Statistical parameterization of inverse problems

Image restoration, computerized tomography, and other similar problems are considered as a unified class of stochastic inverse problems. The conventional approach to these problems that proceeds from some integral or functional equations suffers from three main shortcomings: (i) subjectivity, (ii) inability to account for the inner (radiational) noise, and (iii) inability to include the fundamental concept of the natural limit of solution accuracy. A general approach is developed, the Statistical Parameterization of Inverse Problems (SPIPR), that takes into account both the inner and external random noise and gives an explicit form of the above-mentioned natural limit. Applications of the SPIPR to various problems show that the maximum likelihood method as the concrete way to obtain an object estimate has practically limiting efficiency.Two new fields of applications of the SPIPR are outlined along with the image restoration problem: the elimination of blurring due to atmosphere turbulence and reconstruction of an object structure in the computerized tomography. The expressions for the main distribution function in all these problems are found. The corresponding real examples and model cases are considered as well.     

Ridge systems related to Martian impact craters

Wrinkle ridge systems within and around Martian highland craters were studied in order to find their basin-induced and regional aspects. Most prominent ridge directions indicate regional tectonic patterns. Radial ridges near large craters are often slightly deflected along regional or global ridge systems. Crater floor ridges have simpler local distributions. Smaller or older craters are less resistant against the effects of global or regional stress systems. In craters concentric ridge rings locate at 0.8 crater radius with additional minor rings at 0.66, 0.44 and 0.94 crater radius. This pattern illustrates compression of lava fill over buried topography.     

Experimental simulation of Titan's atmosphere: Detection of ammonia and ethylene oxide

For several years now, an experimental simulation of Titan's atmosphere has been on going at LISA. A cold plasma is established in a gas mixture representative of the atmosphere of the satellite. In these experiments, more than 70 organic compounds have been identified, including the first identification in this type of experimental simulation of C₄N₂ already detected in its solid form on Titan, which suggests that the setup correctly mimics the chemistry of Titan's atmosphere.We have carried out the first experimental simulation including O-containing compounds in order to study the influence of the presence of CO on the chemical behavior of Titan's atmosphere. With the help of gas chromatography–mass spectrometry (GC–MS) and infrared spectroscopy (IRS) we can thus determine which minor species still undetected in Titan's atmosphere are likely to be present and understand the complex chemistry of the atmosphere of this satellite. Surprisingly we have identified unpredicted O-containing gaseous compounds, mainly ethylene oxide (also named oxirane, C₂H₄O). This molecule has been observed in the interstellar medium by observation in the millimeter region (Astrophys. J. 489 (1997) 553; Astron. Astrophys. 337 (1998) 275). On the contrary, the predicted O-compounds (formaldehyde and methanol) have not been identified in this experiment. Furthermore, we have identified NH₃ in the gaseous products with an initial mixture of N₂ (98%) and CH₄ (2%).The paper describes the experimental device used in this work, in particular the IRS and GC–MS techniques. We also comment the results related to the detection of the O-containing compounds and NH₃ and their implications on our knowledge of the chemistry of Titan's atmosphere and on the retrieval of the future Titan data expected from Cassini-Huygens.     

Simulating methane emission from a Chinese rice field as influenced by fertilizer and water level

Natural and agricultural wetlands are considered to be the major sources of global atmospheric methane (CH₄). A one‐dimensional model was developed to simulate methane emission and used to examine the influence of various physical processes on the rate of methane emission. Three processes involved in the methane emission are implemented in the model: production, reoxidation and transport. Three transport pathways were considered: diffusion across water–air or soil–air interfaces, ebullition and diffusion through plants. These pathways are influenced by soil properties, plant growth, water‐table conditions, temperature and external inputs (e.g. fertilizer). The model was used to examine the seasonal variation of the methane emission at a rice field in Hunan, China, which was observed during a field experiment for consecutive (early and late) rice seasons in 1992. The observed seasonal variations of methane emission, and role of plants in transporting methane to the atmosphere, are captured by the model simulation. Further model applications were conducted to simulate effects of fertilizer and water‐level condition on the methane emission. The results indicate that unfermented organic fertilizer produces a higher methane emission rate than mineral fertilizer. The simulations with treatments of a deep‐water covering and constant moisture reduced the methane emission. The rice field study provides a framework for further development of the model towards simulations based on spatially distributed variables (e.g. water table, soil temperature and vegetation) at a regional scale. Copyright © 2003 John Wiley & Sons, Ltd.     

Resonant behaviour of MHD waves on magnetic flux tubes

Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.     

Frequency distributions and correlations of solar X-ray flare parameters

We have determined frequency distributions of flare parameters from over 12000 solar flares recorded with the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM) satellite. These parameters include the flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons (the latter two computed assuming a thick-target flare model). The energies were computed above a threshold energy between 25 and 50 keV. All of the distributions can be represented by power laws above the HXRBS sensitivity threshold. Correlations among these parameters are determined from linear regression fits as well as from the slopes of the frequency distributions. Variations of the frequency distributions were investigated with respect to the solar activity cycle.Theoretical models for the frequency distribution of flare parameters depend on the probability of flaring and the temporal evolution of the flare energy build-up. Our results are consistent with stochastic flaring and exponential energy build-up, with an average build-up time constant that is 0.5 times the mean time between flares. The measured distributions of flares are also consistent with predicted distributions of flares from computer simulations of avalanche models that are governed by the principle of self-organized criticality.     

Current convection in solar active regions

Current carrying magnetic fields which penetrate sunspots can be unstable to current convective modes caused by the large gradient of electrical conductivity. The linear growth rates and wavelengths of the unstable modes are found. The unstable modes produce fine-scale vortices perpendicular to the magnetic field, which overshoot well into the solar corona. The modes provide a turbulent vorticity source at the photospheric footpoints of the field. This can cause braiding and reconnection of the coronal magnetic field. The modes twist the coronal magnetic field into loops with a typical radius of 200 km, consistent with recent X-ray observations.     

Interplanetary dust particles and solar radiation

The problem of the action of the solar radiation on the motion of interplanetary dust particle is discussed. Differences between the action of electromagnetic solar radiation and that of the solar wind are explained not only from the point of view of the physical nature of these phenomena but also from the point of view of dust particle's orbital evolution. As for the electromagnetic solar radiation, general equation of motion for the particle is written and the most important consequences are: (i) the process of inspiralling toward the Sun is not the only possible motion - even spiralling from the Sun is also possible, and, (ii) the orbital plane of the particle (its inclination) may change in time. As for the solar wind, the effect corresponding to the fact that solar wind particles spread out from the Sun in nonradial direction causes that the process of inspiralling toward the Sun is in more than 50% less effective than for radial spread out; in the region of the asteroid belt (long period orbits) the process of inspiralling is changed into offspiralling. Also shift in the perihelion of dust particle's orbit exists.