上山 大信

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. (C) 2017 Elsevier Ltd. All rights reserved.

This study demonstrates that the Marangoni flow in a channel network can solve maze problems such as exploring and visualizing the shortest path and finding all possible solutions in a parallel fashion. The Marangoni flow is generated by the pH gradient in a maze filled with an alkaline solution of a fatty acid by introducing a hydrogel block soaked with an acid at the exit. The pH gradient changes the protonation rate of fatty acid molecules, which translates into the surface tension gradient at the liquid-air interface through the maze. Fluid flow maintained by the surface tension gradient (Marangoni flow) can drag water-soluble dye particles toward low pH (exit) at the liquid-air interface. Dye particles placed at the entrance of the maze dissolve during this motion, thus exhibiting and finding the shortest path and all possible paths in a maze.

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.

We investigate the mechanism of the phenomenon called the "faster-is-slower" effect in pedestrian flow studies analytically with a simplified phenomenological model. It is well known that the flow rate is maximized at a certain strength of the driving force in simulations using the social force model when we consider the discharge of self-driven particles through a bottleneck. In this study, we propose a phenomenological and analytical model based on a mechanics-based modeling to reveal the mechanism of the phenomenon. We show that our reduced system, with only a few degrees of freedom, still has similar properties to the original many-particle system and that the effect comes from the competition between the driving force and the nonlinear friction from the model. Moreover, we predict the parameter dependences on the effect from our model qualitatively, and they are confirmed numerically by using the social force model.

We consider the problem where W in vades the (U, V) system in the three species Lotka-Volterra competition-diffusion model. Numerical simulation indicates that the presence of W can dramatically change the competitive interaction between U and V in some parameter range if the invading W is not too small. We also construct exact travelling wave solutions with non-trivial three components and track the bifurcation branches of these solutions by AUTO.

The pattern transition between periodic precipitation pattern formation ( Liesegang phenomenon) and pure crystal growth regimes is investigated in silver nitrate and potassium dichromate system in mixed agarose-gelatin gel. Morphologically different patterns were found depending on the quality of the gel, and transition between these typical patterns can be controlled by the concentration of gelatin in mixed gel. Effect of temperature and hydrodynamic force on precipitation pattern structure was also investigated. (C) 2008 Elsevier B. V. All rights reserved.

We investigate three-dimensional Turing patterns in two-component reaction diffusion systems. The FitzHugh-Nagumo equation, the Brusselator, and the Gray-Scott model are solved numerically in three dimensions. Several interconnected structures of domains as well as lamellar, hexagonal, and spherical domains are obtained as stable motionless equilibrium patterns. The relative stability of these structures is studied analytically based on the reduction approximation. The relation with the microphase-separated structures in block copolymers is also discussed.

A new geometrical criterion for the transition to spatio-temporal chaos (STC) arising in the Gray-Scott model is presented. This is based on the inter-relationship of global bifurcating branches of ordered patterns with respect to supply and removal rates contained in the model. This viewpoint not only gives us a new criterion for the onset of STC but also clarifies how the orbit itinerates among several ordered patterns in infinite-dimensional space. Moreover, the geometrical characterization gives us a universal viewpoint about the onset and termination of STC. There are at least two different mechanisms that cause re-injection dynamics and drive the STC: one is a generalized heteroclinic cycle consisting of self-replication and self-destruction processes, and the other involves annihilation of colliding waves instead of self-destruction. (C) 2001 Elsevier Science B.V. All rights reserved.

Self-replicating patterns (SRP) have been observed in several chemical reaction models, such as the Gray-Scott (GS) model, as well as in physical experiments, Watching these experiments (computational and physical) is like watching the more familiar coarsening processes but in reverse: the number of unit localized patterns increases until they fill the domain completely. Self-replicating dynamics, then, can be regarded as a transient process from a localized trigger to a stable stationery or oscillating Turing pattern, Since it is a transient process, it is very difficult to give a suitable definition to characterize SRP, It cannot be described in terms of well-studied structures such as the attractor or a singular saddle orbit for a dynamical system. In this paper, we present a new point of view to describe the transient dynamics of SRP over a finite interval of time. We focus our attention on the basic mechanism causing SRP from a global bifurcational point of view and take our clues from two model systems including the GS model. A careful analysis of the anatomy of the global bifurcation diagram suggests that the dynamics of SRP is related to a hierarchical structure of limit points of folding bifurcation branches in parameter regions where the branches have ceased to exist. Thus, the skeleton structure mentioned in the title refers to the remains of bifurcation branches, the aftereffects of which are manifest in the dynamics of SRP. One of the natural and important problems is about the existence of an organizing center from which the whole hierarchical structure of limit points emerges. In our setting, the numerics suggests a strong candidate for that, i.e., Bogdanov-Takens-Turing (BTT) singularity together with the presence of a stable critical point, and so this indicates a universality of the above structure in the class of equations sharing this characteristic. (C) 1999 Elsevier Science B.V. All rights reserved.