Driven tracers in narrow channels.

Steady-state properties of a driven tracer moving in a narrow two-dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one-dimensional (1D) SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean-field theory and exact solution in the limit where no exchange is allowed gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.

Hard disks in narrow channels.

The thermodynamic and dynamical behavior of a gas of hard disks in a narrow channel is studied theoretically and numerically. Using a virial expansion, we find that the pressure and collision frequency curves exhibit a singularity at a channel width corresponding to twice the disk diameter. As expected, the maximum Lyapunov exponent is also found to display a similar behavior. At high density, these curves are dominated by solidlike configurations which are different from the bulk ones, due to the channel boundary conditions.

Lyapunov instability of two-dimensional fluids: Hard dumbbells.

We generalize Benettin's classical algorithm for the computation of the full Lyapunov spectrum to the case of a two-dimensional fluid composed of linear molecules modeled as hard dumbbells. Each dumbbell, two hard disks of diameter sigma with centers separated by a fixed distance d, may translate and rotate in the plane. We study the mixing between these qualitatively different degrees of freedom and its influence on the full set of Lyapunov exponents. The phase flow consists of smooth streaming interrupted by hard elastic collisions. We apply the exact collision rules for the differential offset vectors in tangent space to the computation of the Lyapunov exponents, and of time-averaged offset-vector projections into various subspaces of the phase space. For the case of a homogeneous mass distribution within a dumbbell we find that for small enough d/sigma, depending on the density, the translational part of the Lyapunov spectrum is decoupled from the rotational part and converges to the spectrum of hard disks. (c) 1998 American Institute of Physics.

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.

Negative specific heat, the thermodynamic limit, and ergodicity.

Thermodynamic stability, in particular, the positivity of the specific heat in the microcanonical ensemble, is not an automatic consequence of the thermodynamic limit. But it holds under special circumstances such as for the most important case of quantum-mechanical Coulomb systems. Therefore, it is surprising that there are experimental indications to the contrary. In this Letter we study a simple model for which the microcanonical specific heat is positive, if the system is ergodic. However, if the system is not ergodic, the energy shell in phase space has some ergodic components with a negative specific heat. This provides another possible general pathway for a negative specific heat in addition to the commonly accepted, the small number of particles.