Escape of the Atmosphere of Rotating Planet

M.K.M. Ahmed and Z.M. Hayman*
Astronomy & Meteorology Department, Faculty of Science, Cairo University, Giza, Egypt, 12613

Abstract:

The problems of escape of a planetary atmosphere is reviewed. Formulae are derive for the rates of loss of mass and angular momentum from a unit area and from the whole planetary surface. The resulting formulae are applied to find the residence times of H, O, N2, O2 and CO2 in Martian atmosphere. All constituents are so stable while hydrogen is never stable and cannot be retained to my extent.

Keywords: Escape of a planetary atmosphere, loss of mass-residence times
Affiliation: Astronomy&Meteorology Department, Faculty of Science, Cairo Universiy, Giza, Egypt

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Nonlinear Image Recovery with Half-Quadratic Regularization

Donald Geman and Chengda Yang
July, 1993

Abstract

One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function which enforces a roughness penalty in addition to coherence with the data. Linear estimates are relatively easy to compute but generally introduce systematic errors; for example, they are incapable of recovering discontinuities and other important image attributes. In contrast, nonlinear estimates are more accurate, but often far less accessible. This is particularly true when the objective function is non-convex and the distribution of each data component depends on many image components through a linear operator with broad support. Our approach is based on an auxiliary array and an extended objective function in which the original variables appear quadratically and the auxiliary variables are decoupled. Minimizing over the auxiliary array alone yields the original function, so the original image estimate can be obtained by joint minimization. This can be done efficiently by Monte Carlo methods, for example by FFT-based annealing using a Markov Chain which alternates between (global) transitions from one array to the other. Experiments are reported in optical astronomy, with Space Telescope data, and computed tomography.

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