Chaotic properties of isokinetic-isobaric atomic systems under planar shear and elongational flows

Estimating the largest Lyapunov exponent and noise level from chaotic time series

A novel method for estimating simultaneously the largest Lyapunov exponent (LLE) and noise level (NL) from a noisy chaotic time series is presented in this paper. We research the influence of noise on the average distance of different pairs of points in an embedding phase space and provide a rescaled formula for calculating the LLE when the time series is contaminated with noise. Our algorithm is proposed based on this formula and the invariant of the LLE in different dimensional embedding phase spaces. With numerical simulation, we find that the proposed method provides a reasonable estimate of the LLE and NL when the NL is less than 10% of the signal content. The comparison with Kantz algorithm shows that our method gives more accurate results of the LLE for the noisy time series. Furthermore, our method is not sensitive to the distribution of the noise.

Planar mixed flow and chaos: Lyapunov exponents and the conjugate-pairing rule

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.