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.

The self-assembly of nanoscopic building blocks into higher order macroscopic patterns is one possible approach for the bottom-up fabrication of complex functional systems. Macroscopic pattern formation, in general, is determined by the reaction and diffusion of ions and molecules. In some cases macroscopic patterns emerge from diffusion and interactions existing between nanoscopic or microscopic building blocks. In systems where the distribution of the interaction-determining species is influenced by the presence of a diffusion barrier, the evolving macroscopic patterns will be determined by the spatiotemporal evolution of the building blocks. Here we show that a macroscopic pattern can be generated by the spatiotemporally controlled aggregation of like-charged carboxyl-terminated gold nanoparticles in a hydrogel, where clustering is induced by the screening effect of the sodium ions that diffuse in a hydrogel. Diffusion fronts of the sodium ions and the induced nanoparticle aggregation generate Voronoi diagrams, where the Voronoi cells consist of aggregated nanoparticles and their edges are aggregation-free and nanoparticle-free zones. We also developed a simple aggregation-diffusion model to adequately describe the evolution of the experimentally observed Voronoi patterns.

Unconventional computational methods provide alternative ways to solve numerous mathematical and computational problems compared to conventional approaches. Maze solving and finding the shortest path is one of the most challenging problems in this field. In the past few decades, several chemical, physical, and other techniques have been developed. Here we investigated the maze solving behavior of chemotactic particles in two geometrical orientations of channels, in a simple rectangular domain and in a complex maze, to show that both the fluctuation of Brownian particle motion and the geometry of the maze can play an important role in maze solving. We systematically studied the effect of stochastic (Brownian motion) and deterministic (chemotactic motion) parts on the characteristic of particle motion and maze solving.

The pH-induced Marangoni flow has been recently shown to be of use for analog computing of topological problems, such as maze solving. Here we show that the temperature-induced Marangoni flow can also be used to find the shortest path in a maze filled with a hot solution of a fatty acid, where the temperature gradient is created by cooling down the exit of the maze. Our method utilizes the fact that the temperature-induced Marangoni flow can transport dye particles at the liquid-air interface added to the entrance of the maze which subsequently dissolve in water during their motion revealing the most likely paths. The most intense flow is maintained through the shortest path which is, therefore, marked by the most intense color of the dissolved dye particles.

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.

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.

Spontaneous spiral formation has been observed in heterogeneous excitable media, and identified unidirectional paths as the origin of the spiral cores. Our numerical results showed unidirectional propagation always appeared at the spiral core as reported on the previous paper (Kinoshita et al., 2013). To clarify the cause of unidirectional behavior, we focused on the inhibitor concentration around the path and found a spatial asymmetric profile. We concluded that the asymmetric inhibitor profile, which was generated by a simple asymmetric construction of the suppressed blocks, induced spiral wave on the heterogeneous reaction field. (C) 2014 Elsevier B.V. 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.

Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.

A new type of mesh generator is developed by using a self-organized pattern in a reaction-diffusion system. The system is the Gray-Scott model, which creates a spot pattern in a specific parameter region. The spots correspond to nodes of a mesh. The mesh generator has several advantages: the algorithm is simple and processes to improve the mesh, such as smoothing, (locally) addition, and removal of nodes, are automatically performed by the system. (C) 2012 Elsevier Ltd. All rights reserved.

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. © Springer-Verlag Berlin Heidelberg 2013.

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.

Existence and dynamics of chaotic pulses on a one- dimensional lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh - Nagumo equations. Such pulses annihilate when they collide with each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off. like elastic balls. We consider the behavior of such a localized pattern on one- dimensional lattice, i. e., an infinite system of ODEs with nearest interaction of diffusive type. Besides the usual standing and traveling pulses, a new type of localized pattern, which moves chaotically on a lattice, is found numerically. Employing the strength of diffusive interaction as a bifurcation parameter, it is found that the route from standing pulse to chaotic pulse is of intermittent type. If two chaotic pulses collide with appropriate timing, they form a periodic oscillating pulse called a molecular pulse. Interaction among many chaotic pulses is also studied numerically.

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.

We study the self-replicating pattern (SRP) that is observed in the one-dimensional Gray-Scott model from aglobal bifurcational view point. It is shown that the existence of the hierarchy structure of the limiting points of stationary Turing patterns causes SRP of static type as an after effect. The main difficulty lies in the fact that SRP is a real transient phenomenon and it can not be captured as an invariant set in a function space. The after effect is the reflection of the fact that each element of hierarchy structure is connected by unstable manifolds. © 1999 by the University of Notre Dame. All rights reserved.

A hidden bifurcational structure which drives the self-replicating patterns (SRP) of reaction diffusion system is presented. Self-replicating dynamics on a finite interval can be regarded as a transient process from a localized trigger to a stable Turing pattern or oscillatory Turing pattern. SRP looks like a cell division in two-dimensional space. It is truly a transient phenomenon in the sense that it only appears temporarily on the way to the final pattern. The present aim is to give a new point of view to describe such a transient dynamics of SRP. Especially we concentrate on the basic mechanism causing SRP from a bifurcational view point by employing a new model system and its finite-dimensional compartment model which shares common features with the Gray-Scott model. The basic mechanism means how an oscillatory single pulse splits into two parts, it turns out that the essential dynamics of SRP comes from the subcritical bifurcating loop of oscillatory branch of pulse type. Any part of this loop does not appear in the phase space; the aftereffect of the limiting point born from the subcriticality manifests the dynamics of SRP.

A hidden bifurcational structure which drives the self-replicating patterns (SRP) of reaction diffusion system is presented. Self-replicating dynamics on a finite interval can be regarded as a transient process from a localized trigger to a stable Turing pattern or oscillatory Turing pattern. SRP was found in several chemical reaction models, for instance, the Gray-Scott model as well as in real experiments. It looks like a cell-differentiation in two-dimensional space. The most difficult point to describe SRP lies in the fact that it is truely a transient phenomenon in the sense that it only appears temporarily on the way to the final pattern. There seems to be no good dynamical framework to guide the motion of SRP. The aim is to give a new point of view to describe such a transient dynamics of SRP. Especially we concentrate on the basic mechanism causing SRP from a bifurcational view point by employing a new model system and its finite-dimensional compartment model which shares common features with the Gray-Scott model. The basic mechanism means how an oscillatory 1-pulse splits into two parts. It turns out that the essential dynamics of SRP comes from the subcritical bifurcating loop of oscillatory branch of pulse type. It should be noted that ally part of this loop does not appear in the phase space In other words, the after effect; of the limiting point born from the subcriticality manifests the dynamics of SRP.