Higher Order Contact on Cayley's Ruled Cubic Surface

It is well known that Cayley's ruled cubic surface carries a three-parameter family of twisted cubics sharing a common point, with the same tangent and the same osculating plane. We report on various results and open problems with respect to contact of higher order and dual contact of higher order for these curves

Onsager's Wien Effect on a Lattice

The Second Wien Effect describes the non-linear, non-equilibrium response of a weak electrolyte in moderate to high electric fields. Onsager's 1934 electrodiffusion theory along with various extensions has been invoked for systems and phenomena as diverse as solar cells, surfactant solutions, water splitting reactions, dielectric liquids, electrohydrodynamic flow, water and ice physics, electrical double layers, non-Ohmic conduction in semiconductors and oxide glasses, biochemical nerve response and magnetic monopoles in spin ice. In view of this technological importance and the experimental ubiquity of such phenomena, it is surprising that Onsager's Wien effect has never been studied by numerical simulation. Here we present simulations of a lattice Coulomb gas, treating the widely applicable case of a double equilibrium for free charge generation. We obtain detailed characterisation of the Wien effect and confirm the accuracy of the analytical theories as regards the field evolution of the free charge density and correlations. We also demonstrate that simulations can uncover further corrections, such as how the field-dependent conductivity may be influenced by details of microscopic dynamics. We conclude that lattice simulation offers a powerful means by which to investigate system-specific corrections to the Onsager theory, and thus constitutes a valuable tool for detailed theoretical studies of the numerous practical applications of the Second Wien Effect.Comment: Main: 12 pages, 4 figures. Supplementary Information: 7 page

Language vs. grammatical tradition in Ancient India: how real was Pāṇinian Sanskrit? Evidence from the history of late Sanskrit passives and pseudo-passives

by Pāṇinian grammarians and the forms and constructions that are actually attested in the Vedic corpus (a part of which is traditionally believed to underlie Pāṇinian grammar). Concentrating on one particular aspect of the Old Indian verbal system, viz. the morphology and syntax of present formations with the suffix ‑ya-, I will provide a few examples of such discrepancy. I will argue that the most plausible explanation of this mismatch can be found in the peculiar sociolinguistic situation in Ancient India: a number of linguistic phenomena described by grammarians did not appear in Vedic texts but existed within the semi-colloquial scholarly discourse of the learned community of Sanskrit scholars (comparable to Latin scholarly discourse in Medieval Europe). Some of these phenomena may result from the influence of Middle Indic dialects spoken by Ancient Indian scholars, thus representing syntactic and morphological calques from their native dialects onto the Sanskrit grammatical system

Thermodynamics of the Harmonic Oscillator: Wien's Displacement Law and the Planck Spectrum

A thermodynamic analysis of the harmonic oscillator is presented. Motivation for the study is provided by the blackbody radiation spectrum; when blackbody radiation is regarded as a system of noninteracting harmonic oscillator modes, the thermodynamics follows from that of the harmonic oscillators. Using the behavior of a harmonic oscillator thermodynamic system under a quasi-static change of oscillator frequency w, we show that the thermodynamic functions can all be derived from a single function of w/T, analogous to Wien's displacement theorem. The high- and low-frequency energy limits allow asymptotic energy forms involving T alone or w alone, corresponding to energy equipartition and zero-point energy. It is noted that the Planck spectrum with zero-point radiation corresponds to the function satisfying the Wien displacement result which provides the smoothest possible interpolation between energy equipartition at low frequency and zero-point energy at high frequency.Comment: 10 page

Polynomial Chaos Expansion method as a tool to evaluate and quantify field homogeneities of a novel waveguide RF Wien Filter

For the measurement of the electric dipole moment of protons and deuterons, a novel waveguide RF Wien filter has been designed and will soon be integrated at the COoler SYnchrotron at J\"ulich. The device operates at the harmonic frequencies of the spin motion. It is based on a waveguide structure that is capable of fulfilling the Wien filter condition ($\vec{E} \perp \vec{B}$) \textit{by design}. The full-wave calculations demonstrated that the waveguide RF Wien filter is able to generate high-quality RF electric and magnetic fields. In reality, mechanical tolerances and misalignments decrease the simulated field quality, and it is therefore important to consider them in the simulations. In particular, for the electric dipole moment measurement, it is important to quantify the field errors systematically. Since Monte-Carlo simulations are computationally very expensive, we discuss here an efficient surrogate modeling scheme based on the Polynomial Chaos Expansion method to compute the field quality in the presence of tolerances and misalignments and subsequently to perform the sensitivity analysis at zero additional computational cost.Comment: 12 pages, 19 figure

A Common Election Day for Euro Zone Member States?

