Daishin Ueyama

Maze solving using fatty acid chemistry

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.

Maze solving using temperature-induced Marangoni flow

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.

Pulse Wave Propagation in a Large Number of Coupled Bistable Oscillators

A simple model of inductor-coupled bistable oscillators is shown to exhibit pulse wave propagation. We demonstrate numerically that there exists a pulse wave which propagates with a constant speed in comparatively wide parameter region. In particular, the propagating pulse wave can be observed in non-uniform lattice with noise. The propagating pulse wave can be observed for comparatively strong coupling case, and for weak coupling case no propagating pulse wave can be observed (propagation failure). We also demonstrate various interaction phenomena between two pulses.

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.

Self-assembly of like-charged nanoparticles into Voronoi diagrams

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.

A self-organized mesh generator using pattern formation in a reaction–diffusion system

Abstract 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.

Marangoni Flow Driven Maze Solving

Algorithmic approaches to maze solving problems and finding shortest paths are generally NP-hard (Non-deterministic Polynomial-time hard) and thus, at best, computationally expensive. Unconventional computational methods, which often utilize non-local information about the geometry at hand, provide an alternative to solving such problems much more efficiently. In the past few decades several chemical, physical and other methods have been proposed to tackle this issue. In this chapter we discuss a novel chemical method for maze solving which relies on the Marangoni flow induced by a surface tension gradient due to a pH gradient imposed between the entrance and exit of the maze. The solutions of the maze problem are revealed by paths of a passive dye which is transported on the surface of the liquid in the direction of the acidic area, which is chosen to be the exit of the maze. The shortest path is visualized first, as the Marangoni flow advecting the dye particles is the most intense along the shortest path. The longer paths, which also solve the maze, emerge subsequently as they are associated with weaker branches of the chemically-induced Marangoni flow which is key to the proposed method.

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.