Harald A. Posch

Collision induced light scattering from fluids composed of tetrahedral molecules: II. Intensities

The collision induced isotropic and anisotropic spectra of light scattered from fluids of tetrahedral molecules are examined. The interaction function used includes the dipole-induced dipole effect (DID) and the collision induced rotational Raman effect (CIRR) to lowest order. The spectra are expressed as the Fourier transforms of four point correlation functions which contain the number density and the orientational density of the particles. The polarization ratio I VV CIRR(ω)/I VH CIRR(ω) for the CIRR contributions considered is shown to be 37/9 for all densities. The various terms contributing to the integrated intensity for the pair and triplet collisions are expressed in terms of the irreducible expansion coefficients of the orientation dependent pair distribution function. As an example, these terms are evaluated numerically for carbon tetrachloride for two different densities corresponding to a liquid and a vapour state.

Direct measurement of Lyapunov exponents

Abstract Benettin, Calgani and Strelcyn studied the dynamical separation of neighboring phase-space trajectories, determining the corresponding Lyapunov exponents by discrete rescaling of the intertrajectory separation. We incorporate rescaling directly into the equations of motion, preventing Lyapunov instability by using an effective constraint force.

Dissipative Irreversibility from Nosé's Reversible Mechanics

Abstract Noses Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nose-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox ...

Depolarized light-scattering in liquid SF6

The spectra of depolarized light scattered by liquid SF6 have been obtained for states along the co-existence curve. They can be decomposed into a broad background and a narrow component. The intensity of the latter amounts to about 80 per cent and 65 per cent of the total depolarized intensity near the critical point and the triple point, respectively, and decreases with increasing density. In a restricted frequency range ⩽-20 cm-1 its line-shape is roughly a lorentzian with a half width of around 6 cm-1. This component is explained by the so-called ‘dipole-induced dipole’ effect (DID) and is assumed to reflect the collective motion of a molecule and its neighbours. The background is of rather exponential shape and its intensity is almost constant within experimental uncertainty in the density range studied. It is assumed that this behaviour reflects the increased importance of short-range contributions to the polarizability anisotropy at high densities in addition to the classical DID term.

Kolmogorov-Sinai entropy and Lyapunov spectra of a hard-sphere gas

The mixing behavior of a hard-sphere gas has its origin in the exponential growth of small perturbations in phase space. This instability is characterized by the so-called Lyapunov exponents. In this work, we compute full spectra of Lyapunov exponents for the hard-sphere gas for a wide range of densities ϱ and particle numbers by using a recently developed algorithm. In the dilute-gas regime, the maximum Lyapunov exponent is found to obey the Krylov relation λ ∝ ϱ ln ϱ, a formula exactly derived for the low-density Lorentz gas by Dorfman and van Beijeren. We study the system-size dependence and the effect of the fluid-solid-phase transition on the spectra. In the second part of this work we describe and test a direct simulation Monte Carlo method (DSMC) for the computation of Lyapunov spectra and present results for dilute hard-sphere gases. Excellent agreement is obtained with the results of the deterministic simulations. This suggests that the Lyapunov instability of a hard sphere gas may be analyzed within the framework of kinetic theory.

Direct measurement of equilibrium and nonequilibrium Lyapunov spectra

Abstract Lyapunov spectra are measured for a three-dimensional many-body dense fluid, not only at equilibrium, but also in the presence of an isoenergetic nonequilibrium field generating a pair of equal and opposite currents. The Lyapunov spectra bear a strong resemblance to the Debye spectrum of solid-state physics.

Atomic pair dynamics in a Lennard-Jones fluid: Comparison of theory with computer simulation

The dynamics of pairs of atoms in a dense Lennard-Jones fluid is studied by evaluating mean square displacements and related properties by computer simulation. These results are compared with theory for an anharmonic brownian oscillator and with solutions of the stochastic Langevin equation obtained using three different approximations for the pair friction coefficient tensor. It is concluded that the anharmonic oscillator model works well for short times when the initial separations are those for the first coordination shell. The stochastic Langevin equation, which involves the use of the exact average force, best reproduces the simulations when one uses a distance dependent friction tensor that contains the Oseen correction for hydrodynamic effects but also approaches zero at distances of the order of the Lennard Jones σ.

Depolarized light scattering from dense noble gases

Depolarized Rayleigh spectra for four different thermodynamic states of krypton are reported. At large liquidlike densities and for low frequency shifts (<20 cm−1) the existence of a Lorentzian component previously discovered in liquid argon is confirmed. For large ν the line shapes are mainly exponential with the exception of a weak shoulder located at around 50 cm−1. These spectral features are interpreted in the light of a recent theory by Madden. In comparing the results for krypton and argon the law of corresponding states is found to hold. The dependence of the Lorentzian half‐width on the diffusion coefficient is not the same as inferred from the Madden theory.

Lyapunov instability, local curvature, and the fluid-solid phase transition in two-dimensional particle systems

We study the relation between the Lyapunov spectrum and the multidimensional geometry of the potential energy surface in terms of the distribution of stable and unstable modes for different models. For this purpose we determined Lyapunov exponents for the so-called correlated cell model and its smooth generalization as a function of the density for various energies. In the smooth case averaged structural quantities, such as the fraction of unstable modes, the Gaussian curvature, and the Riemannian curvature were computed and compared to the mechanical instability of the system in the sense of Lyapunov. A similar analysis was also carried out for 36-disk systems representing various fluid and solid states. In all studied cases the most-positive Lyapunov exponent exhibits a maximum at the phase transition in agreement with results for the fluid-solid transition in many-particle systems.

Statistical measures derived from the correlation integrals of physiological time series

In this work correlation integrals are used for the analysis of various EEG signals from rabbits in resting states and under the influence of an anesthetic. The comparison with surrogate data reveals nonlinear dynamics in all of the time series. Our attempt to determine the correlation dimension D(2) by the modified algorithm of Theiler [Phys. Rev. A 34, 2427 (1986)] failed since no saturation is reached with increasing embedding dimension. The hypothesis of low-dimensional chaos turns out to be inconsistent with our results, but we can still distinguish, at least qualitatively, between different states of brain dynamics. A quantitative characterization of the time series is possible by defining correlation parameters P(a) derived from correlation integrals reflecting also autocorrelation of the signal. (c) 1996 American Institute of Physics.