Dynamic stability of space vehicles. Volume 8 - Atmospheric disturbances that affect flight control analysis

Space vehicle and control system dynamic response to atmospheric disturbance

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process

The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturbance of the system by the measurement is also discussed. A class of minimally disturbing measurements is characterised. It is shown that the distribution of measured values then coincides with one of the smoothed Wigner functions described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final published versio

A Computer Simulation of the Oxygen Reduction Reaction in Carbonate Melts

A computer simulation of the oxygen reduction reaction in various carbonate melts has been carried out under steady-state conditions on the basis of a proposed kinetic model which takes into consideration the autocatalytic reaction involving oxygen and other reducible oxygen species in the melt, and the neutralization of oxide ions by dissolved carbon dioxide. A simulation of the presence of (physically) dissolved oxygen, in the diffusion layer region of the melt, corresponding to the possible situation in porous electrodes, causes a significant enhancement in the polarization curves, particularly in the mass-transfer control region. On the other hand, high levels of dissolved CO2 in the melt reduce the current density in the mass-transfer control region by reducing the concentration of active dioxygen ions, but enhance it considerably in the kinetic limiting (CO2 neutralization) region. High rates of the autocatalytic and neutralization reactions display the same effects on the polarization curves as dissolved O2 and CO2, respectively, but to a lesser degree. Comparison of the simulated polarization curves in various carbonate melts indicates that Li-rich melts show the best kinetic performance. On the contrary, the highest limiting currents are observed in K- or Na-rich melts. Variation of the cation composition in Li/K carbonate melts indicates that melts of high Li-content should give better kinetic performance

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010