Externally perturbed unstable systems

We discuss computer solutions of Newton's equations of motion for unstable systems in a container with time-dependent walls. An expansion leads to the formation of a cluster and a significant increase of the temperature. The question of entropy increase for expansion and compression of the system and the related problem of the feasibility of a perpetum mobile of the second kind are investigated.     

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.     

Ultraschalluntersuchungen über die Dimerisation von Essigsäure in Mischungen mit Tetrachlorkohlenstoff

Zusammenfassung In einer früheren Arbeit wurde das volumetrische und dielektrische Verhalten von Essigsäure in Mischungen mit unpolaren Lösungsmitteln auf Grund von zwei Voraussetzungen diskutiert: 1. Die Interpretation vonFreedman, welcher das Dimerisationsgleichgewicht von Essigsäure als die Ursache der Ultraschallrelaxation bei niederen Frequenzen ansah und danach Dimerisationskonstanten in reiner Essigsäure berechnete, wird als korrekt angesehen. 2. Für die Konzentrationsabhängigkeit der DimerisationskonstantenK in Mischungen wird näherungsweise angenommen, daß InK linear mit der Konzentration der Essigsäure geht. In dieser Arbeit werden Ultraschallgeschwindigkeiten für das binäre System Essigsäure—CCl₄ bei 2 und 6 MHz und bei 20, 30 und 40°C mitgeteilt. Weiters wurde die Schallabsorption bei 20°C und beiden Frequenzen gemessen. Auf Grund der experimentellen Resultate kann die Konzentrationsabhängigkeit der Relaxationsfrequenz und des Relaxationsbetrages abgeschätzt werden. Sie ist konsistent mit den beiden oben angegebenen Voraussetzungen. Eine Kritik derFreedmanschen Interpretation auf Grund von Messungen an sehr verdünnten Essigsäuremischungen scheint daher nicht berechtigt zu sein. Die außerordentlich starke Konzentrationsabhängigkeit der Dimerisationskonstanten in Essigsäure—CCl₄- Mischungen zeigt deutlich, wie empfindlich Assoziationsgleichgewichte gegenüber Änderungen in der molekularen Umgebung bzw. Änderungen in der Dielektrizitätskonstanten sind.

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In a previous paper, the volumetric and dielectric behaviour of acetic acid and its mixtures with nonpolar solvents has been discussed on the basis of two assumptions: (1) The interpretation ofFreedman, explaining the low frequency ultrasonic relaxation of pure acetic acid on the basis of a monomer-dimer equilibrium and resulting in values of the dimerisation constant, is correct; (2) The variation of the dimerisation constantK with concentration of the mixture may be approximated by a linear behaviour of InK. In this paper, ultrasonic sound velocities are presented at 2 and 6 Mc per sec for the binary system acetic acid—CCl₄ at 20, 30, and 40°C, resp. Also absorption values are given for 20°C at both frequencies. From these data, the concentration dependence of the relaxation frequency and the relaxation amount can be estimated. It is consistent with the two assumptions cited above. Therefore, criticism onFreedman's interpretation, made on the basis of measurements in very dilute acetic acid mixtures, seem to be invalid. The rapid variation of the dimerisation constant in the mixture of acetic acid with carbon tetrachloride demonstrates very clearly, how sensitive association equilibria are to changes in the molecular surrounding, or to changes in the dielectric constant, resp.

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Mit 3 Abbildungen

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Herrn Prof.Wessely zum 70. Geburtstag gewidmet.

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Auszugsweise vorgetragen auf der Tagung der American Chemical Society in Miami Beach, Florida, am 14. April 1967.     

Stellar stability by thermodynamic instability

For gravity-dominated systems the three features shrinking <=> energy decrease <=> temperature increase are dynamically linked together. So are their inverses: expansion <=> energy increase <=> temperature decrease. We exhibit these features by one classical particle in a suitable environment, and by many particles with purely attractive interactions. We then show how the ensuing negative heat capacity tames an explosive energy input.     

Solution of the one-dimensional linear Boltzmann equation for charged Maxwellian particles in an external field

The one-dimensional linear homogeneous Boltzmann equation is solved for a binary mixture of quasi-Maxwellian particles in the presence of a time-dependent external field. It is assumed that the charged particles move in a bath of neutral scatterers. The neutral scatterers are in thermal equilibrium and the concentration of the charged particles is low enough to neglect collisions between them. Two cases are considered in detail, the constant and the periodic external field. The quantities calculated are the equilibrium and the stationary distribution function, respectively, from which any desired property can be derived. The solution of the Boltzmann equation for Maxwellian particles can be reduced to the solution of the so-called cold gas equation by employing the one-dimensional variant of a convolution theorem due to Wannier. The two limiting cases, the Lorentz gas (m _A0) and the Rayleigh gas (m _A) are treated explicitly. Furthermore, by computing the central moments, the deviations from the Gaussian approximation are discussed, and in particular the large-velocity tails are evaluated.     

Chaos and irreversibility in simple model systems

The multifractal link between chaotic time-reversible mechanics and thermodynamic irreversibility is illustrated for three simple chaotic model systems: the Baker Map, the Galton Board, and many-body color conductivity. By scaling time, or the momenta, or the driving forces, it can be shown that the dissipative nature of the three thermostated model systems has analogs in conservative Hamiltonian and Lagrangian mechanics. Links between the microscopic nonequilibrium Lyapunov spectra and macroscopic thermodynamic dissipation are also pointed out. (c) 1998 American Institute of Physics.     

What Does Dynamical Systems Theory Teach Us about Fluids?

We use molecular dynamics simulations to compute the Lyapunov spectra of many-particle systems resembling simple fluids in thermal equilibrium and in non-equilibrium stationary states. Here we review some of the most interesting results and point to open questions.     

Covariant Lyapunov vectors for rigid disk systems

We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.