櫻井 建成

I n our original manuscript, the parameter values were incorrectly described in the caption of Figure 5. The parameters should be “au/a = 1 and av/a = 0.1” instead of “αu/α = αv/α = 0.1”. In addition, “au = av = 3.7” was incorrect, and it should be “au = 37 and av = 3.7”. The errors are typographical, and thus, these corrections do not affect the conclusions of this work.

Collective cell migration is seen in many developmental and pathological processes, such as morphogenesis, wound closure, and cancer metastasis. When a fish scale is detached and adhered to a substrate, epithelial keratocyte sheets crawl out from it, building a semicircular pattern. All the keratocytes at the leading edge of the sheet have a single lamellipodium, and are interconnected with each other via actomyosin cables. The leading edge of the sheet becomes gradually longer as it crawls out from the scale, regardless of the cell-to-cell connections. In this study, we found leading-edge elongation to be realized by the interruption of follower cells into the leading edge. The follower cell and the two adjacent leader cells are first connected by newly emerging actomyosin cables. Then, the contractile forces along the cables bring the follower cell forward to make it a leader cell. Finally, the original cables between the two leader cells are stretched to tear by the interruption and the lamellipodium extension from the new leader cell. This unique actomyosin-cable reconnection between a follower cell and adjacent leaders offers insights into the mechanisms of collective cell migration.

A concentric pulse by motile cells of Escherichia coli (E. coli) propagates and the cells aggregate to form self-organized patterns.We summarize experimental and numerical results on the self-organized pattern formation of E. coli to elucidate some aspects of its mechanism. Our presentation includes experiments on E. coli patterns, as well as numerical simulations on the basis of a reaction-diffusionchemotaxis model.We find good agreement for one-dimensional propagating fronts in observation and simulation. However, corresponding results for two-dimensional circular bacterial clusters have still not been obtained.

We investigated the phase-response curve of a coupled system of density oscillators with an analytical approach. The behaviors of two-, three-, and four-coupled systems seen in the experiments were reproduced by the model considering the phase-response curve. Especially in a four-coupled system, the clustering state and its incidence rate as functions of the coupling strength are well reproduced with this approach. Moreover, we confirmed that the shape of the phase-response curve we obtained analytically was close to that observed in the experiment where a perturbation is added to a single-density oscillator. We expect that this approach to obtaining the phase-response curve is general in the sense that it could be applied to coupled systems of other oscillators such as electrical-circuit oscillators, metronomes, and so on.

We investigated the spontaneous recurrence of deposition and dissolution of camphor layer on the surface of camphor methanol solution. This recurrence is a novel rhythmic process concerned with solid-liquid phase transition. To elucidate the underlying mechanism, we measured the solution temperature at different times, and found that the temperature increased, and decreased repetitively, correlating with the camphor layer's deposition and dissolution. These experimental results show that the solution temperature plays an important role in recurrence of deposition and dissolution.

© 2015 Elsevier Ltd. All rights reserved. Autonomous pattern formation phenomena are ubiquitous throughout nature. The goal of this paper is to show the possibility to effectively generate various desired spatial patterns by guiding such phenomena suitably. To this end, we employ a reaction-diffusion system as a mathematical model, and formulate and solve a novel pattern formation control problem. First, we describe the control objective in terms of spatial spectrum consensus, which enables utilize recent advances on networked control system theory. Next, the effectiveness of the proposed control law is evaluated theoretically by exploiting the center manifold theorem, and also numerically by simulation. The Turing instabilities play a crucial role throughout the paper.

This paper presents a two-dimensional numerical simulation method for modeling a convective flow structure induced by chemical concentration waves of Belousov-Zhabotinsky (BZ) reaction in a two-dimensional rectangular domain of horizontal space and vertical depth. The method assumes a scenario in which an air-liquid interface of the BZ chemical solution has an elastic property and the Marangoni effect drives the surface motion of the interface. As a result of the surface motion, a convective flow is organized in the bulk of the chemical solution. The bulk flow of the chemical solution is described with the Navier-Stokes equations, and the chemical reaction is described with the Oregonator model. Thus, we couple the three systems of the bulk flow, the chemical reaction and the surface motion described with an elastic equation in the numerical simulation method. Results of several numerical simulations performed with the method show that a single chemical concentration wave propagates with a broad convective flow structure and a chemical concentration wave train propagates with a global flow structure. These flow structures are similar to those observed in real laboratory experiments.

