Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems

  • Evgeny¬†Barkhudarov

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Evgeny Barkhudarov
    Pages 1-14
  3. Equilibrium Statistical Mechanics: Coulomb Gas

    1. Front Matter
      Pages 15-15
    2. Evgeny Barkhudarov
      Pages 17-26
    3. Evgeny Barkhudarov
      Pages 27-39
  4. Non-Equilibrium Statistical Mechanics: Randomly Stirred Magnetohydrodynamics

    1. Front Matter
      Pages 41-41
    2. Evgeny Barkhudarov
      Pages 43-84
    3. Evgeny Barkhudarov
      Pages 85-120
    4. Evgeny Barkhudarov
      Pages 121-123
  5. Back Matter
    Pages 125-163

About this book

Introduction

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.

Keywords

Coulomb Gas Feynman Diagrams Functional Integral Galilean Symmetry Magnetohydrodynamic Turbulence Navier-Stokes Equation Renormalization Group Applications Vertex Renormalization

Authors and affiliations

  • Evgeny¬†Barkhudarov
    • 1
  1. 1.The Blackett LaboratoryImperial College LondonLondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-06154-2
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-06153-5
  • Online ISBN 978-3-319-06154-2
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • About this book
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