今村 卓史

The propagation speed of people's reaction in a relaxation process of a queue, so-called starting-wave, has an essential role for pedestrians and vehicles to achieve smooth movement. For example, a queue of vehicles with appropriate headway (density) alleviates the traffic jams, since the delay of reaction to start is minimized. In the previous study (Tomoeda et al., Fifth international conference on pedestrian and evacuation dynamics. Springer), it was found that the fundamental relation between the propagation speed of starting-wave and density is well approximated by the power law function. We have revealed the existence of optimal density, where the travel time of last pedestrian in a queue with the starting-wave to pass the head position of the initial queue is minimized. This optimal density inevitably plays a significant role to achieve smooth movement of crowds. © Springer-Verlag Berlin Heidelberg 2013.

The propagation speed of a starting wave, which is a wave of people's successive reactions in the relaxation process of a queue, has an essential role for pedestrians and vehicles to achieve smooth movement. For example, a queue of vehicles with appropriate headway (or density) alleviates traffic jams since the delay of reaction to start is minimized. In this paper, we have investigated the fundamental relation between the propagation speed of a starting wave and the initial density by both our mathematical model built on the stochastic cellular automata and experimental measurements. Analysis of our mathematical model implies that the relation is characterized by the power law alpha rho(-beta) (beta not equal 1), and the experimental results verify this feature. Moreover, when the starting wave is characterized by the power law (beta > 1), we have revealed the existence of optimal density, where the required time, i.e., the sum of the waiting time until the starting wave reaches the last pedestrian in a queue and his/her travel time to pass the head position of the initial queue, is minimized. This optimal density inevitably plays a significant role in achieving a smooth movement of crowds and vehicles in a queue.

For disordered quantum wires which belong to all ten universality classes, the universal quantities of transport properties are obtained through DMPK approach. Calculated are the universal parts of one- and two-point correlation functions for probability distribution functions of transmission eigenvalues. In this analysis, the asymptotic solution of DMPK equation is used. Transport properties for new universality classes (chiral and Bogoliubov–de Gennes classes) are discussed comparing with those for standard class.

For the quantum wires which belong to the Bogoliubov–de Gennes universality class, the averages and variances of the conductance and shot-noise power are calculated by the method of the moment expansion based on the DMPK equation. We discuss the universal behaviors of the transport properties.