Mayuko Iwamoto

The advantage of mucus for adhesive locomotion in gastropods.

For many gastropods, locomotion is driven by a succession of periodic muscular waves (contractions and relaxations) moving along the foot. The force generated by these waves is coupled to the substratum by a thin layer of pedal mucus. Gastropod pedal mucus has unusual physical properties: the mucus is a viscoelastic solid at small deformation and shows a sharp yield point; then, at greater strains, the mucus is a viscous liquid, although it will recover its solidity if allowed to heal for a certain period. In this paper, to clarify the role of the mucus and the flexible muscular waves in adhesive locomotion, we use a simple mathematical model to verify that directional migration can be realized through the interaction between the periodic muscular waves and the specific physical features of mucus. Our results indicate that the hysteresis property of mucus is essential in controlling kinetic friction for the realization of crawling locomotion. Furthermore, our numerical calculations show that both the hysteresis property of mucus and the contraction ratio of muscle give rise to two styles of locomotion, direct waves and retrograde waves, which until now have been explained by different mechanisms. The biomechanical effectiveness of mucus in adhesive locomotion is also discussed.

Effects of an Obstacle Position for Pedestrian Evacuation: SF Model Approach

In order to study pedestrian dynamics, mathematical models play an important role. It is well-known that a social force model exhibits clogging or what is called the “faster-is-slower effect” (Helbing et al., Nature 407:487–490, 2000). Also, the authors in Frank and Dorso (Phys A 390:2135–2145, 2011) and Kirchner et al. (Phys Rev E 67:056122, 2003) reported that an obstacle facilitates and obstructs evacuation of pedestrians trying to get out of a room with an exit, dependently on its position, size, and shape. In particular, as stated in Frank and Dorso (Phys A 390:2135–2145, 2011), an obstacle has a strong influence on pedestrians if it is put in a site shifted a little from the front of the exit. However, it has not been shown where and how it is the most efficiency to set up an obstacle. Thus we investigate the dynamics of pedestrians and clarify the effect of a disk-shaped obstacle with various sizes placed in several positions via numerical simulations for a social force model. Finally, we calculate a leaving time of pedestrians for each size and position of an obstacle, and determine an “optimal size” of an obstacle in the case that it is set up in a site shifted from the front of the exit.

Basis of self-organized proportion regulation resulting from local contacts

One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual is aware of the overall situation without a leader. In various species, a specific ratio exists at multiple levels, from the process of cell differentiation in multicellular organisms to the situation of social dilemma in a group of human beings. This study determines a common basis for regulating collective behavior that is realized by a series of local contacts between individuals. In this theory, the most essential behavior of individuals is to change their internal mode by sharing information when in contact with others. Our numerical simulations regulate the proportion of population in two kinds of modes. Furthermore, using theoretical analysis and numerical calculations, we show that asymmetric properties in local contacts are essential for adaptive regulation in response to global information such as group size and overall density. Particle systems are crucial in allowing flexible regulation in no-leader groups, and the critical condition that eliminates overlap with other individuals (the excluded volume effect) also affects the resulting proportion at high densities. The foremost advantage of this strategy is that no global information is required for each individual, and minimal mode switching can regulate the overall proportion. This simple mechanism indicates that proportion regulation in well-organized groups in nature can be realized through and limited to local contacts, and has the potential to explain various phenomena in which microscopic individual behavior results in orderly macroscopic behavior.

Dynamic Structure in Pedestrian Evacuation: Image Processing Approach

We show that there exists a typical dynamic arch-shape structure in pedestrian evacuation system governed by the social force model. It is well known that the simulation of pedestrian evacuation from a square room using the social force model shows arch-shape formation and clogging in front of the exit. It is also known experimentally and numerically that an obstacle near the exit could improve the flow rate, but detailed mechanism of this effect is not clear. In this paper, we show the existence of the “dynamic arch”, the typical structure in the long term, by using the social force model and the image processing. The time-averaged image of the system shows us the existence of the typical structure in the system and it can be interpreted as the probability distribution of the arch formation. With this method, we discuss the possible physical mechanism of the effect of an obstacle in the pedestrian system. From the observation of the morphological feature of the arch obtained by the simulation and image processing, we show that the obstacle affects the structure of the arch in three ways. These effects could lead the easy-to-break arch that enhances the flow rate of the system.

Arch-Shaped Equilibrium Solutions in Social Force Model

In the present paper, we investigate arch-shaped equilibrium solutions in the social force model proposed by Helbing and Molnar (Phys Rev E 51:4282, 1995) and Helbing et al. (Nature 407:487, 2000). The social force model is a system of ordinary differential equations, which describe the motion of the pedestrians under a panic situation. In the simulation of the social force model, we observe an intermittent appearance of arch-shaped structures (i.e. the “Blocking clusters” Parisi and Dorso, Physica A 354:606, 2005; Physica A 385:343, 2007; Frank and Dorso, Physica A 390:2135, 2011) around an exit which block up the flow of pedestrians. To understand such a dynamic behavior, we study arch-shaped equilibrium solutions around an exit under the simplest configuration.