Design and Control of Wave Propagation Patterns in Excitable Media

Sakurai, Tatsunari; Mihaliuk, Eugene; Chirila, Florin; Showalter, Kenneth

doi:10.1126/science.1071265

Cited by 199 publications

(135 citation statements)

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“…An increasing number of experimental systems appears in the literature for which finely spatially distributed actuation-coupled with sensing-is available; chemical reactions addressed through light (Sakurai et al, 2002;Wolff et al, 2001) and colloidal particles manipulated through electric fields (Ristenpart et al, 2003) constitute such examples. When experiments can be initialized at will, the methods we discussed can be applied to laboratory-rather than computationalexperiments.…”

Section: The Equation-free Approachmentioning

confidence: 99%

Equation‐free: The computer‐aided analysis of complex multiscale systems

2004

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T he best available descriptions of systems often come at a fine level (atomistic, stochastic, microscopic, agent based), whereas the questions asked and the tasks required by the modeler (prediction, parametric analysis, optimization, and control) are at a much coarser, macroscopic level. Traditional modeling approaches start by deriving macroscopic evolution equations from microscopic models, and then bringing an arsenal of computational tools to bear on these macroscopic descriptions. Over the last few years with several collaborators, we have developed and validated a mathematically inspired, computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly. We call this the "equation-free" approach, since it circumvents the step of obtaining accurate macroscopic descriptions. The backbone of this approach is the design of computational "experiments". In traditional numerical analysis, the main code "pings" a subroutine containing the model, and uses the returned information (time derivatives, etc.) to perform computer-assisted analysis. In our approach the same main code "pings" a subroutine that runs an ensemble of appropriately initialized computational experiments from which the same quantities are estimated. Traditional continuum numerical algorithms can, thus, be viewed as protocols for experimental design (where "experiment" means a computational experiment set up, and performed with a model at a different level of description). Ultimately, what makes it all possible is the ability to initialize computational experiments at will. Short bursts of appropriately initialized computational experimentation -through matrix-free numerical analysis, and systems theory tools like estimation-bridge microscopic simulation with macroscopic modeling. If enough control authority exists to initialize laboratory experiments "at will" this computational enabling technology can lead to experimental protocols for the equation-free exploration of complex system dynamics. The Equation-Free ApproachA persistent feature of many complex systems is the emergence of macroscopic, coherent behavior from the interactions of microscopic agents such as molecules, cells, or individuals in a population. The implication is that macroscopic rules (a description of the system at a coarse-grained, high level) can somehow be deduced from microscopic ones (a description at a much finer level). For laminar Newtonian fluid mechanics, a successful coarse-grained description (the Navier-Stokes equations) was known on a phenomenological basis long before its approximate derivation from kinetic theory. Today, we must frequently study systems for which the physics can be modeled at a microscopic, fine scale; yet, it is practically impossible to derive a good macroscopic description from the microscopic rules. Hence, we look to the computer to explore the macroscopic behavior, based on the microscopic description.

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Section: The Equation-free Approachmentioning

confidence: 99%

Equation‐free: The computer‐aided analysis of complex multiscale systems

2004

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“…The spatiotemporal dynamics of such networks (2, 4) is especially challenging and interesting to understand, and to reproduce in synthetic model systems (2,3,5,(9)(10)(11). Simplified physical or chemical model systems are attractive for understanding biological complexity because these models can be made simple to probe, analyze, and understand.…”

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confidence: 99%

Modular chemical mechanism predicts spatiotemporal dynamics of initiation in the complex network of hemostasis

Kastrup

Runyon

Shen

et al. 2006

Proc. Natl. Acad. Sci. U.S.A.

