Intruders in the Dust: Air-Driven Granular Size Separation

Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, non-monotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and show how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.Comment: 5 pages, 4 figure

Discrete stochastic models for traffic flow

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.Comment: Revtex, 30 pages, full postscript version (including figures) available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory "pub/incoming/" paper accepted for publication in Phys.Rev.

Stochastic Description of a Bistable Frustrated Unit

Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing oscillatory behaviour. Our model consists of two interacting species A and B, where A activates not only its own production, but also that of its repressor B. While the self-activation of A leads already to a bistable unit, the coupling with a negative feedback loop via B makes the unit frustrated. In the deterministic limit of infinitely many molecules, such a bistable frustrated unit is known to show excitable and oscillatory dynamics, depending on the maximum production rate of A which acts as a control parameter. We study this model in its fully stochastic version and we find oscillations even for parameters which in the deterministic limit are deeply in the fixed-point regime. The deeper we go into this regime, the more irregular these oscillations are, becoming finally random excitations whenever fluctuations allow the system to overcome the barrier for a large excursion in phase space. The fluctuations can no longer be fully treated as a perturbation. The smaller the system size (the number of molecules), the more frequent are these excitations. Therefore, stochasticity caused by demographic noise makes this unit even more flexible with respect to its oscillatory behaviour.Comment: 28 pages, 17 figure

Subdiffusion and cage effect in a sheared granular material

We investigate experimentally the diffusion properties of a bidimensional bidisperse dry granular material under quasistatic cyclic shear.The comparison of these properties with results obtained both in computer simulations of hard spheres systems and Lenard-Jones liquids and experiments on colloidal systems near the glass transition demonstrates a strong analogy between the behaviour of granular matter and these systems. More specifically, we study in detail the cage dynamics responsible for the subdiffusion in the slow relaxation regime, and obtain the values of relevant time and length scales.Comment: 4 pages, 6 figures, submitted to PR

The Effect of absorbing sites on the one-dimensional cellular automaton traffic flow with open boundaries

The effect of the absorbing sites with an absorbing rate $\beta_{0}$, in both one absorbing site (one way out) and two absorbing sites (two ways out) in a road, on the traffic flow phase transition is investigated using numerical simulations in the one-dimensional cellular automaton traffic flow model with open boundaries using parallel dynamics.In the case of one way out, there exist a critical position of the way out $i_{c1}$ below which the current is constant for $\beta_{0}$$<$$\beta_{0c2}$ and decreases when increasing $\beta_{0}$ for $\beta_{0}$$>$$\beta_{0c2}$. When the way out is located at a position greater than $i_{c2}$, the current increases with $\beta_{0}$ for $\beta_{0}$$<$$\beta_{0c1}$ and becomes constant for any value of $\beta_{0}$ greater than $\beta_{0c1}$. While, when the way out is located at any position between $i_{c1}$ and $i_{c2}$ ($i_{c1}$$<$$i_{c2}$), the current increases, for $\beta_{0}$$<$$\beta_{0c1}$, with $\beta_{0}$ and becomes constant for $\beta_{0c1}$$<$$\beta_{0}$$<$$\beta_{0c2}$ and decreases with $\beta_{0}$ for $\beta_{0}$$>$$\beta_{0c2}$. In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at $\beta_{0}$$=$$\beta_{0c1}$ and from intermediate density to the low one at $\beta_{0}$$=$$\beta_{0c2}$. In the case of two ways out located respectively at the positions $i_{1}$ and $i_{2}$, the two successive transitions occur only when the distance $i_{2}$-$i_{1}$ separating the two ways is smaller than a critical distance $d_{c}$. Phase diagrams in the ($\alpha,\beta_{0}$), ($\beta,\beta_{0}$) and ($i_{1},\beta_{0}$) planes are established. It is found that the transitions between Free traffic, Congested traffic and maximal current phase are first order

Presence of Many Stable Nonhomogeneous States in an Inertial Car-Following Model

A new single lane car following model of traffic flow is presented. The model is inertial and free of collisions. It demonstrates experimentally observed features of traffic flow such as the existence of three regimes: free, fluctuative (synchronized) and congested (jammed) flow; bistability of free and fluctuative states in a certain range of densities, which causes the hysteresis in transitions between these states; jumps in the density-flux plane in the fluctuative regime and gradual spatial transition from synchronized to free flow. Our model suggests that in the fluctuative regime there exist many stable states with different wavelengths, and that the velocity fluctuations in the congested flow regime decay approximately according to a power law in time.Comment: 4 pages, 4 figure