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We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited mode has a novel horizontal drift in which one end of the dimer stays on the plate during most of the cycle, while the other end bounces in phase with the plate. The speed and direction of the drift depend on the aspect ratio of the dimer. We employ event-driven simulations based on a detailed treatment of frictional interactions between the dimer and the plate in order to elucidate the nature of the transport mechanism in the drift mode., Comment: 4 pages, 5 figures, Movies: http://physics.clarku.edu/~akudrolli/dimer

The dynamics of a set of rods bouncing on a vertically vibrated plate is investigated using experiments, simulations, and theoretical analysis. The experiments and simulations are performed within an annulus to impose periodic boundary conditions. Rods tilted with respect to the vertical are observed to spontaneously develop a horizontal velocity depending on the acceleration of the plate. For high plate acceleration, the rods are observed to always move in the direction of tilt. However, the rods are also observed to move opposite to direction of tilt for a small range of plate acceleration and rod tilt. A phase diagram of the observed motion is presented as a function of plate acceleration and the tilt of the rods which is varied by changing the number of rods inside the annulus. Next we introduce a novel molecular dynamics method to simulate the dynamics of the rods using the dimensions and dissipation parameters from the experiments. We reproduce the observed horizontal rod speeds as a function of rod tilt and plate acceleration in the simulations. By decreasing the friction between the rods and the base plate to zero in the simulation, we identify the friction during the collision as the crucial ingredient for occurrence of the horizontal motion. Guided by the data from the experiments and the simulations, we construct a mechanical model for the dynamics of the rods in the limit of thin rods. The starting point of the analysis is the collision of a single rod with an oscillating plate. Three friction regimes are identified: slide, slip-stick, and slip reversal. A formula is derived for the observed horizontal velocity as a function of tilt angle. Good agreement for the horizontal velocity as a function of rod tilt and plate acceleration is found between experiments, simulations and theory., Comment: 13 pages,13 figures, submitted to Phys. Rev. E

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates multi-stability. That is, for a strong enough positive feedback it exhibits a non-zero stationary mean field and a variety of stable oscillatory mean field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level, i.e., the system demonstrates coherence resonance. While away from the transition points the system dynamics is well described by a Gaussian approximation, near the bifurcation points a description in terms of a dichotomous theory is more adequate., Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. Lett

The continuum theory of partially fluidized shear granular flows is tested and calibrated using two dimensional soft particle molecular dynamics simulations. The theory is based on the relaxational dynamics of the order parameter that describes the transition between static and flowing regimes of granular material. We define the order parameter as a fraction of static contacts among all contacts between particles. We also propose and verify by direct simulations the constitutive relation based on the splitting of the shear stress tensor into a``fluid part'' proportional to the strain rate tensor, and a remaining ``solid part''. The ratio of these two parts is a function of the order parameter. The rheology of the fluid component agrees well with the kinetic theory of granular fluids even in the dense regime. Based on the hysteretic bifurcation diagram for a thin shear granular layer obtained in simulations, we construct the ``free energy'' for the order parameter. The theory calibrated using numerical experiments with the thin granular layer is applied to the surface-driven stationary two dimensional granular flows in a thick granular layer under gravity., Comment: 20 pages, 19 figures, submitted to Phys. Rev. E

The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization (DSS), displays analogies with neurodynamic events which occur in the build-up of long term memories., Comment: Submitted to Phys. Rev. Lett., 13 pages, 7 figures

Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. In this two-state approximation, we found analytical formulae for the autocorrelation function, the power spectrum, and the linear response to a periodic perturbation. They show very good agreement with direct numerical simulations of the original Langevin equation. The power spectrum has a pronounced peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics., Comment: 4 pages, 4 figures, submitted to Physical Review Letters

We develop the theory for stick-slip motion in ultra-thin liquid films confined between two moving atomically-flat surfaces. Our model is based on hydrodynamic equation for the flow coupled to the dynamic order parameter field describing the ``shear melting and freezing'' of the confined fluid. This model successfully accounts for observed phenomenology of friction in ultra-thin films, including periodic and chaotic sequences of slips, transitions from stick-slip motion to steady sliding., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

