TY - JOUR

T1 - Numerical integration of variational equations for Hamiltonian systems with long range interactions

AU - Christodoulidi, Helen

AU - Bountis, Tassos

AU - Drossos, Lambros

N1 - Funding Information:
This research has been co-financed by the European Union ( European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALES – Investing in knowledge society through the European Social Fund . Computer simulations were performed in the facilities offered by the High Performance Computing Systems and Distance Learning Lab (HPCS-DL Lab), Technological Educational Institute of Western Greece.

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

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U2 - 10.1016/j.apnum.2015.08.009

DO - 10.1016/j.apnum.2015.08.009

M3 - Article

AN - SCOPUS:84945567190

VL - 104

SP - 158

EP - 165

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -