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Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems (Hardcover, 2014 ed.)
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Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems (Hardcover, 2014 ed.)
Series: Springer Theses
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This thesis has two parts, each based on an application of the
renormalization-group (RG). The first part is an analysis of the
d-dimensional Coulomb gas. The goal was to determine if the Wilson
RG could provide input into particle-in-cell simulations in plasma
physics, which are the main family of simulation methods used in
this field. The role of the RG was to identify the effect of
coarse-graining on the coupling constants as a function of the
cut-offs. The RG calculation reproduced established results, but in
a more concise form, and showed the effect of the cut-offs on the
Debye screening length.
The main part of the thesis is the application of the dynamic RG to
turbulence in magnetohydrodynamics. After transformation to
Elsasser variables, which is a symmetrisation of the original
equations, the solution is presented as a functional integral,
which includes stirring forces, their conjugates and functional
Jacobian. The coarse-graining of the functional integral is
represented as a diagrammatic expansion, followed by rescaling, and
casting the results into differential equations for the analysis of
RG trajectories. Detailed comparisons are made with the
Navier-Stokes limit and with previous calculations for MHD.
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