Thermal reactor

A thermal reactor apparatus and method of pyrolyticaly decomposing silane gas into liquid silicon product and hydrogen by-product gas is disclosed. The thermal reactor has a reaction chamber which is heated well above the decomposition temperature of silane. An injector probe introduces the silane gas tangentially into the reaction chamber to form a first, outer, forwardly moving vortex containing the liquid silicon product and a second, inner, rewardly moving vortex containing the by-product hydrogen gas. The liquid silicon in the first outer vortex deposits onto the interior walls of the reaction chamber to form an equilibrium skull layer which flows to the forward or bottom end of the reaction chamber where it is removed. The by-product hydrogen gas in the second inner vortex is removed from the top or rear of the reaction chamber by a vortex finder. The injector probe which introduces the silane gas into the reaction chamber is continually cooled by a cooling jacket

Nucleation of Spontaneous Vortices in Trapped Fermi Gases Undergoing a BCS-BEC Crossover

We study the spontaneous formation of vortices during the superfluid condensation in a trapped fermionic gas subjected to a rapid thermal quench via evaporative cooling. Our work is based on the numerical solution of the time dependent crossover Ginzburg-Landau equation coupled to the heat diffusion equation. We quantify the evolution of condensate density and vortex length as a function of a crossover phase parameter from BCS to BEC. The more interesting phenomena occur somewhat nearer to the BEC regime and should be experimentally observable; during the propagation of the cold front, the increase in condensate density leads to the formation of supercurrents towards the center of the condensate as well as possible condensate volume oscillations.Comment: 5 pages, 3 figure

Die Characterprobleme bei Shakespeare. Eine Einfuhrung in das Verstandnis des Dramatikers

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Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances

Warping the young stellar disc in the Galactic Centre

We examine influence of the circum-nuclear disc (CND) upon the orbital evolution of young stars in the Galactic Centre. We show that gravity of the CND causes precession of the orbits which is highly sensitive upon the semi-major axis and inclination. We consider such a differential precession within the context of an ongoing discussion about the origin of the young stars and suggest a possibility that all of them have originated in a thin disc which was partially destroyed due to the influence of the CND during the period of ~6Myr.Comment: proc. conf. "The Universe Under the Microscope - Astrophysics at High Angular Resolution", 21-25 April 2008, Bad Honnef, German

Influence of roughness on near-field heat transfer between two plates

The surface roughness correction to the near-field heat transfer between two rough bulk materials is discussed by using second-order perturbation theory. The results allow for estimating the impact of surface roughness to the heat transfer in recent experiments between two plates and between a microsphere and a plate (using the Derjaguin approximation). Furthermore, we show that the proximity approximation for describing rough surfaces is valid for distances much smaller than the correlation length of the surface roughness even if the heat transfer is dominated by the coupling of surface modes

Effect of rivet or bolt holes on the ultimate strength developed by 24S-T and Alclad 75S-T sheet in incomplete diagonal tension

Strength tests were made of a number of 24S-T and Alclad 75S-T aluminum alloy shear webs to determine the effect of rivet or bolt holes on the shear strength. Data were obtained for webs which approached a condition of pure shear stress as well as for webs with well-developed diagonal tension. The rivet factor (pitch minus diameter), divided by pitch, was varied from approximately 0.81 to 0.62. These tests indicated that the shear stresses on the gross section were nearly constant for all values of the rivet factor investigated if the other properties of the web were not changed

Comparison of Measured and Calculated Stresses in Built-up Beams

Web stresses and flange stresses were measured in three built-up beams: one of constant depth with flanges of constant cross-section, one linearly tapered in depth with flanges of constant cross section, and one linearly tapered in depth with tapered flanges. The measured stresses were compared with the calculated stresses obtained by the methods outlined in order to determine the degree of accuracy that may be expected from the stress analysis formulas. These comparisons indicated that the average measured stresses for all points in the central section of the beams did not exceed the average calculated stresses by more than 5 percent. It also indicated that the difference between average measured flange stresses and average calculated flange stresses on the net area and a fully effective web did not exceed 6.1 percent

Elliptic Schlesinger system and Painlev{\'e} VI

We construct an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the parameters in the moduli space of the complex structure). ESS is a non-autonomous Hamiltonian system with pair-wise commuting Hamiltonians. The system is bihamiltonian with respect to the linear and the quadratic Poisson brackets. The latter are the multi-color generalization of the Sklyanin-Feigin-Odeskii classical algebras. We give the Lax form of the ESS. The Lax matrix defines a connection of a flat bundle of degree one over the elliptic curve with first order poles at the marked points. The ESS is the monodromy independence condition on the complex structure for the linear systems related to the flat bundle. The case of four points for a special initial data is reduced to the Painlev{\'e} VI equation in the form of the Zhukovsky-Volterra gyrostat, proposed in our previous paper.Comment: 16 pages; Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190