Gaussian distributions of rotational velocities in a granular medium.

We investigate experimentally a homogeneously driven granular medium. It consists of spheres, each one containing a magnetic dipole, rolling on a horizontally placed dish and subject to a magnetic field which is sinusoidal in time and spatially homogeneous. A gaslike state is obtained. Except for extremely low amplitudes of the magnetic field, non-Gaussian distributions are found for the translatory velocities, as well as for the horizontal components of the rotational velocities. However, the vertical component of the rotational velocity obeys an almost invariant Gaussian distribution within a large range of parameters, namely frequencies and amplitudes of the magnetic field and friction coefficients on the dish's bottom. The results are close to predictions from simulations by Cafiero [Europhys. Lett. 60, 854 (2002)].

Fluctuation theorem for a single particle in a moving billiard: experiments and simulations.

A single particle within a periodically driven Sinai-billiard-like system is tracked experimentally and is simulated via hard-sphere molecular dynamics. Both experiments and simulations confirm the fluctuation theorem (FT); thus, in this setup, one driven particle is sufficient for the FT to hold. Furthermore, in the simulations the chaoticity of the system can be adjusted using the restitution coefficient of collisions. It is also shown that the FT breaks down when unstable periodic orbits appear for small restitution coefficients.

Velocity distributions of camphor particle ensembles.

The spatial distribution of ensembles of camphor particles on a water surface can be classified into four phases with the following properties, for increasing density: (I) no clustering of particles and a minimum distance distribution similar to that of a 2D ideal gas; (II) reminiscent of a gas with clustering of particles; (III) net-like structure with occasional rearrangements; and (IV) motionless. While single particles have varying velocity distributions, the overall velocity distribution is Laplacian (the width decreasing with increasing camphor density) for all phases.

Multipeaked probability distributions of recurrence times.

We determine probabilities of recurrence time into finite-sized, physically meaningful subsets of phase space. We consider three different autonomous chaotic systems: (i) scattering in a three-peaked potential, (ii) connected billiards, and (iii) Lorenz equations. We find multipeaked probability distributions, similar to the distributions found in (driven) stochastically resonant systems. In nondriven systems, such as ours, only monotonic decaying distributions (exponentials, stretched exponentials, power laws, and slight variations or combinations of these) have hitherto been reported. Discrete peaks in autonomous systems have as yet escaped attention in autonomous systems and correspond to specific trajectory subsets involving an integer number of loops.

Experimental observations of oscillations and segregation in a binary granular mixture.

We present experimental evidence for a "granular clock." We use a setup in which vertical vibrations (10-20 Hz) of a bidisperse granular medium cause horizontal oscillations (periods in the order of minutes) between two connected compartments. Moreover, we present the first experimental evidence for full segregation of smaller particles into one compartment, leaving the larger ones in the other compartment. Simulations, using a simple model, describe phenomenologically the observed oscillations.

Fluctuation theorem for a deterministic one-particle system.

A Duffing oscillator is driven by a sum of N chaotic time series. These time series are solutions of the undriven Duffing equation. It is shown that N=1 is sufficient to render the fluctuation theorem [Phys. Rev. Lett. 74, 2694 (1995)]; J. Math. Phys. 41, 4061 (2000)]; Adv. Phys. 51, 1529 (2002)]] for the power J(tau) averaged within intervals of length tau . In particular, the probabilities p( J(tau) ) follow a nearly Gaussian distribution. Also, ln[p( J(tau) )/p(- J(tau) )] versus J(tau) can be fitted by strikingly linear functions, the slopes being proportional to tau for large tau . These results indicate that validity of the fluctuation theorem requires neither a many-particle system nor a stochastic process, which are requirements used in previous works.

On-off intermittency and intermingledlike basins in a granular medium.

Molecular dynamic simulations of a medium consisting of disks in a periodically tilted box yield two dynamic modes differing considerably in the total potential and kinetic energies of the disks. Depending on parameters, these modes display the following features: (i) hysteresis (coexistence of the two modes in phase space); (ii) intermingledlike basins of attraction (uncertainty exponent indistinguishable from zero); (iii) two-state on-off intermittency; and (iv) bimodal velocity distributions. Bifurcations are defined by a cross-shaped phase diagram.