We report a novel morphological transition in a Bacillus subtilis colony initially growing under ambient conditions, after ultraviolet radiation exposure. The bacteria in the central regions of the colonies are observed to migrate towards the colony edge forming a ring during uniform spatial exposure. When the radiation is switched off, the colonies were observed to grow both inward into the evacuated regions as well as outward indicating that the pattern is not formed due to depletion of nutrients at the center of the colony. We also propose a reaction-diffusion model in which waste-limited chemotaxis initiated by the UV radiation leads to the observed phenomenology., Comment: 4 pages, 4 figures Reaction diffusion model has been added

We report an experimental study of the dynamics of an air-fluidized thin granular layer. Near-onset behavior of this shallow fluidized bed was described in the earlier paper (Tsimring et al, 1999). Above the threshold of fluidization the system exhibits a Hopf bifurcation as the layer starts to oscillate at a certain frequency due to a feedback between the layer dilation and the airflow drag force. After application of temporal band-pass filtering of this frequency we discovered the spatio-temporal dynamics in the form of defect turbulence. This type of dynamics is natural for spatio-temporal systems close to the threshold of a Hopf bifurcation. At high flow rates, low-frequency short-wavelength structures appear in addition to the long-wavelength excitations. A simple model describing the instability and occurrence of oscillations in a shallow fluidized bed, is proposed., Comment: 4 pages, 5 figures, submitted to PRL

Theoretical and experimental study of high-acceleration patterns in vibrated granular layers is presented. The order parameter model based on parametric Ginzburg-Landau equation is used to describe strongly nonlinear excitations including hexagons, interface between flat anti-phase domains and new localized objects, super-oscillons. The experiments confirmed the existence of super-oscillons and bound states of super-oscillons and interfaces. On the basis of order parameter model we predict analytically and confirm experimentally that the additional subharmonic driving results in controlled motion of the interfaces., Comment: 18 pages, 16 figures, submitted to Phys. Rev. E

Utilization of chaotic signals for covert communications remains a very promising practical application. Multiple studies indicated that the major shortcoming of recently proposed chaos-based communication schemes is their susceptibility to noise and distortions in communication channels. In this talk we discuss a new approach to communication with chaotic signals, which demonstrates good performance in the presence of channel distortions. This communication scheme is based upon chaotic signals in the form of pulse trains where intervals between the pulses are determined by chaotic dynamics of a pulse generator. The pulse train with chaotic interpulse intervals is used as a carrier. Binary information is modulated onto this carrier by the pulse position modulation method, such that each pulse is either left unchanged or delayed by a certain time, depending on whether ``0'' or ``1'' is transmitted. By synchronizing the receiver to the chaotic pulse train we can anticipate the timing of pulses corresponding to ``0'' and ``1'' and thus can decode the transmitted information. Based on the results of theoretical and experimental studies we shall discuss the basic design principles for the chaotic pulse generator, its synchronization, and the performance of the chaotic pulse communication scheme in the presence of channel noise and filtering., Comment: Presented at 7th International Conference on Advances in Communications and Control, Telecommunications/Signal Processing, Athens, Greece, 28 June - 2 July 1999

We present experimental study of a topological excitation, {\it interface}, in a vertically vibrated layer of granular material. We show that these interfaces, separating regions of granular material oscillation with opposite phases, can be shifted and controlled by a very small amount of an additional subharmonic signal, mixed with the harmonic driving signal. The speed and the direction of interface motion depends sensitively on the phase and the amplitude of the subharmonic driving., Comment: 4 pages, 6 figures, RevTex

The order parameter model based on parametric Ginzburg-Landau equation is used to describe high acceleration patterns in vibrated layer of granular material. At large amplitude of driving both hexagons and interfaces emerge. Transverse instability leading to formation of ``decorated'' interfaces and labyrinthine patterns, is found. Additional sub-harmonic forcing leads to controlled interface motion., Comment: 4 pages, 3 figures, submitted to Phys. Rev. Lett