This paper tests for the Euro zone the hypothesis put forward by Sapir and Sekkat (1999) that synchronizing elections might improve welfare. After identifying a political budget cycle in the Euro zone we build a politico-macroeconomic model and simulate the effects of adopting a common election day in the 12 Euro zone member states. The results support most of the theoretical predictions by Sapir-Sekkat: (i) Synchronizing the elections could enhance GDP growth, reduce unemployment, but leads to increased inflation and in some countries to a deterioration of the budget; higher inflation forces ECB to monetary restrictions. (ii) If the synchronization happens asymmetrically - either only in the large or only in the small Euro zone countries - the result depends on the size of the spillovers. (iii) As anticipated in Sapir -Sekkat a common election day is a further step towards the desired "European business cycle", however, at the cost of increasing its amplitude. Harmonizing elections is another method of policy coordination. Whether this leads to higher welfare is a matter of weighting the different macroeconomic outcomes and it also depends on the model applied. (author's abstract)Series: EI Working Papers / Europainstitu

Electromagnetic Simulation and Design of a Novel Waveguide RF Wien Filter for Electric Dipole Moment Measurements of Protons and Deuterons

The conventional Wien filter is a device with orthogonal static magnetic and electric fields, often used for velocity separation of charged particles. Here we describe the electromagnetic design calculations for a novel waveguide RF Wien filter that will be employed to solely manipulate the spins of protons or deuterons at frequencies of about 0.1 to 2 MHz at the COoler SYnchrotron COSY at J\"ulich. The device will be used in a future experiment that aims at measuring the proton and deuteron electric dipole moments, which are expected to be very small. Their determination, however, would have a huge impact on our understanding of the universe.Comment: 10 pages, 10 figures, 4 table

Fine Structure of Dark Energy and New Physics

Following our recent work on the cosmological constant problem, in this letter we make a specific proposal regarding the fine structure (i.e., the spectrum) of dark energy. The proposal is motivated by a deep analogy between the blackbody radiation problem, which led to the development of quantum theory, and the cosmological constant problem, which we have recently argued calls for a conceptual extension of the quantum theory. We argue that the fine structure of dark energy is governed by a Wien distribution, indicating its dual quantum and classical nature. We discuss a few observational consequences of such a picture of dark energy.Comment: 14 pages, LaTeX, typos fixed, comments, references, and footnotes added, Sec. 4 revise

Exact solution for the Green's function describing time-dependent thermal Comptonization

We obtain an exact, closed-form expression for the time-dependent Green's function solution to the Kompaneets equation. The result, which is expressed as the integral of a product of two Whittaker functions, describes the evolution in energy space of a photon distribution that is initially monoenergetic. Effects of spatial transport within a homogeneous scattering cloud are also included within the formalism. The Kompaneets equation that we solve includes both the recoil and energy diffusion terms, and therefore our solution for the Green's function approaches the Wien spectrum at large times. We show that the Green's function can be used to generate all of the previously known steady-state and time-dependent solutions to the Kompaneets equation. The new solution allows the direct determination of the spectrum, without the need to numerically solve the partial differential equation. Based upon the Green's function, we obtain a new time-dependent solution for the photon distribution resulting from the reprocessing of an optically thin bremsstrahlung initial spectrum with a low-energy cutoff. The new bremsstrahlung solution possesses a finite photon number density, and therefore it displays proper equilibration to a Wien spectrum at large times. The relevance of our results for the interpretation of emission from variable X-ray sources is discussed, with particular attention to the production of hard X-ray time lags, and the Compton broadening of narrow features such as iron lines.Comment: text plus 9 figures, MNRAS 2003, in pres