Lyapunov modes in three-dimensional Lennard-Jones fluids

Abstract

Recent studies on the phase-space dynamics of a one-dimensional Lennard-Jones fluid reveal the existence of regular collective perturbations associated with the smallest positive Lyapunov exponents of the system, called hydrodynamic Lyapunov modes, which previously could only be identified in hard-core fluids. In this work we present a systematic study of the Lyapunov exponents and Lyapunov vectors, i.e. perturbations along each direction of phase space, of a three-dimensional Lennard-Jones fluid. By performing the Fourier transform of the spatial density of the coordinate part of the Lyapunov vector components and then time-averaging this result we find convincing signatures of longitudinal modes, with inconclusive evidence of transverse modes for all studied densities. Furthermore, the longitudinal modes can be more clearly identified for the higher density values. Thus, according to our results, the mixing of modes induced both by the dynamics and the dimensionality induce a hitherto unknown type of order in the tangent space of the model herein studied at high density values.

Characterizing the dynamics of higher dimensional nonintegrable conservative systems

“…Close-to-zero FTLEs play also an important role in other higher-dimensional system, for example in connection to hydrodynamic modes [35,36] (among others) and the analysis of hyperbolicity [6,37]. Results of the present work contribute to categorize the rich and complicated quasiregular dynamics of higher-dimensional conservative systems and also to understand how nonlinearity is distributed along different unstable directions [19,38].…”

A review of the hydrodynamic Lyapunov modes of hard disk systems

“…The first computationally feasible method of applying the Lyapunov analysis to chaotic dynamical systems was presented by Benettin et al over 30 years ago [1][2][3]. Since then, the most prevalent systems analysed were coupled map lattices [4][5][6][7][8][9][10][11], simplified two or three dimensional fluid and gas models [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], chains of harmonic oscillators [27][28][29][30][31][32][33] and chaotic differential equations [34][35][36][37][38]. Despite the variation in the configuration and evolution of each model, comparisons between each analysis show an underlying structure independent of system.…”

Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices

“…These vectors convey important dynamical information. For example, LVs have been useful to discover and quantify the so-called hydrodynamic modes [4][5][6], to study extensivity properties [7,8] and to address predictability questions in weather forecasting [9,10], among other applications.…”