Lyapunov instability of rigid diatomic molecules in three dimensions

Abstract

We study the Lyapunov instability of a three-dimensional fluid composed of rigid diatomic molecules by molecular dynamics simulation. We use center-of-mass coordinates and angular variables for the configurational space variables. The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the Weeks-Chandler-Andersen potential for various bond lengths and densities. We show the general trends and characteristic features of the spectra of the Lyapunov exponents, and discuss the different contributions between translational and rotational degrees of freedom depending on the density and the bond length from the calculation of the projection of a certain subspace of the tangent space vectors.

Lyapunov instability of rigid diatomic molecules in three dimensions: A simpler method

“…We compare present results with those appeared in Ref. [1], which uses two coordinates representations to avoid the singularity occurring in the equations of motion by combining with the adaptive Runge-Kutta-Fehlberg method of order four.…”

“…This is also true in Ref. [1], where the bond length is naturally fixed without using any additional constraint.…”

“…However, the equations of motion in our model are much simpler than those used in Ref. [1], and they are easy to implement.…”

“…In this paper we propose a new method to calculate Lyapunov exponents of the rigid diatomic molecules in three dimensions, which does not require periodic rescaling of the bond length. Rigid diatomic molecules are often described by hard dumbbells and there have been several works on the Lyapunov instability for the diatomic molecular models [1,10,11,12,13,14,15].…”

“…

We present a new method to calculate Lyapunov exponents of rigid diatomic molecules in three dimensions (12N dimensional phase space). The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the Weeks-Chandler-Anderson(WCA) potential for various bond length and densities, and compared with those in Y.-H. Shin et al [1]. Our algorithm is easy to implement and total CPU time is relatively inexpensive.

…”