Numerical integration of variational equations for Hamiltonian systems with long range interactions

Helen Christodoulidi, Tassos Bountis, Lambros Drossos

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study numerically classical 1-dimensional Hamiltonian lattices involving inter-particle long range interactions that decay with distance like 1/rα, for α≥0. We demonstrate that although such systems are generally characterized by strong chaos, they exhibit an unexpectedly organized behavior when the exponent α<1. This is shown by computing dynamical quantities such as the maximal Lyapunov exponent, which decreases as the number of degrees of freedom increases. We also discuss our numerical methods of symplectic integration implemented for the solution of the equations of motion together with their associated variational equations. The validity of our numerical simulations is estimated by showing that the total energy of the system is conserved within an accuracy of 4 digits (with integration step τ=0.02), even for as many as N=8000 particles and integration times as long as 106 units.

Original languageEnglish
Pages (from-to)158-165
Number of pages8
JournalApplied Numerical Mathematics
Volume104
DOIs
Publication statusPublished - Jun 1 2016
Externally publishedYes

Fingerprint

Hamiltonians
Variational Equation
Long-range Interactions
Numerical integration
Hamiltonian Systems
Symplectic Integration
Time Integration
Digit
Chaos theory
Lyapunov Exponent
Equations of motion
Equations of Motion
Numerical methods
Chaos
Degree of freedom
Exponent
Numerical Methods
Decay
Numerical Simulation
Decrease

Keywords

  • Hamiltonian systems
  • Long range interactions
  • Symplectic integration
  • Variational equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical integration of variational equations for Hamiltonian systems with long range interactions. / Christodoulidi, Helen; Bountis, Tassos; Drossos, Lambros.

In: Applied Numerical Mathematics, Vol. 104, 01.06.2016, p. 158-165.

Research output: Contribution to journalArticle

Christodoulidi, Helen ; Bountis, Tassos ; Drossos, Lambros. / Numerical integration of variational equations for Hamiltonian systems with long range interactions. In: Applied Numerical Mathematics. 2016 ; Vol. 104. pp. 158-165.
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