Electromagnetic surface wave propagation in a metallic wire and the Lambert WW function

We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, namely, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM$_{01}$ mode) in a cylindrical metallic wire, and his iterative method to solve the transcendental equation that appears in the determination of the propagation wave number from the boundary conditions. We present an elementary analysis of the convergence of Sommerfeld's iterative solution of the approximate problem and compare it with both the numerical solution of the exact transcendental equation and the solution of the approximate problem by means of the Lambert $W$ function.Comment: REVTeX double column, 9 pages, 3 figures, minor differences between v3 and published version; "Editor's Pick" for June 2019 edition of AJ

Thermostatistics of overdamped motion of interacting particles

We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures of the thermal bath, the system displays a mixed behavior that follows a novel type of thermostatistics, where the entropy is given by a linear combination of Tsallis and Boltzmann-Gibbs entropies.Comment: 4 pages, 2 figure

Kinky D-branes and straight strings of open string tachyon effective theory

In this letter we construct the kink D1-brane super D-helix solution and its T-dual the D2-brane supertube using the effective action of non-BPS tachyonic D-branes . In the limit of zero angular momentum, both types of solutions collapse to zero radius, giving rise respectively to a degenerate string configuration corresponding to a particle travelling with the speed of light and to a static straight string configuration. These solutions share all the properties of fundamental strings and do not have the pathological behavior of other solutions previously found in this context. A short discussion on the ``generalized gauge transformations'' suggested by Sen is used to justify the validity of our approach.Comment: 10 pages, latex, typos corrected and references adde

Quasi-normal frequencies: Key analytic results

The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for the double-delta potential in terms of the Lambert W function. V3: Minor edits for clarity. Four references added. No physics changes. Still 31 page

A \textsf{C++} reasoner for the description logic \shdlssx (Extended Version)

We present an ongoing implementation of a \ke\space based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic \dlssx (shortly \shdlssx). The reasoner checks the consistency of \shdlssx-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports \shdlssx-KBs serialized in the OWL/XML format. To the best of our knowledge, this is the first attempt to implement a reasoner for the consistency checking of a description logic represented via a fragment of set theory that can also classify standard OWL ontologies.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1702.03096, arXiv:1804.1122