Equations of Motion and Energy Conservation in Molecular Dynamics

Stochastic and dynamic properties of molecular dynamics systems: Simple liquids, plasma and electrolytes, polymers

“…The E value fluctuates about the average value from step to step, and the trajectory obtained in molecular dynamics simulations does not lie on the surface E = const, in contrast to exact solutions to Newton equations (1). This trajectory is situated in some layer of thickness E > 0 near the surface E = const [7,8]. The value E 2 ∼ t p depends on the accuracy and the scheme of numerical integration [7,8,[19][20][21][22].…”

“…Set (1) is exponentially unstable for a system of more than two particles (e.g., see [3][4][5][6][7][8][9][10][11][12][13][14][15][16]). The parameter that determines the degree of instability, that is, the rate of divergence of initially close phase trajectories, is the averaged Lyapunov exponent or K-entropy K. It can be determined in several ways.…”

“…The idea of MDM is very simple: all possible classical systems and media are simulated by a set of N moving atoms and/or molecules, which interact with each other (e.g., see [4][5][6][7][8][9][10][11]). The numerical integration of the corresponding system of Newton equations…”

“…The K-values were calculated by MDM for systems of neutral particles [3,[7][8][9][10][11][12]23,24], two-component [15] and one-component [16] plasmas and the primitive polymer model [25]. Estimates of dynamical memory times showed that, e.g., in Ar fluid [14], t m lies in the picosecond range.…”

K‐Entropies of Electrons and Ions in Nonideal Plasmas

“…(6) The potentials (5) and (6) satisfy the dynamics similarity, thus, the value K depends only on nonideality parameter 7. To elucidate the relative contributions of Coulomb long range interaction and non-Coulomb short range part of the interaction in K-entropy the computations were performed for the following electron-ion potential as well U ( T ) = 0.1 k~ (e2/ekTr)12e z / T .…”