Nonlinear Spin Dynamics in Nuclear Magnets

A method is developed for solving nonlinear systems of differential, or integrodifferential, equations with stochastic fields. The method makes it possible to give an accurate solution for an interesting physical problem: What are the peculiarities of nonlinear spin dynamics in nonequilibrium nuclear magnets coupled with a resonator? Evolution equations for nuclear spins are derived basing on a Hamiltonian with dipole interactions. The ensemble of spins is coupled with a resonator electric circuit. Seven types of main relaxation regimes are found: free induction, collective induction, free relaxation, collective relaxation, weak superradiance, pure superradiance, and triggered superradiance. The initial motion of spins can be originated by two reasons, either by an imposed initial coherence or by local spin fluctuations due to nonsecular dipole interactions. The relaxation regimes caused by the second reason cannot be described by the Bloch equations. Numerical estimates show good agreement with experiment.Comment: 1 file, 47 pages, LaTe

Applications of a revived Euler--Shohat Perturbation expansion technique in the study of ocean circulation. [Coastal waters]

Consideration of geophysical vertical plane flows in estuaries and on continental shelves results in nonlinearly coupled partial differential equations for flow and density variables. For the case of steady flow, the equations are reduced to ordinary differential equations by the use of similarity transformations. The remaining nonlinearly coupled ordinary differential equations are solved using a revised Euler-Shohat perturbation technique. An existence theorem for this application of the technique is stated and proved