Gravitational instability occurs at the interface of two solutions when a higher-density solution (HDS) is placed on the surface of a lower-density solution (LDS). As the HDS sinks, a cell pattern forms on the surface. We investigate the size distribution of the cells in this pattern. We show that the cumulative size distribution obeys a power law with a power index that is independent of time as long as it is possible to neglect the interactions among the cells. To understand the power law mechanism, a simple model excluding the interactions is proposed, and we demonstrate that this simple model provides the power law measured in experiments. Our results indicate that independent cell generation and growth are key factors to understand the feature of the cell pattern. DOI: 10.1103/PhysRevE.87.012903

In this paper, we formulate and solve feedback stabilization problem of unstable non-uniform spatial pattern in reaction-diffusion systems. By considering spatial spectrum dynamics, we obtain a finite dimensional approximation that takes over the semi-passivity of the original partial differential equation. By virtue of this property, we can show the diffusive coupling in the spatial frequency domain achieves the desired pattern formation. © 2013 AACC American Automatic Control Council.

The spontaneous droplet motion of a Belousov-Zhabotinsky (BZ) reaction medium was previously reported; however, the attempts to control such motion have not been successful. In the present study, we first succeeded in controlling the direction of a droplet motion by using a photosensitive BZ reaction catalyzed by ruthenium complex under illumination with a spatial gradient. We were also able to stop the droplet motion using high-intensity light illumination. These results will help in the understanding of motion coupling with pattern formation.

Minima and one of the authors (1996) proposed a mathematical model for the pattern dynamics of aggregating regions of biological individuals possessing the property of chemotaxis. For this model, Tello and Winkler (2007) [22] obtained infinitely many local branches of nonconstant stationary solutions bifurcating from a positive constant solution, while Kurata et al. (2008) numerically showed several spatio-temporal patterns in a rectangle. Motivated by their work, we consider some qualitative behaviors of stationary solutions from global and local (bifurcation) viewpoints in the present paper. First we study the asymptotic behavior of stationary solutions as the chemotactic intensity grows to infinity. Next we construct local bifurcation branches of stripe and hexagonal stationary solutions in the special case when the habitat domain is a rectangle. For this case, the directions of the branches near the bifurcation points are also obtained. Finally, we exhibit several numerical results for the stationary and oscillating patterns. (C) 2012 Elsevier B.V. All rights reserved.

Spiral patterns that have concave and convex surfaces were discovered on a bulk metallic glass (BMG), Zr55Cu30Al10Ni5 atom % alloy after electropolishing under certain conditions. The observed spiral pattern had a wavelength of 2.4 mu m and peaks that were 0.19 mu m high. Electropolishing produces smooth metal and alloy surfaces. These patterns depend on the spatiotemporal properties during electropolishing.

We introduce a short review of chemically driven convection together with a series of our experiments on hydrodynamic instabilities induced by chemical waves excited in the batch reactor of a Belousov-Zhabotinsky reaction. Several unresolved phenomena are picked out and possible mechanisms are discussed extensively. Interesting features of these phenomena can be summarized as being caused by the 'global and dynamic hydrodynamic pattern induced by chemical waves'. These chemically induced global pattern of hydrodynamic phenomena may not be simply explained by the reaction-diffusion-convection model based on Marangoni instability (surface tension-driven convection), which produces only a localized structure of the convection pattern. Observed flow waves show global and dynamic patterns of convection that generate a functional structure associated with hierarchical patterns appearing in the reaction-diffusion-convection system. In particular, we clarify the existence of a continuous stream of hydrodynamic flow with growing amplitude and its rotating direction. We find that the flow does not stabilize to a motionless state until the system has self-collapsed. This new picture of the flow waves requires a revision of the reaction-diffusion-convection model. The established flow structure can be regarded as a mixing and/or transport process to supply the substrate from the peripheral region to the centre of the chemical waves to sustain the reaction. This characteristic may be a function of the hierarchical structure. A new mechanism for the viscous-elastic feature of the gas-liquid interface is discussed in order to understand these curious phenomena of interest. (C) 2009 Elsevier B.V. All rights reserved.

Supplement 2009This paper is concerned with the Belousov-Zhabotinskii reaction model. We consider the reaction-diffusion model due to Keener-Tyson. After constructing a dynamical system, we will construct exponential attractors and will estimate the attractor dimension from below. In particular, it will be shown that, as the excitability ε> 0 tends to zero, the attractor dimension tends to infinity, although the exponential attractor can depend on the excitability continuously.

