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Fermi Acceleration and Time-Dependent Elliptic Billiards.

Fain, V. (2013) Fermi Acceleration and Time-Dependent Elliptic Billiards. Doctoral thesis, University of Surrey (United Kingdom)..

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Abstract

Billiard maps are one of the most common types of dynamical systems. In recent years, billiards with time-depending boundaries became popular objects of study, especially due to their relevance in physical models. One fundamental question is whether a billiard particle may accelerate to unbounded energies due to collisions with the moving boundary. This unbounded energy growth in systems with impacts is known as Fermi acceleration mechanism. Recently, it has been numerically shown that Fermi acceleration exists in elliptic time-dependent billiards. Due to the Hamiltonian nature of billiard dynamics, they can be analysed via techniques from the Hamiltonian mechanics. We present some basic properties of symplectic (twist) maps and Hamiltonian flows. The analysis of the relevant facts from the theory of static elliptic billiards is presented. Then we present some recent relevant results from the area of KAM theory and Arnol’d diffusion, as KAM-type approaches have been used in rigorous mathematical formulation of Fermi acceleration. We review some milestones in the development of Fermi acceleration up to the current state of affairs. Finally, we outline an approach that could be used to prove the existence of orbits with growing energy in elliptic billiards and present the results we have achieved so far in this direction.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors : Fain, V.
Date : 2013
Additional Information : Thesis (M.Phil.)--University of Surrey (United Kingdom), 2013.
Depositing User : EPrints Services
Date Deposited : 24 Apr 2020 15:26
Last Modified : 24 Apr 2020 15:26
URI: http://epubs.surrey.ac.uk/id/eprint/855299

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