Internal structures of self-organized relaxed states and self-similar decay phase

"A thought analysis on relaxation due to nonlinear processes is presented to lead to a set of general thoughts applicable to general nonlinear dynamical systems for finding out internal structures of the self-organized relaxed state without using ""invariant"". Three applications of the set of general thoughts to energy relaxations in resistive MHD plasmas, incompressible viscous fluids, and incompressible viscous MHD fluids are shown to lead to the internal structures of the self-organized relaxed states. It is shown that all of the relaxed states in these three dynamical systems are followed by self-similar decay phase without significant change of the spatial structure. The well known relaxed state of nabla x B = pm lambda B is shown to be derived generally in the low beta plasma limit."