Hitoshi Mahara

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.

Self-organized Archimedean spiral pattern: Regular bundling of fullerene through solvent evaporation

We report the spontaneous generation of an Archimedean spiral pattern of fullerene via the evaporation of solvent. The self-organized spiral pattern exhibited equi-spacing on the order of μm between neighboring stripes. The characteristics of the spirals, such as the spacing between stripes, the number of stripes, and the band width of stripes, could be controlled by tuning the thickness of the liquid bridge and the concentration of solution. The mechanism of pattern formation is interpreted in terms of a specific traveling wave on the liquid-solid interface accompanied by a stick-slip process of the contact line.

Calculation of the Entropy Balance Equation in a Non-equilibrium Reaction-diffusion System

In this article, we discuss the relationships between thermodynamic quantities and the spatial pattern in a reaction-diffusion model based on the reversible Gray-Scott model. This model is introduced for calculation of the entropy production in a reaction-diffusion system. First, we show the relationship between entropy production and pattern formation, and suggest that the entropy production could be an index of different patterns. Then the entropy production is applied for searching the parameter region where the pattern is bistable. Moreover, the entropy change is calculated by using the relative chemical potential that is defined based on the equilibrium state and not on the standard chemical potential. The results of the entropy change are consistent with the intrinsic property of the entropy, therefore, the entropy change calculated in this way may be regarded as an appropriate quantity for the discussion of the thermodynamic properties in a non equilibrium system.

Entropy production in a two-dimensional reversible Gray-Scott system

The entropy production sigma is calculated in the time evolution processes toward a Turing-like pattern and a chaotic pattern in a two-dimensional reaction-diffusion system. The contributions of reaction and diffusion to the entropy production are evaluated separately. Though its contribution to total sigma is about 5%, the entropy production in diffusion foretells the moving direction of the dots (reaction spots) and the line-shaped patterns. The entropy production of the entire system sigma depicts well the cooperative dynamics and evolution of chaotic dot patterns. It is suggested that sigma can be a scalar measure for quantitative studies of hierarchic pattern dynamics. The relation is also discussed between the bifurcation parameter and the distance from thermodynamic equilibrium.

‘Initial state’ coordinations reproduce the instant flexibility for human walking

An important feature of human locomotor control is the instant adaptability to unpredictable changes of conditions surrounding the locomotion. Humans, for example, can seamlessly adapt their walking gait following a sudden ankle impairment (e.g., as a result of an injury). In this paper, we propose a theoretical study of the mechanisms underlying flexible locomotor control. We hypothesize that flexibility is achieved by modulating the posture at the beginning of the stance phase—the initial state. Using a walking model, we validate our hypothesis through computer simulations

Hierarchical Self-organization and Self-assembly: Metal Nanoparticles in Polymer Matrices

Although thermodynamically different, self-assembly and dissipative structure formation often work together to bring about highly ordered structures in an open system. This mutual assistance between self-assembly and dissipative structure formation is regarded as self-organization for a system to increase the degrees of hierarchy and complexity. An example for this comprehensive idea is given by hierarchic self-organization of organo-passivated metal nanoparticles in dissipatively isolated polymer matrices.