Nuclear systems, sensitivity functions

Many predictive applications of perturbation theory techniques for the design, analysis, and optimization of various nuclear systems, as well as for the evaluation and adjustment of nuclear data, are based on sensitivity functions. Section VI presents the fundamentals of perturbation-based sensitivity studies, describes the origin of sensitivity functions, and discusses several areas of application for sensitivity studies. These include cross-section sensitivity studies and optimization studies which are emerging as important fields for the application of perturbation theory. 

One class of optimization problems encountered in nuclear engineering is the search for the material composition distribution or the geometry of a nuclear system that will extremize (minimize or maximize) one property of the system while keeping other properties within given bounds. Numerous methods have been developed for attacking this type of optimization problem. Reviews and references for these methods are provided (56, 114, 115). One approach to optimization is the perturbation approach. It makes use of material density or boundary displacement sensitivity functions. 

Much work is still required before many of the perturbation theory formulations reviewed and presented here can be implemented in practice. If full benefit is to be drawn from perturbation theory techniques for a wide variety of problems concerned with the design, analysis, and optimization of nuclear systems, computer code systems of the future must include basic and specific modules for calculations based on perturbation theory formulations. The basic modules are intended for the calculation of different sensitivity functions. Specific modules should enable performanee of dilTerent studies sueh as cross-section sensitivity studies, analysis of alterations in the design or operating conditions of nuclear systems, and optimization studies. 

A number of experimental parameters have to be optimized in order to obtain the best SPECT image. These include attenuation, scatter, linearity of detector response, spatial resolution of the collimator and camera, system sensitivity, minimization of mechanical movements, image slice thickness, reconstruction matrix size and filter methods, sampling intervals and system deadtime. In a hospital, calibrating and monitoring these functions are usually performed by a Certified Nuclear Medicine Technician or a medical physicist. 

Aurbach and co-workers performed a series of ex situ as well as in situ spectroscopic analyses on the surface of the working electrode upon which the cyclic voltammetry of electrolytes was carried out. On the basis of the functionalities detected in FT-IR, X-ray microanalysis, and nuclear magnetic resonance (NMR) studies, they were able to investigate the mechanisms involved in the reduction process of carbonate solvents and proposed that, upon reduction, these solvents mainly form lithium alkyl carbonates (RCOsLi), which are sensitive to various contaminants in the electrolyte system. For example, the presence of CO2 or trace moisture would cause the formation of Li2COs. This peculiar reduction product has been observed on all occasions when cyclic carbonates are present, and it seems to be independent of the nature of the working electrodes. A single electron mechanism has been shown for PC reduction in Scheme 1, while those of EC and linear carbonates are shown in Scheme 7. ... 

It is clear that Mn and Gd can be sensitive EPR probes of structure and function in membrane enzyme systems. If problems of purity and concentration can be overcome, several other membrane enzymes should be amenable to EPR investigations of the type described here. Moreover, the combination of nuclear relaxation studies and EPR studies of free and bound metals can provide sufficient data for the construction of models of active sites for membrane enzymes. For each paramagnetic probe which can be located unambiguously and uniquely at the active site, one more spatial dimension is added to the picture. Thus the identification of a single Mn2+ site on the (Na+ + K+)-ATPase has permitted the determination of three distances between Mn2+ and... 

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