Kinematics of Persistent Random Walkers with Distinct Modes of Motion

We study the stochastic motion of active particles that undergo spontaneous transitions between distinct modes of motion. Each mode is characterized by a speed distribution and an arbitrary (anti-)persistence. We develop an analytical framework to provide a quantitative link between the particle dynamics properties and macroscopically observable transport quantities of interest. For exponentially distributed residence times in each state, we derive analytical expressions for the initial anomalous exponent, the characteristic crossover time to the asymptotic diffusive dynamics, and the long-term diffusion constant. We also obtain exact expressions for the time evolution of the arbitrary moments of displacement -- particularly the mean square displacement -- over all time scales. Our approach enables us to disentangle the combined effects of speed, directional persistence, and switching probabilities between the states on the kinematics of particles in a wide range of multistate stochastic active/passive processes and to optimize the transport quantities of interest with respect to any of the particle dynamics properties.Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:1909.0503

Characteristics of Vehicular Traffic Flow at a Roundabout

We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated within the framework of the probabilistic cellular automata and the delay experienced by the traffic at each individual street is evaluated for specified time intervals. We discuss the impact of the geometrical properties of the roundabout on the total delay. We compare our results with traffic-light signalisation schemes, and obtain the critical traffic volume over which the intersection is optimally controlled through traffic light signalisation schemes.Comment: 10 pages, 17 eps figures. arXiv admin note: text overlap with arXiv:cond-mat/040107

Amoeboid Cell Migration through Regular Arrays of Micropillars under Confinement

Migrating cells often encounter a wide variety of topographic features—including the presence of obstacles—when navigating through crowded biological environments. Unravelling the impact of topography and crowding on the dynamics of cells is key to better understand many essential physiological processes such as the immune response. We study how migration and search efficiency of HL-60 cells differentiated into neutrophils in quasi two-dimensional environments are influenced by the lateral and vertical confinement and spatial arrangement of obstacles. A microfluidic device is designed to track the cells in confining geometries between two parallel plates with distance h, in which identical micropillars are arranged in regular pillar forests. We find that at each cell-pillar contact event, the cell spends a finite time near the pillar surface, which is independent of the height h and the interpillar spacing e. At low pillar density regime, the directional persistence of cells reduces with decreasing h or e, influencing their diffusivity and first-passage properties. The dynamics is strikingly different at high pillar density regime, where the cells are in simultaneous contact with more than one pillar; the cell velocity and persistence are distinctly higher compared to dilute pillar configurations with the same h. Our simulations reveal that the interplay between cell persistence and cell-pillar interactions can dramatically affect cell diffusivity and, thus, its first-passage properties

Diffusive transport of light in three-dimensional disordered Voronoi structures

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: a constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for transport-mean-free path fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in {dry} foams.Comment: 8 pages, 8 figure

Diffusive transport of light in two-dimensional granular materials

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.Comment: 9 pages, 3 figure