Integrating the nonintegrable: analytic structure of the Lorenz system revisited
Physica D - Progress in Chaotic Dynamics
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Radiation damping with inhomogeneous broadening: limitations of the single bloch vector model
Concepts in Magnetic Resonance: an Educational Journal
Mathematical and Computer Modelling: An International Journal
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The techniques of Painlevé analysis and Lie algebra analysis were applied to the nonlinear Bloch equations with radiation damping. Painlevé analysis is useful in finding when explicit solutions exist to a nonlinear system. It was applied to the radiation-damped system with damping time Tr, and with T1 and T2 relaxation, but with no externally applied radiofrequency (RF) pulse. Two cases were identified where explicit solutions could be found. The first case ( 1/T1:0) is well known, the second case ( 1/T1=1/Tγ+1/T2) is apparently not previously known. Lie algebra analysis was used to show that the system with no relaxation, but with an externally applied RF pulse, could be transformed into a linear system. This simplifies the forward problem of finding the magnetization response to a given pulse. It also allows the inverse problem to be solved, where the pulse is calculated to result in a given magnetization response as functions of both resonance offset and radiation damping time.