Dynamics of Classical Scattering in a Periodic Lattice

Tim Birger Tejsner

Student thesis: Termpaper

Abstract

This project concerns the analysis of mathematical model of classical scattering. I consider a 2-dimensional model of a particle that is scattered through a symmetric lattice and interact through the Lennard-Jones potential. The model is investigated as a Hamiltonian system and simulations are done in the context of molecular dynamics. The analysis is done following the formalism of chaotic scattering. In particular, the fractal dimension d_c of the scattering function and the mean exit time tau from the scattering region are computed. By increasing the lattice size from 2-by-2 to 4-by-4, I find an increase in both tau and d_c. This is an indication of an increase in the positive Lyapunov exponent chi_1 with increasing lattice size.

EducationsMathematic, (Bachelor/Graduate Programme) Undergraduate or graduate
LanguageEnglish
Publication date20 Jan 2015
SupervisorsJesper Schmidt Hansen

Keywords

  • Dynamical Systems
  • Molecular Dynamics
  • Scattering
  • Chaotic Scattering
  • Hamiltonian Systems