System dynamics revealed by recurrence quantification analysis: Application to molecular dynamics simulations

The present work examines the applicability and efficacy of recurrence plots and recurrence quantification analysis in interpreting statistical-mechanics-based simulations of classical fluids and solids. We analyze temperature time series obtained from molecular dynamics simulations of a Lennard-Jones system at various fluid and solid states. It turns out that the structure of the recurrence plots reflects the different regimes of atomic motion as well as the degree of atomic diffusivity as the system density and temperature are varied. Recurrence plots (RPs) can help to localize a region where a phase transition occurs, while recurrence quantitative analysis descriptors confirm in a more clear way the results of RPs. The trends identified in our results are in qualitative agreement with direct computation of Lyapunov exponents for liquid Lennard-Jones systems reported in the literature.

Figure 1

(Color online) Phase diagram of the Lennard-Jones system (from [14]). The simulated states are marked in red.

Figure 2

(Color) Recurrence plots for various system densities and temperatures. (a) $T^{*}=1.5$ and ${\rho }^{*}=0.2$ $({\tau }_d=17)$; (b) $T^{*}=2.5$ and ${\rho }^{*}=0.2$ $({\tau }_d=13)$; (c) $T^{*}=1.5$ and ${\rho }^{*}=0.4$ $({\tau }_d=16)$; (d) $T^{*}=2.5$ and ${\rho }^{*}=0.4$ $({\tau }_d=11)$; (e) $T^{*}=1.5$ and ${\rho }^{*}=0.8$ $({\tau }_d=11)$; (f) $T^{*}=2.5$ and ${\rho }^{*}=0.8$ $({\tau }_d=10)$; (g) $T^{*}=1.5$ and ${\rho }^{*}=1.4$ $({\tau }_d=4)$; (h) $T^{*}=2.5$ and ${\rho }^{*}=1.4$ $({\tau }_d=4)$. (Time is in units of simulation time steps, i.e., ${10}^{-14}\mathrm{s}$.)

Figure 3

Typical trajectories of atoms (projection on $y\text{−}z$ plane) in the liquid phase. (a) $T^{*}=1.5$ and ${\rho }^{*}=0.2$; (b) $T^{*}=1.5$ and ${\rho }^{*}=0.8$.

Figure 4

(Color) (a)–(d) Zoom along the diagonal for the lowest fluid density [${\rho }^{*}=0.2$, $T^{*}=1.5$, $({\tau }_d=17)$]; (e)–(h) zoom along the diagonal for the solid state [${\rho }^{*}=1.2$, $T^{*}=1.5$ $({\tau }_d=6)$]. (Time is in units of simulation time steps, i.e., ${10}^{-14}\mathrm{s}$.)

Figure 5

(a) Mean square displacement at $T^{*}=1.5$ and various system densities. (b) Same as in (a) but zoomed at small time scale.

Figure 6

(Color) Zoom at representative recurrence plots. (a) $T^{*}=1.5$ and ${\rho }^{*}=0.2$, (b) $T^{*}=2.5$ and ${\rho }^{*}=0.2$, (c) $T^{*}=1.5$ and ${\rho }^{*}=0.8$, and (d) $T^{*}=2.5$ and ${\rho }^{*}=0.8$. (Time is in units of simulation time steps, i.e., ${10}^{-14}\mathrm{s}$.)

Figure 7

(Color online) ${\mathcal{R}}_{\mathrm{DET}}$ obtained from the temperature time series at various system densities and temperatures (lines are only a guide to the eye).

Figure 8

(Color online) Maxline obtained from the temperature time series at various system densities and temperatures (lines are only a guide to the eye).

Figure 9

(Color online) Trapping time obtained from the temperature time series at various system densities and temperatures (lines are only a guide to the eye).