ENGLISH

Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems

By Evgeny Barkhudarov (auth.)

Book information

Publisher
Springer International Publishing
Year
2014
ISBN
978-3-319-06153-5, 978-3-319-06154-2
DOI
10.1007/978-3-319-06154-2
Language
english
Format
PDF
Filesize
3 MB (2755000 bytes)
Series
Springer Theses
Edition
1
Pages
163\168
Time added
2014-06-12 06:00:00
Mathematical Methods in Physics; Fluid- and AerodyQuantum Field Theory; Mathematical Applications in

Description

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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