We investigate a simple experimental system using candles; stable combustion is seen when a single candle burns, while oscillatory combustion is seen when three candies burn together. If we consider a set of three candles as a component oscillator, two oscillators, that is, two sets of three candles, can Couple with each other, resulting in both in-phase and antiphase synchronization depending on the distance between the two sets. The mathematical model indicates that the oscillatory combustion in a set of three candles is induced by a lack of oxygen around the burning point. Furthermore, we suggest that thermal radiation may be an essential factor of the synchronization.

We found a rotating global structure induced by the dynamical force of local chemical activity in a thin solution layer of excitable Belousov-Zhabotinsky reaction coupled with diffusion. The surface flow and deformation associated with chemical spiral waves (wavelength about 1 mm) represents a global unidirectional structure and a global tilt in the entire Petri dish (100 mm in diameter), respectively. For these observations, we scanned the condition of hierarchal pattern selection. From this result, the bromomalonic acid has an important role to induce the rotating global structure. An interaction between a reaction-diffusion process and a surface-tension- driven effect leads to such hierarchal pattern with different scales.

We study a discrete model described by coupled excitable elements following the monostable FitzHugh-Nagumo equations. Our model has a weakly coupled activator and a strongly coupled inhibitor. For two-coupled excitable elements, we show that the trivial state always exists stably, while nontrivial stable states appear depending on the coupling strengths. In a one-dimensional array, only the elements near the initial condition step remain at nontrivial states. We discuss stationary pattern formation in a one-dimensional array and a two-dimensional lattice using the analytical results of a two-coupled system.

Using a kinematic approach, we propose a model of arc-like wave segments in which the free ends are stabilized by using a feedback algorithm. The model can demonstrate the experimental results and numerical Computations of a reaction-diffusion system. This model also reveals some aspects of spiral wave dynamics with the free ends including not only the stabilization of wave segments using feedback, but also a critical behavior with respect to the initial wave size in media with fixed excitability. (C) 2008 Elsevier B.V. All rights reserved.

A quite simple but useful approach is performed for the analysis of chemical wave segments with free ends. By integrating a reaction-diffusion system we can obtain an analytical expression to understand the dynamics of the wave segments. This integration can yield qualitative information regarding wave development under an external forcing having feedback or noise effects. We conclude that this wave development is influenced not only by medium excitability but also by wave size. (C) 2006 Elsevier B.V. All rights reserved.

A surface deformation wave coupled with an oscillatory hydrodynamic flow is observed in a thin solution layer of the Belousov-Zhabotinsky reaction. The observation is carried out with a Mach-Zehnder interferometric system under the excitation of chemical spiral waves in the solution. The surface deformation wave is induced spontaneously at the end of a dish. It propagates towards the center of the spiral waves, and disappears there. This fact leads to understand the oscillatory flow as a propagating convection waves having long-scale surface deformation. The Marangoni effect or surface tension driven convection with deformable surface plays an important role to establish the oscillatory flow.

The present paper proposes a computational model for the realization of visual functions of edge and/or feature detection and segmentation. The model utilizes a reaction-diffusion model which is an extended version of the diffusion-based Difference of Gaussians (DOG) filter previously proposed by Marr and Hildreth as an edge detection model. The proposed model self-organizes spatial patterns having edges and/or features and segments. These patterns are sustained by the intrinsic mechanism of the proposed model under specific conditions. In addition, the model also helps to solve the stereo matching problem in random dot stereograms and the aperture problem in optical flow computation. These Visual functions of the proposed model are demonstrated with both artificial and real images.

The excitable Belousov-Zhabotinsky (BZ) reaction coupled with diffusion can exhibit a large variety of spatial patterns. In this letter, we report on superimposed spiral structures, providing evidence of a hierarchical self-organized order that connects two complex phenomena involving the coupling of a reaction-diffusion pattern with convection. A macroscopic propagating spiral flow wave (wavelength about 50 mm) is induced spontaneously by the preexcited reaction-diffusion structure of chemical spiral waves (wavelength about 1 mm). The pattern dynamics links two different hierarchical levels of structure formation in a nonlinear system.

