Nobuhiko J. Suematsu

Three-variable reversible Gray-Scott model.

Even though the field of nonequilibrium thermodynamics has been popular and its importance has been suggested by Demirel and Sandler [J. Phys. Chem. B 108, 31 (2004)], there are only a few investigations of reaction-diffusion systems from the aspect of thermodynamics. A possible reason is that model equations are complicated and difficult to analyze because the corresponding chemical reactions need to be reversible for thermodynamical calculations. Here, we introduce a simple model for calculation of entropy production rate: a three-variable reversible Gray-Scott model. The rate of entropy production in self-replicating pattern formation is calculated, and the results are compared with those reported based on the Brusselator model in the context of biological cell division.

Suppression and Regeneration of Camphor-Driven Marangoni Flow with the Addition of Sodium Dodecyl Sulfate

We investigated the Marangoni flow around a camphor disk on water with the addition of sodium dodecyl sulfate (SDS). The flow velocity decreased with an increase in the concentration of SDS in the aqueous phase, and flow was hardly observed around the critical micelle concentration (cmc), because SDS reduced the driving force of Marangoni flow. However, the flow velocity increased with a further increase in the concentration of SDS. Thus, the Marangoni flow is maximally inhibited around the cmc of SDS. In this paper, we concluded that the regeneration of Marangoni flow originates from an increase in the dissolution rate of camphor into the SDS aqueous solution.

Quantitative Estimation of the Parameters for Self-Motion Driven by Difference in Surface Tension

Quantitative information on the parameters associated with self-propelled objects would enhance the potential of this research field; for example, finding a realistic way to develop a functional self-propelled object and quantitative understanding of the mechanism of self-motion. We therefore estimated five main parameters, including the driving force, of a camphor boat as a simple self-propelled object that spontaneously moves on water due to difference in surface tension. The experimental results and mathematical model indicated that the camphor boat generated a driving force of 4.2 μN, which corresponds to a difference in surface tension of 1.1 mN m(-1). The methods used in this study are not restricted to evaluate the parameters of self-motion of a camphor boat, but can be applied to other self-propelled objects driven by difference in surface tension. Thus, our investigation provides a novel method to quantitatively estimate the parameters for self-propelled objects driven by the interfacial tension difference.

Swarming of Self-Propelled Camphor Boats

When an ensemble of self-propelled camphor boats move in a one-dimensional channel, they exhibit a variety of collective behaviors. Under certain conditions, the boats tend to cluster together and move in a relatively tight formation. This type of behavior, referred to as clustering or swarming here, is one of three types recently observed in experiment. Similar clustering behavior is also reproduced in simulations based on a simple theoretical model. Here we examine this model to determine the clustering mechanism and the conditions under which clustering occurs. We also propose a method of quantifying the behavior that may be used in future experimental work.

Localized Bioconvection of Euglena Caused by Phototaxis in the Lateral Direction

Localized pattern of bioconvection was newly observed in a suspension of Euglena gracilis , which was a photosensitive micro-organism. The suspension was exposed bright illumination from the bottom, in which the cells swam away from the light source. Then high-density spots, i.e., settling the cells, were formed at a part of a sealed chamber. This localized pattern was contrast with a general bioconvection where pattern was generated whole of a chamber. The experimental observations were reproduced by a mathematical model that was based on the phototaxis of individual cells in both vertical and lateral directions. Our results indicate that convection is maintained by upward swimming, as with general bioconvection, and the localization originates from lateral phototaxis.

Synchronized Intermittent Motion Induced by the Interaction between Camphor Disks

A new mode of collective motion was discovered in a system of camphor disks floating on the water surface in a circular chamber. The mode was induced by tuning the number of the disks. A single or few disks are known to continuously move on the water surface. Conversely, when many disks are present, motion comes to a stop and the disks form ordered spatial patterns by repulsive interaction. Here we found the third mode that emerged at an intermediate disk number, in which inactive and active motion phases alternated non-periodically. This new mode exhibited synchronization as the disk number increased.

Oscillation of Speed of a Self-Propelled Belousov-Zhabotinsky Droplet.

Self-propelled objects can become potential biomimetic micromachines, but a versatile strategy is required to add the desired functions. Introducing a characteristic chemical reaction is a simple answer; however, the problem is how the chemical reaction is coupled to the self-propelled motion. We propose a strategy to select the chemical reaction so that its product or intermediate affects the driving force of a self-propelled object. To demonstrate this strategy, we put an aqueous droplet of nonlinear chemical reaction, the Belousov-Zhabotinsky (BZ) reaction, into an oil phase including a surfactant, where an aqueous droplet was driven by an interfacial reaction of the surfactant and bromine. The results exhibited oscillation of speed, and it was synchronized with the redox oscillation of the BZ reaction in the droplet. Bromine is one of the intermediates of the BZ reaction, and thus the droplet motion well-reflected the characteristics of the BZ reaction.

A Developmental Model for Branching Morphogenesis of Lake Cress Compound Leaf

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves.

Collective Motion and Phase Transitions of Symmetric Camphor Boats

The motion of several self-propelled boats in a narrow channel displays spontaneous pattern formation and kinetic phase transitions. In contrast with previous studies on self-propelled particles, this model does not require stochastic fluctuations and it is experimentally accessible. By varying the viscosity in the system, it is possible to form either a stationary state, correlated or uncorrelated oscillations, or unidirectional flow. Here, we describe and analyze these self organized patterns and their transitions.

Characteristic oscillatory motion of a camphor boat sensitive to physicochemical environment

A self-propelled camphor boat on water was investigated from the viewpoint of characteristic features of motion and mode-bifurcation depending on the diffusion length of camphor molecules. When a camphor disk was connected to the bottom of a larger plastic plate and then was placed on water, either oscillatory motion (repetition between rest and motion) or continuous motion was observed. In this paper, we report the novel features of this motion and mode-bifurcation as a function of the diffusion length of camphor molecules, e.g., multiple accelerations during oscillation, period-2 or irregular oscillatory motion, and reciprocating oscillation. These characteristic motion and mode-bifurcation are discussed in relation to the diffusion length of camphor molecules under the camphor boat and the development of camphor molecules from the camphor boat on water.