3 resultados para Difference equations

em QUB Research Portal - Research Directory and Institutional Repository for Queen's University Belfast


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The harsh environment presented by engines, particularly in the exhaust systems, often necessitates the use of robust and therefore low bandwidth temperature sensors. Consequently, high frequencies are attenuated in the output. One technique for addressing this problem involves measuring the gas temperature using two sensors with different time-constants and mathematically reconstructing the true gas temperature from the resulting signals. Such a technique has been applied in gas turbine, rocket motor and combustion research. A new reconstruction technique based on difference equations has been developed and its effectiveness proven theoretically. The algorithms have been successfully tested and proven on experimental data from a rig that produces cyclic temperature variations. These tests highlighted that the separation of the thermocouple junctions must be very small to ensure that both sensors are subjected to the same gas temperatures. Exhaust gas temperatures were recorded by an array of thermocouples during transient operation of a high performance two-stroke engine. The results show that the increase in bandwidth arising from the dual sensor technique allowed accurate measurement of exhaust gas temperature with relatively robust thermocouples. Finally, an array of very fine thermocouples (12.5 - 50 microns) was used to measure the in-cycle temperature variation in the exhaust.

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In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.