Abstract/Details

GEOMETRIC PERTURBATION THEORY AND PLASMA PHYSICS (SYMPLECTIC GEOMETRY, HAMILTONIAN MECHANICS, KRUSKAL AVERAGING, MAXIMUM ENTROPY FORMATION, EIKONAL WAVES)

OMOHUNDRO, STEPHEN MALVERN.   University of California, Berkeley ProQuest Dissertations Publishing,  1985. 8525071.

Abstract (summary)

Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism in the same way the structure for classical mechanics arises from quantum mechanics via path integrals. The new structure for thermodynamics is used to generalize Maxwell's equal area rule.

Indexing (details)


Subject
Fluid dynamics;
Gases;
Plasma physics
Classification
0759: Plasma physics
Identifier / keyword
Pure sciences
Title
GEOMETRIC PERTURBATION THEORY AND PLASMA PHYSICS (SYMPLECTIC GEOMETRY, HAMILTONIAN MECHANICS, KRUSKAL AVERAGING, MAXIMUM ENTROPY FORMATION, EIKONAL WAVES)
Author
OMOHUNDRO, STEPHEN MALVERN
Number of pages
579
Degree date
1985
School code
0028
Source
DAI-B 46/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9798661753205
University/institution
University of California, Berkeley
University location
United States -- California
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8525071
ProQuest document ID
303333208
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303333208