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 language | English |
|---|---|
| Pages (from-to) | 158-165 |
| Number of pages | 8 |
| Journal | Applied Numerical Mathematics |
| Volume | 104 |
| DOIs | |
| Publication status | Published - Jun 1 2016 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Numerical integration of variational equations for Hamiltonian systems with long range interactions
AU - Christodoulidi, Helen
AU - Bountis, Tassos
AU - Drossos, Lambros
PY - 2016/6/1
Y1 - 2016/6/1
N2 - 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.
AB - 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.
KW - Hamiltonian systems
KW - Long range interactions
KW - Symplectic integration
KW - Variational equations
UR - http://www.scopus.com/inward/record.url?scp=84945567190&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84945567190&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2015.08.009
DO - 10.1016/j.apnum.2015.08.009
M3 - Article
VL - 104
SP - 158
EP - 165
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -