Overview
- Nominated as an outstanding Ph.D. thesis by Imperial College London, UK
- Analysis of Feynman diagrams arising in randomly stirred MHD and Navier-Stokes
- Detailed application of renormalization group techniques to various problems in modern physics
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (6 chapters)
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Front Matter
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Equilibrium Statistical Mechanics: Coulomb Gas
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Front Matter
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Non-Equilibrium Statistical Mechanics: Randomly Stirred Magnetohydrodynamics
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems
Authors: Evgeny Barkhudarov
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-3-319-06154-2
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-06153-5Published: 22 May 2014
Softcover ISBN: 978-3-319-36028-7Published: 10 September 2016
eBook ISBN: 978-3-319-06154-2Published: 09 May 2014
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: XV, 163
Number of Illustrations: 18 b/w illustrations, 10 illustrations in colour
Topics: Mathematical Methods in Physics, Fluid- and Aerodynamics, Elementary Particles, Quantum Field Theory, Mathematical Applications in the Physical Sciences