Argonne National Laboratory, Argonne, IL60439, US
Continuum models of large-scale coherence in dense assemblies of self-propelled particles: from shaken granular rods to molecular motors and swimming bacteria

Dense assemblies of active self-propelled particles, such as vigorously shaken anisotropic grains, microtubules interacting with molecular motor, and hydrodynamically entrained swimming bacteria, often exhibit large-scale spatio-temporal patterns of collective motion whose correlation length greatly exceeds the size of individual particle. Despite a vast difference in the physical mechanisms controlling onset of large-scale coherence, continuum description of such systems can be derived from an analogy with a gas of inelastically colliding granular rods. Thus, starting from a generic stochastic microscopic model of inelastic polar rod-like particles with an anisotropic interaction kernel, we derive set of equations for the local rods concentration and orientation. Above certain critical density of the rods, the model exhibits spontaneous orientational instability and the onset of large-scale coherence. For the system of microtubules interacting with molecular motors we demonstrate that the orientational instability leads to the formation of vortices and asters seen in recent experiments. Similar approach is applied to colonies of swimming bacteria Bacillus subtilis confined in a thin fluid film. The model is formulated in term of two-dimensional equations for local density and orientation of bacteria coupled to the low Reynolds number Navier-Stokes equation for the fluid flow velocity. The collective swimming of bacteria is represented by additional source term in the Navier-Stokes equation. We demonstrate that this system exhibits formation of dynamic large-scale patterns with the typical scale determined by the density of bacteria.

Indian Institute of Technology, Kanpur, India
Models of Vehicular Traffic: An Engineering Perspective

The aim of the talk is to present an engineers viewpoint of vehicular traffic streams and their models both at the macroscopic and microscopic levels. The talk concentrates on two classes of macroscopic models; namely, stream description models and travel time estimation models. At the microscopic level, longitudinal vehicle control models, and recent developments in longitudinal and lateral vehicle control models are discussed. The talk highlights the importance of microscopic traffic flow models and presents some properties which all microscopic models of traffic flow should possess. The talk also mentions how certain paradigms like long-run behaviour, behaviour at equilibrium, etc. are becoming less attractive and how the need has shifted to evolving theories which can explain transient system behaviour and make reliable predictions in the short term. The talk also identifies areas where research will bring about a qualitative jump in the understanding of how traffic flows and how they are impacted by a variety of static and dynamic features of the road.

Alexander DUNN
Stanford University, USA.
Regulation of the cell's dynamic city plan and the myosin family of molecular motors
in collaboration with Jim Spudich
Every cell has a dynamic city plan, organized by the cytoskeleton. Molecular motors carry cargo to specific locations with all the same regulatory elements found in traffic flow in major cities in the world. Tension sensing is one fundamental regulatory element, but it is poorly studied due to the lack of tools. The molecular basis of how myosin motors work has been significantly advanced by studies of myosins V and VI. Myosin V moves processively by stepping arm-over-arm, walking along the 36-nm pseudo-repeat of an actin filament by swinging its long lever arms through an angle of ~70 deg, and hydrolyzing one ATP per step. Intramolecular tension sensing establishes a bias in the behavior of the two heads with regard to nucleotide kinetics that allows the rear head to most often release from the actin by binding ATP. Recently, we have improved time resolution to submilliseconds by tracking single gold nanoparticle-myosin V conjugates using darkfield imaging, and have directly observed the behavior of the unbound head as the motor translocates. We have also developed a technique called single-molecule high resolution co-localization (SHREC), which allows simultaneous co-localization of two chromatically differing fluorophores only 10 nm apart. We used SHREC to directly observe myosin V molecules walking hand-over-hand. We are now adapting SHREC to observe myosin V's nucleotide dynamics using dye-labeled ATP molecules. Myosin VI has a very short lever arm that is only two light chains long. Nevertheless, the molecule surprisingly steps processively 36 nm along an actin filament. Furthermore, myosin VI moves in the opposite direction to that of myosin II and myosin V. Our most recent work shows how this unusual motor achieves these feats. Myosin VI is now a paradigm of how intermolecular tension sensing is translated into biologically important trafficking regulation.