103

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This article demonstrates that a simple chemical model system, built by using a modular approach, may be used to predict the spatiotemporal dynamics of initiation of blood clotting in the complex network of hemostasis. Microfluidics was used to create in vitro environments that expose both the complex network and the model system to surfaces patterned with patches presenting clotting stimuli. Both systems displayed a threshold response, with clotting initiating only on isolated patches larger than a threshold size. The magnitude of the threshold patch size for both systems was described by the Damkö hler number, measuring competition of reaction and diffusion. Reaction produces activators at the patch, and diffusion removes activators from the patch. The chemical model made additional predictions that were validated experimentally with human blood plasma. These experiments show that blood can be exposed to significant amounts of clot-inducing stimuli, such as tissue factor, without initiating clotting. Overall, these results demonstrate that such chemical model systems, implemented with microfluidics, may be used to predict spatiotemporal dynamics of complex biochemical networks.complexity ͉ microfluidics ͉ networks ͉ tissue factor ͉ nonlinear

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“…In particular, the stabilization and control of various patterns [3][4][5][6][7][8][9] through local, nonlocal, or global feedback, and pattern formation in media with designed heterogeneities [10 -12] are the source of novel insights for spatiotemporal dynamics.…”

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confidence: 99%

Gentle Dragging of Reaction Waves

et al. 2003

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Using a recently realized ''addressable catalyst surface'' [Science 294, 134 (2001)] we study the interaction of chemical reaction waves with prescribed spatiotemporal fields. In particular, we study how a traveling chemical pulse is ''dragged'' by a localized, moving temperature heterogeneity as a function of its intensity and speed. The acceleration and eventual ''detachment'' of the wave from the heterogeneity is also explored through simulation and stability analysis. DOI: 10.1103/PhysRevLett.90.018302 PACS numbers: 82.40.Bj, 05.45.-a, 82.40.Np, 82.45.Jn As the elements of spontaneous pattern formation are progressively understood through theory, experimentation, and scientific computation [1], ways to purposefully interact with the coherent structures (pulses and fronts) that constitute the building blocks of spatiotemporal patterns are becoming the focus of extensive research [2,3]. In particular, the stabilization and control of various patterns [3-9] through local, nonlocal, or global feedback, and pattern formation in media with designed heterogeneities [10 -12] are the source of novel insights for spatiotemporal dynamics.To explore such phenomena, we have recently constructed an ''addressable catalyst'': A focused laser beam, manipulated through computer-controlled mirrors and capable of ''writing'' spatiotemporal temperature heterogeneity patterns on a metal single crystal catalyst. The loop between this actuation and sensing (both resolved in space and time) through nonintrusive microscopies is then closed through the computer or the experimentalist herself/himself in real time. Our model system is the low-pressure catalytic oxidation of CO on Pt(110), a reaction exhibiting well-documented spatiotemporal patterns [13][14][15][16], and whose macroscopic modeling has reached an advanced level [17][18][19][20].In this Letter we study the interaction of reactive pulses with a single, spatially coherent but temporally mobile heterogeneity. In particular, we use a temperature heterogeneity, localized in space and steadily moving in time, to ''drag'' spontaneously isothermally forming reactive pulses and fronts with speeds differing from their natural speed. We examine the shapes acquired by these dragged waves and their limits of stability (that is, the range of dragging speeds for which they can exist). Through computer-aided analysis we examine the nature of the detachment instability, marking the loss of the ability of the heterogeneity to drag a pulse in 1D or 2D. Two possible paths to instability (depending on the linearized spectrum crossing) are detected. We explore the postdetachment transient dynamics and the interactions of a pulse with successive elements of a 1D periodic, constant speed array of identical heterogeneities. The theme of pulse dragging is currently also being explored in a variety of physically relevant Hamiltonian systems, or weakly perturbed dissipative variations thereof (targeted transfer of pulses in optical media or the motion/displacement of harmonic traps or optical l...

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Design and Control of Wave Propagation Patterns in Excitable Media

Cited by 199 publications

References 22 publications

Equation‐free: The computer‐aided analysis of complex multiscale systems

Equation‐free: The computer‐aided analysis of complex multiscale systems

Modular chemical mechanism predicts spatiotemporal dynamics of initiation in the complex network of hemostasis

Gentle Dragging of Reaction Waves

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