By Evgeny Barkhudarov
This thesis has components, each one in response to an software of the renormalization-group (RG). the 1st half is an research of the d-dimensional Coulomb fuel. The target used to be to figure out if the Wilson RG may provide enter into particle-in-cell simulations in plasma physics, that are the most relatives of simulation equipment utilized in this box. The function of the RG used to be to spot the impact of coarse-graining at the coupling constants as a functionality of the cut-offs. The RG calculation reproduced verified effects, yet in a extra concise shape, and confirmed the impression of the cut-offs at the Debye screening length.
The major a part of the thesis is the appliance of the dynamic RG to turbulence in magnetohydrodynamics. After transformation to Elsasser variables, that is a symmetrisation of the unique equations, the answer is gifted as a sensible necessary, inclusive of stirring forces, their conjugates and practical Jacobian. The coarse-graining of the sensible quintessential is represented as a diagrammatic enlargement, through rescaling, and casting the implications into differential equations for the research of RG trajectories. special comparisons are made with the Navier-Stokes restrict and with past calculations for MHD.