradual to efficiently exploit the useful life of the installed communications infrastructure and to ensure backward compatibility with long-term users. In work conducted over the past year, a number of alternatives for supporting high data rate Mars-Earth communications have been analyzed with respect to their compatibility with gradual evolution of the space communications infrastructure. The alternatives include RF, millimeter wave (MMW), and optical implementations, and incorporate both surface and space-based relay terminals in the Mars and Earth regions. Each alternative is evaluated with respect to its ability to efficiently meet a projected growth in data rate over time, its technology readiness, and its capability to satisfy the key conditions and constraints imposed by evolutionary transition. As a result of this analysis, a set of attractive alternative communications architectures have been identified and described, and a road map is developed that illustrates the most rational and beneficial evolutionary paths for the communications infrastructure

Quasi-particle dephasing time in disordered d-wave superconductors

We evaluate the low-temperature cutoff for quantum interference 1/tf induced in a d-wave superconductor by the diffusion enhanced quasiparticle interactions in the presence of disorder. We carry out our analysis in the framework of the non-linear sigma-model which allows a direct calculation of 1/tf, as the mass of the transverse modes of the theory. Only the triplet amplitude in the particle-hole channel and the Cooper amplitude with is pairing symmetry contribute to 1/tf. We discuss the possible relevance of our results to the present disagreement between thermal transport data in cuprates and the localization theory for d-wave quasiparticles

Separating Use and Reuse to Improve Both

Context: Trait composition has inspired new research in the area of code reuse for object oriented (OO) languages. One of the main advantages of this kind of composition is that it makes possible to separate subtyping from subclassing; which is good for code-reuse, design and reasoning. However, handling of state within traits is difficult, verbose or inelegant. Inquiry: We identify the this-leaking problem as the fundamental limitation that prevents the separation of subtyping from subclassing in conventional OO languages. We explain that the concept of trait composition addresses this problem, by distinguishing code designed for use (as a type) from code designed for reuse (i.e. inherited). We are aware of at least 3 concrete independently designed research languages following this methodology: TraitRecordJ, Package Templates and DeepFJig. Approach: In this paper, we design $42_\mu$ a new language, where we improve use and reuse and support the This type and family polymorphism by distinguishing code designed for use from code designed for reuse. In this way $42_\mu$ synthesise the 3 approaches above, and improves them with abstract state operations: a new elegant way to handle state composition in trait based languages. Knowledge and Grounding: Using case studies, we show that $42_\mu$'s model of traits with abstract state operations is more usable and compact than prior work. We formalise our work and prove that type errors cannot arise from composing well typed code. Importance: This work is the logical core of the programming language 42. This shows that the ideas presented in this paper can be applicable to a full general purpose language. This form of composition is very flexible and could be used in many new languages