An increasing attention is focused on information processing by reaction-diffusion system, in which temporal and spatial patterns are self-organized. In the system, two interesting phenomena of Turing pattern formation and stochastic resonance have been reported. We have been proposed a new approach for image segmentation and edge detection based on a reaction-diffusion model (Fitz-Hugh & Nagumo (FHN) model). In this paper, noisy image or low contrast image are tested to confirm effectiveness of the method. Compared to the conventional method, the Turing condition realizes more reliable tool for noisy image segmentation. And, addition of moderate noise improves the performance of image segmentation. Stochastic resonance condition acts as more powerful tool for edge detection and segmentation for low contrast image. © 2003, The Institute of Image Electronics Engineers of Japan. All rights reserved.

Propagating wave segments are stabilized to a constant size and shape by applying negative feedback from the measured wave area to the excitability of the medium. The locus of steady-state wave size as a function of excitability defines the perturbation threshold for the initiation of spiral waves. This locus also defines the excitability boundary for spiral wave behavior in active media.

Intricate patterns of wave propagation are exhibited in a chemical reaction-diffusion system with spatiotemporal feedback, Wave behavior is controlled by feedback-regulated excitability gradients that guide propagation in specified directions. Waves interacting with boundaries and with other waves are observed when interaction terms are incorporated into the control algorithm. Spatiotemporal feedback offers wide flexibility for designing and controlling wave behavior in excitable media.

Experimental and theoretical studies of the excitability boundary for spiral wave behavior are presented. The boundary is defined by unstable wave segments, which are stabilized by using a negative-feedback control algorithm. A kinematic description of the constant-size, constant-shape wave segments is presented.

We introduce a simple method for motion enhancement. The method enables us to realize brightness enhancement of moving objects, to reduce the influence of non-uniform illumination in motion analysis and to visualize dynamic streamlines in fluid flow analysis. (C) 1999 Elsevier Science B.V. All rights reserved.

In actual scene analysis, the influence of non-ideal conditions such as non-uniform illumination should be taken into account. The conventional methods for the estimation of motion fields are violated in this situation. In this study, two approaches are proposed to extract reliable motion fields under spatio-temporal non-uniform illumination. These are an extended constraint equation with spatio-temporal local optimization and a pixel-based temporal filtering. Experiments have been made to confirm the performance of the proposed methods and to clarify the difference of characteristics between them. (C) 1999 Elsevier Science B.V. All rights reserved.

Oscillation of surface deformation synchronized with oscillation of convection was found in a thin solution layer of a Belousov-Zhabotinsky reaction in which a spiral wave train was excited. To clarify the underlying mechanism of establishing oscillatory convection in the system, we measured the velocity of the convective flow at the surface and the angle of the surface tilt of the solution simultaneously. The convection and surface deformation showed propagation behavior. The propagating waves had a long wavelength (more than 100 mm) and a rapid propagation velocity (about 2.5 mm/s) compared to those of a chemical wave train.

Spiral patterns are representative dissipative structures that can be observed in reaction-diffusion systems such as Belousov-Zhabotinsky (BZ) reactions. We found periodic initiation of moving structures of convection from the collision line of the fronts of two spiral patterns triggered in a shallow layer of a BZ solution. The waves of convection propagated toward the respective centers of the spirals, and were annihilated there. The flow direction of the convection waves reversed every 15-16 s. These curious pattern dynamics can he interpreted as a demonstration of a hierarchical and/or a functional order in the complex system of reaction, diffusion and convection.

Numerical experiments on the Oregonator model of the Belousov-Zhabotinsky reaction with 2 variables (activator and inhibitor) are carried out. Influences of an inhibitory diffusion coefficient and inhibitory initial condition (concentration) on its pattern dynamics are studied for several values of a stoichiometric factor of the model. As a result, several pattern formation processes such as decrementally propagating waves and self replicating processes are found by changing the initial condition of the inhibitor and the stoichiometric factor under the Turing instability. In the self replicating process, new pattern dynamics acting as birth and death of waves is also found.

We propose a method to measure Brownian motion based on image sequence processing. Random motion of sub-micron sphere particles is visualized under an inverted microscope with laser light illumination. We analyze a long image sequence of the motion by a spatial-filtering method, which corresponds to dynamic light scattering. We confirm that bigger particle (diameter=1.09 μm) show ideal Brownian motion with an inverse power-law spectrum P(f) α f-2. In tiny particles (diameter=0.46 and 0.20 μm), however, we observe a deviation from f-2 behavior. When the motion of particles is limited within a two-dimensional plane by use of heavy water, ordinary behavior of f-2 spectrum is recovered. We confirm high reliability and big advantages of the proposed method compared to dynamic light scattering.