ABSTRACT:The recent analytical solutions to the Bloch NMR equations for a general RF excitation have opened many possibilities for further investigations to NMR theory and experiments even at the molecular level. Fortunately, many of the most important but hidden applications of blood flow and general physiological fluid flow parameters can be revealed without too much difficulty if appropriate mathematical techniques are used to explore the new NMR equations derived from the Bloch equations. Generally, we should be very much concerned with analytical results that the Bloch NMR flow equations can provide for different physical, biomedical, geophysical, medical, and environmental situations especially at the molecular level for the purpose of interdisciplinary approach to solve difficult problems. It can be motivating, exciting, and rewarding if attention are focused on the possible application of these analytical techniques and methods suitable for describing each of the various normal and pathological biological conditions. Most solutions presented in this study are described both in isotropic and anisotropic geometries with minimum mathematical assumptions. We discussed a general expression for the diffusion coefficients in the common geometries. These analytical results can prove to be very invaluable in the analysis of restricted flows. It is so much special because it could tell us when restricted flows occur and also reveal the causes of such restriction. Such knowledge can help in finding the causes of many diseases (whose causes are yet unknown) and suggest the best treatment for them.
Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at each stage of MRI techniques. In this study, we present new sets of non-exponential generating functions representing the NMR transverse magnetizations and signals which are mathematically designed based on the theory and dynamics of the Bloch NMR flow equations. These signals are functions of many spinning nuclei of materials and can be used to obtain information observed in all flow systems. The Bloch NMR flow equations are solved using the Boubaker polynomial expansion scheme (BPES) and analytically connect most of the experimentally valuable NMR parameters in a simplified way for general analyses of magnetic resonance imaging with adiabatic condition.
We present general analytical solutions to the nuclear dynamics-related Neutron Boltzmann Transport Equation inside nanoenergy reactors. Finding a particular solution to the neutron equation by making use of boundary conditions and initial conditions may be too much for the present study and reduce the generality of the solutions. Some simple assumptions have been introduced in the main system thanks to the Boubaker Polynomial Expansion Scheme, BPES, in order to make the general analytical procedure simple and adaptable for solving similar real-life problems.
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