Departamento de Física y Matemática Aplicada, Universidad de Navarra, Spain
Flow and jamming of granular matter through an orifice

When a dense assembly of particles is forced to pass through an orifice, jamming can occur. Many different systems can get jammed: traffic, glasses, colloidal gels, people in panic, foams, ... The question is whether all these arrangements share some basic features, enabling us to think of jammed structure as a new state of matter. Furthermore, a deeper understanding of jamming can inspire new methods for restoring the flow.
A particular experiment aimed at understanding these phenomenon is presented here. It consists of a silo filled with grains, with an orifice at the base. Grains begin to pour freely, and then - if the orifice is not much larger than several grain diameters - the flow stops because an arch is formed and the energy is dissipated. By measuring the number of grains between successive jamming events (an avalanche), the jamming probability is obtained. The probability density function for the avalanche size has been obtained, and from this statistics some interesting characteristic of the process can be described. Notably, it is shown that above a certain orifice size no jamming can occur. For spherical beads, a power law divergence is found for the jamming probability when that value is approached, and in this sense it can be stated that there is a critical orifice diameter for jamming.
The measurement of the flow rate of grains can also shed light on the issue. When the orifice is large, a simple dimensional calculation gives the Beverloo law, which states that the flow driven by gravity depends on the diameter of the orifice to the 5/2 power. But this relation breaks down for small orifices, when intermittent flow and jamming can occur. A new functional dependence is proposed, which reproduces the experimental results and the numerical simulations. Furthermore, the statistical analysis of the fluctuations for small orifices shows anomalous behaviour. This issue is being actively studied.

Institut fur Computerphysik, Univ. Stuttgart, Germany
Pneumatic Conveying of Granular Materials
Sean McNamara (with M. Strauss, F. Zeller, H.J. Herrmann, I. Lecreps, G. Niederreiter, and K. Sommer)
Granular material is often blown through pipes. This method of transport is called pneumatic conveying. It is most efficient when the material forms dense clusters called "plugs" or "slugs" that move along the pipe. It is difficult to predict the behavior of these clusters from simple models, so we have studied them numerically. Our model calculates the trajectory of each grain, but resolves the fluid flow on a scale of several grain diameters. The grains are interact with the fluid as a moving porous medium. The model shows that clusters form spontaneously, and it is possible to obtain realistic results once the model is callibrated. The model also predicts that the pressure drop across a cluster is proportional to its length, thus facilitating the analysis of conveying systems.

SAAD Farida
The drivers behaviour from the psychologists point of view

The aim of the presentation is to discuss the various models referred to by traffic psychologists, especially when assessing the impact of new driver support systems on drivers activity in real driving situations. Comparisons will be made between the variables used in these psychological models and the variables and parameters manipulated in microscopic traffic models.
Previous research works dealing with new systems designed for supporting speed and safety margins control will be presented and discussed (Adaptive Cruise Control, collision avoidance system and speed limiter). The introduction of new support systems into driving, the use that is made of them, their consequences on the performance of the task are indicative of the mechanisms that govern drivers activity and their interactions with other road users. They also reveal the discrepancies existing between the prescribed task (what the driver should do) and the effective task (what the driver really does) and raise the question of the reference models to be used to account for driver behaviour.

Univ. Koln, Germany
Cellular automaton approach to highway traffic: What do we know ?

Cellular automata (CA) models for the simulation of highway traffic have become increasingly more popular in recent years. But how realistic are these models? empirical results.
In the talk we will try to review the current state of this approach and contrast it with other model classes. The focus will be the ability to reproduce the single-vehicle data obtained empirically. These data (fundamental diagrams, headway distributions etc.) provide a kind of benchmark test for the realism of the model. This comparison requires calibration and we will discuss how the model parameters can be determined from the empirical results.

Models of different sophistication will be studied:
1) the Nagel-Schreckenberg model, which is a kind of minimal CA model for highway traffic,
2) extensions with slow-to-start rules that yield a more realistic jam dynamics,
3) models related to 3-phase traffic theory that try to capture more complicated spatio-temporal structures like synchronized flow.

We will discuss the achievements and failures of these models. The latter might happen at various levels, e.g. quantitatively or even qualitatively.
Finally we discuss the application of CA model to traffic networks, planing and forecasting.

Saarland University, Germany
Stochastic Modelling of Intracellular Transport

The function of eukaryotic cells depends largely on the efficiency of the intracellular transport system. The transport in cells is powered by specialised proteins known as molecular motors. These motors transport a large variety of cargo and are responsible for vital functions of the cell, e.g. cell division and locomotion. Next to their importance for the biological function of cells the cellular transport also provides a challenging task for theoretical modelling. Transport by molecular motors is a generic non-equilibrium process, which is strongly related to other transport phenomena like vehicular traffic. This talk tries to give an overview about different modelling approaches to intracellular transport. The focus will be on cooperative phenomena, which arise e.g. when a number of motor proteins are attached to one cargo or if motor proteins interact on the track.