The BCS critical temperature in a weak external electric field via a linear two-body operator

We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in [Frank, Hainzl, Seiringer, Solovej, 2016] using the strategy introduced in [Frank, Hainzl, Langmann, 2018], where we considered the case of an external constant magnetic field.Comment: Dedicated to Herbert Spohn on the occasion of his seventieth birthday; 29 page

The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator

We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in Frank et al. (Commun Math Phys 342(1):189–216, 2016, [5]) using the strategy introduced in Frank et al. (The BCS critical temperature in a weak homogeneous magnetic field, [2]), where we considered the case of an external constant magnetic field

Time and Space Bounds for Reversible Simulation

We prove a general upper bound on the tradeoff between time and space that suffices for the reversible simulation of irreversible computation. Previously, only simulations using exponential time or quadratic space were known. The tradeoff shows for the first time that we can simultaneously achieve subexponential time and subquadratic space. The boundary values are the exponential time with hardly any extra space required by the Lange-McKenzie-Tapp method and the ($\log 3$)th power time with square space required by the Bennett method. We also give the first general lower bound on the extra storage space required by general reversible simulation. This lower bound is optimal in that it is achieved by some reversible simulations.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science, Vol xxx Springer-Verlag, Berlin, 200

Slowly modulated oscillations in nonlinear diffusion processes

It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion

Chromium silicide formation by ion mixing

The formation of CrSi_2 by ion mixing was studied as a function of temperature, silicide thickness and irradiated interface. Samples were prepared by annealing evaporated couples of Cr on Si and Si on Cr at 450°C for short times to form Si/CrSi_2/Cr sandwiches. Xenon beams with energies up to 300 keV and fluences up to 8 X 10^15 cm^(-2) were used for mixing at temperatures between 20 and 300°C. Penetrating only the Cr/CrSi_2 interface at temperatures above 150°C induces further growth of the silicide as a uniform stoichiometric layer. The growth rate does not depend on the thickness of the initially formed silicide at least up to a thickness of 150 nm. The amount of growth depends linearly on the density of energy deposited at the interface. The growth is temperature dependent with an apparent activation energy of 0.2 eV. Irradiating only through the Si/CrSi_2 interface does not induce silicide growth. We conclude that the formation of CrSi_2 by ion beam mixing is an interface-limited process and that the limiting reaction occurs at the Cr/CrSi_2 interface

Effects of anode material on arcjet performance

Anodes fabricated from four different materials were tested in a modular arcjet thruster at 1 kW power level on nitrogen/hydrogen mixtures. A two-percent thoriated tungsten anode served as the control. Graphite was chosen for its ease in fabrication, but experienced severe erosion in the constrictor and diverging side. Hafnium carbide and lanthanum hexaboride were chosen for their low work functions but failed due to thermal stress and reacted with the propellant. When compared to the thoriated tungsten nozzle, thruster performance was significantly lower for the lanthanum hexaboride insert and the graphite nozzle, but was slightly higher for the hafnium carbide nozzle. Both the lanthanum hexaboride and hafnium carbide nozzle operated at higher voltages. An attempt was made to duplicate higher performance hafnium carbide results, but repeated attempts at machining a second anode insert were unsuccessful. Graphite, hafnium carbide, and lanthanum hexaboride do not appear viable anode materials for low power arcjet thrusters

Numerical Simulations of Mass Transfer in Binaries with Bipolytropic Components

We present the first self-consistent, three dimensional study of hydrodynamic simulations of mass transfer in binary systems with bipolytropic (composite polytropic) components. In certain systems, such as contact binaries or during the common envelope phase, the core-envelope structure of the stars plays an important role in binary interactions. In this paper, we compare mass transfer simulations of bipolytropic binary systems in order to test the suitability of our numerical tools for investigating the dynamical behaviour of such systems. The initial, equilibrium binary models possess a core-envelope structure and are obtained using the bipolytropic self-consistent field technique. We conduct mass transfer simulations using two independent, fully three-dimensional, Eulerian codes - Flow-ER and Octo-tiger. These hydrodynamic codes are compared across binary systems undergoing unstable as well as stable mass transfer, and the former at two resolutions. The initial conditions for each simulation and for each code are chosen to match closely so that the simulations can be used as benchmarks. Although there are some key differences, the detailed comparison of the simulations suggests that there is remarkable agreement between the results obtained using the two codes. This study puts our numerical tools on a secure footing, and enables us to reliably simulate specific mass transfer scenarios of binary systems involving components with a core-envelope structure

Application of Monte Carlo-based statistical significance determinations to the Beta Cephei stars V400 Car, V401 Car, V403 Car and V405 Car

We have used Lomb-Scargle periodogram analysis and Monte Carlo significance tests to detect periodicities above the 3-sigma level in the Beta Cephei stars V400 Car, V401 Car, V403 Car and V405 Car. These methods produce six previously unreported periodicities in the expected frequency range of excited pulsations: one in V400 Car, three in V401 Car, one in V403 Car and one in V405 Car. One of these six frequencies is significant above the 4-sigma level. We provide statistical significances for all of the periodicities found in these four stars.Comment: 11 pages, 17 figure