Pattern Formation in Oscillatory Chemical Reactions

Kuramoto, Yoshio; Yamada, Tomoji

doi:10.1143/ptp.56.724

Cited by 81 publications

(36 citation statements)

References 1 publication

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“…Two pendula, mounted together, will always end up swinging in exactly opposite directions, regardless of their respective individual motion. This was one of the first observations of the phenomenon of the coupled harmonic oscillators, which have many applications in physics [89,16,[18][19][20]47,93,5,99], biology and chemistry [93,60,63,64,100,104]. In engineering very spectacular was synchronization of pedestrians on Millennium bridge [1,19,36,37,42,81,84,86].…”

Section: Introductionmentioning

confidence: 94%

“…Greek washstand automaton of the 3rd century BC is the earliest known example of an escapement mechanism [63]. The earliest liquid-driven escapement was described by the Greek engineer Philo of Byzantium (3rd century BC) in his technical treatise Pneumatics (chapter 31) as part of a washstand.…”

Section: 2escapement Mechanismsmentioning

confidence: 99%

“…Once the spoon has emptied, it is pulled up again by the counterweight, closing the door on the pumice by the tightening string. Philo's comment that "its construction is similar to that of clocks" indicates that such escapement mechanisms were already used in ancient water clocks [63].…”

Section: 2escapement Mechanismsmentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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Abstract:In this report we recall the famous Huygens' experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging on the same beam can show the almost complete (in-phase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century. We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendula via oscillating beam allowing the pendula's synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given.

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Section: Introductionmentioning

confidence: 94%

Section: 2escapement Mechanismsmentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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“…To consider the effect of flow on the dispersion relation, we derive the phase dynamics from equation (5), and estimate a dispersion relation for the phase wave. By means of limit cycle perturbations, the dynamics of phase waves in standard reaction-diffusion systems for oscillatory media are described by Burgers equation [10,11,[20][21][22]. We adopt a similar method for oscillatory reaction-diffusion equations with this type of flow term.…”

Section: Derivation Of Phase Dynamics and Estimation Of Dispersion Rementioning

confidence: 99%

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

Yamada¹,

Nakagaki

Baker³

et al. 2007

J. Math. Biol.

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In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

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“…The subvolumes thus define closed, well-mixed reaction spaces of volume c . In order for the reaction system to be well mixed within each subvolume, the subvolume edge lengths have to be much smaller than the Kuramoto length, 51 hence…”

Section: B Discretization-corrected Propensitiesmentioning

confidence: 99%

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Ramaswamy

Sbalzarini

2011

The Journal of Chemical Physics

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Stochastic reaction-di usion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-di usion simulation algorithm that samples realizations from the exact solution of the reaction-di usion master equation. The present algorithm, called Partial-propensity Stochastic Reaction-Di usion (PSRD) method, uses an on-lattice discretization of the reaction-di usion system and relies on partial-propensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two-and three-dimensional pattern-forming Gray-Scott systems, highlighting the role of intrinsic noise in these systems. Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of the reaction-diffusion system and relies on partial-propensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two-and three-dimensional pattern-forming Gray-Scott systems, highlighting the role of intrinsic noise in these systems.

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Pattern Formation in Oscillatory Chemical Reactions

Cited by 81 publications

References 1 publication

Synchronization of clocks

Synchronization of clocks

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

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