Integrable nonlinear field equations and loop algebra structures

We apply the (direct and inverse) prolongation method to a couple of nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system under consideration, we develop a procedure with allows us to generate a new class of integrable nonlinear field equations containing the original ones as a special case.Comment: 13 pages, latex, no figures

Study to determine suitable high temperature, high altitude, total temperature sensors Final report

High temperature, high altitude total temperature sensor development - thermocouple devic

BEC-BCS crossover in "magnetized" Feshbach-resonantly paired superfluids

We map out the detuning-magnetization phase diagram for a ``magnetized'' (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). For large positive FR detuning a normal magnetized Fermi gas is stable above an exponentially small value of the population difference. Below this critical value the phase diagram is dominated by coexistence of a magnetized normal gas and a singlet paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi-sea, is a stable ground state.Comment: 4 RevTeX pages, 2 figures. Minor changes from previous versio

Influence of cold-rolling reduction on retained austenite texture in cold-rolled and intercritically annealed TRIP-assisted steel

The newly developed multiphase transformation-induced plasticity (TRIP) steels are of interest for industrial applications because of their excellent combination of high strength and ductility. Their performance can be successfully controlled by designing an optimum balance in the volume fractions of ferrite, bainite and retained austenite. The characteristics of the retained austenite are considered to be the main key to achieving the desired final properties. Against this background, the effects of retained austenite characteristics, such as volume fraction, carbon concentration, size and shape, on the behaviour of TRIP steels have been studied. The crystallographic orientation of the retained austenite was measured by electron backscattered diffraction (EBSD). The effect of initial cold-rolling reduction on the microtexture development of the retained austenite was studied on an aluminium-containing TRIP steel. The results show that, by increasing the cold-rolling reduction before the final austempering, the main components of the face-centred cubic phase, i.e. copper, brass and Goss, dominate the texture of the retained austenite. In contrast, the copper and Goss components of the retained austenite are absent in the texture of lightly deformed sheets. The features of the preferred orientation of the retained austenite are discussed and explained in terms of the annealing texture of the recrystallized ferrite and bainite

Dirac Spinors and Flavor Oscillations

In the standard treatment of particle oscillations the mass eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. To analyze this additional effect, we discuss the oscillation probability formula obtained by using the Dirac equation as evolution equation for the neutrino mass eigenstates. The initial localization of the spinor state also implies an interference between positive and negative energy components of mass eigenstate wave packets which modifies the standard oscillation probability.Comment: 14 pages, 1 figure, AMS-Te

Equations of the reaction-diffusion type with a loop algebra structure

A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the spectral problem and a whole class of nonlinear field equations containing the original ones as a special case.Comment: 16 pages, LaTex. submitted to Inverse Problem